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David Leal
2021-10-25 13:54:15 -05:00
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commit 37e74e3669
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10
DIRECTORY.md
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@@ -19,6 +19,7 @@
* [Hamming Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/bit_manipulation/hamming_distance.cpp)
## Ciphers
* [A1Z26 Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/a1z26_cipher.cpp)
* [Atbash Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/atbash_cipher.cpp)
* [Base64 Encoding](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/base64_encoding.cpp)
* [Caesar Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/caesar_cipher.cpp)
@@ -45,6 +46,8 @@
* [Main Cll](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/cll/main_cll.cpp)
* [Disjoint Set](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/disjoint_set.cpp)
* [Doubly Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/doubly_linked_list.cpp)
* [Dsu Path Compression](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/dsu_path_compression.cpp)
* [Dsu Union Rank](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/dsu_union_rank.cpp)
* [Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/linked_list.cpp)
* [Linkedlist Implentation Usingarray](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/linkedlist_implentation_usingarray.cpp)
* [List Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/list_array.cpp)
@@ -162,6 +165,7 @@
* [Vector Ops](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/machine_learning/vector_ops.hpp)
## Math
* [Area](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/area.cpp)
* [Armstrong Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/armstrong_number.cpp)
* [Binary Exponent](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/binary_exponent.cpp)
* [Binomial Calculate](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/binomial_calculate.cpp)
@@ -241,12 +245,12 @@
* [Circular Queue Using Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/circular_queue_using_array.cpp)
* [Get Size Of Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/get_size_of_linked_list.cpp)
* [Inorder Successor Of Bst](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/inorder_successor_of_bst.cpp)
* [Intersection Of 2 Arrays](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/intersection_of_2_arrays.cpp)
* [Intersection Of Two Arrays](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/intersection_of_two_arrays.cpp)
* [Reverse A Linked List Using Recusion](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/reverse_a_linked_list_using_recusion.cpp)
* [Reverse Binary Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/reverse_binary_tree.cpp)
* [Selectionsortlinkedlist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/selectionsortlinkedlist.cpp)
* [Trie Multiple Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/trie_multiple_search.cpp)
* [Union Of 2 Arrays](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/union_of_2_arrays.cpp)
* [Union Of Two Arrays](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/union_of_two_arrays.cpp)
## Others
* [Buzz Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/buzz_number.cpp)
@@ -335,7 +339,7 @@
* [Radix Sort2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/radix_sort2.cpp)
* [Random Pivot Quick Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/random_pivot_quick_sort.cpp)
* [Recursive Bubble Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/recursive_bubble_sort.cpp)
* [Selection Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/selection_sort.cpp)
* [Selection Sort Iterative](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/selection_sort_iterative.cpp)
* [Selection Sort Recursive](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/selection_sort_recursive.cpp)
* [Shell Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/shell_sort.cpp)
* [Shell Sort2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/shell_sort2.cpp)

21
bit_manipulation/count_of_set_bits.cpp
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@@ -5,7 +5,8 @@
* integer.
*
* @details
* We are given an integer number. We need to calculate the number of set bits in it.
* We are given an integer number. We need to calculate the number of set bits
* in it.
*
* A binary number consists of two digits. They are 0 & 1. Digit 1 is known as
* set bit in computer terms.
@@ -15,7 +16,7 @@
* @author [Prashant Thakur](https://github.com/prashant-th18)
*/
#include <cassert> /// for assert
#include <iostream> /// for IO operations
#include <iostream> /// for IO operations
/**
* @namespace bit_manipulation
* @brief Bit manipulation algorithms
@@ -33,21 +34,21 @@ namespace count_of_set_bits {
* @param n is the number whose set bit will be counted
* @returns total number of set-bits in the binary representation of number `n`
*/
std::uint64_t countSetBits(std :: int64_t n) { // int64_t is preferred over int so that
// no Overflow can be there.
std::uint64_t countSetBits(
std ::int64_t n) { // int64_t is preferred over int so that
// no Overflow can be there.
int count = 0; // "count" variable is used to count number of set-bits('1') in
// binary representation of number 'n'
while (n != 0)
{
int count = 0; // "count" variable is used to count number of set-bits('1')
// in binary representation of number 'n'
while (n != 0) {
++count;
n = (n & (n - 1));
}
return count;
// Why this algorithm is better than the standard one?
// Because this algorithm runs the same number of times as the number of
// set-bits in it. Means if my number is having "3" set bits, then this while loop
// will run only "3" times!!
// set-bits in it. Means if my number is having "3" set bits, then this
// while loop will run only "3" times!!
}
} // namespace count_of_set_bits
} // namespace bit_manipulation

162
ciphers/a1z26_cipher.cpp Normal file
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@@ -0,0 +1,162 @@
/**
* @file
* @brief Implementation of the [A1Z26
* cipher](https://www.dcode.fr/letter-number-cipher)
* @details The A1Z26 cipher is a simple substiution cipher where each letter is
* replaced by the number of the order they're in. For example, A corresponds to
* 1, B = 2, C = 3, etc.
*
* @author [Focusucof](https://github.com/Focusucof)
*/
#include <algorithm> /// for std::transform and std::replace
#include <cassert> /// for assert
#include <cstdint> /// for uint8_t
#include <iostream> /// for IO operations
#include <map> /// for std::map
#include <sstream> /// for std::stringstream
#include <string> /// for std::string
#include <vector> /// for std::vector
/**
* @namespace ciphers
* @brief Algorithms for encryption and decryption
*/
namespace ciphers {
/**
* @namespace a1z26
* @brief Functions for [A1Z26](https://www.dcode.fr/letter-number-cipher)
* encryption and decryption implementation
*/
namespace a1z26 {
std::map<uint8_t, char> a1z26_decrypt_map = {
{1, 'a'}, {2, 'b'}, {3, 'c'}, {4, 'd'}, {5, 'e'}, {6, 'f'}, {7, 'g'},
{8, 'h'}, {9, 'i'}, {10, 'j'}, {11, 'k'}, {12, 'l'}, {13, 'm'}, {14, 'n'},
{15, 'o'}, {16, 'p'}, {17, 'q'}, {18, 'r'}, {19, 's'}, {20, 't'}, {21, 'u'},
{22, 'v'}, {23, 'w'}, {24, 'x'}, {25, 'y'}, {26, 'z'},
};
std::map<char, uint8_t> a1z26_encrypt_map = {
{'a', 1}, {'b', 2}, {'c', 3}, {'d', 4}, {'e', 5}, {'f', 6}, {'g', 7},
{'h', 8}, {'i', 9}, {'j', 10}, {'k', 11}, {'l', 12}, {'m', 13}, {'n', 14},
{'o', 15}, {'p', 16}, {'q', 17}, {'r', 18}, {'s', 19}, {'t', 20}, {'u', 21},
{'v', 22}, {'w', 23}, {'x', 24}, {'y', 25}, {'z', 26}};
/**
* @brief a1z26 encryption implementation
* @param text is the plaintext input
* @returns encoded string with dashes to seperate letters
*/
std::string encrypt(std::string text) {
std::string result;
std::transform(text.begin(), text.end(), text.begin(),
::tolower); // convert string to lowercase
std::replace(text.begin(), text.end(), ':', ' ');
for (char letter : text) {
if (letter != ' ') {
result += std::to_string(
a1z26_encrypt_map[letter]); // convert int to string and append
// to result
result += "-"; // space out each set of numbers with spaces
} else {
result.pop_back();
result += ' ';
}
}
result.pop_back(); // remove leading dash
return result;
}
/**
* @brief a1z26 decryption implementation
* @param text is the encrypted text input
* @param bReturnUppercase is if the decoded string should be in uppercase or
* not
* @returns the decrypted string in all uppercase or all lowercase
*/
std::string decrypt(const std::string& text, bool bReturnUppercase = false) {
std::string result;
// split words seperated by spaces into a vector array
std::vector<std::string> word_array;
std::stringstream sstream(text);
std::string word;
while (sstream >> word) {
word_array.push_back(word);
}
for (auto& i : word_array) {
std::replace(i.begin(), i.end(), '-', ' ');
std::vector<std::string> text_array;
std::stringstream ss(i);
std::string res_text;
while (ss >> res_text) {
text_array.push_back(res_text);
}
for (auto& i : text_array) {
result += a1z26_decrypt_map[stoi(i)];
}
result += ' ';
}
result.pop_back(); // remove any leading whitespace
if (bReturnUppercase) {
std::transform(result.begin(), result.end(), result.begin(), ::toupper);
}
return result;
}
} // namespace a1z26
} // namespace ciphers
/**
* @brief Self-test implementations
* @returns void
*/
static void test() {
// 1st test
std::string input = "Hello World";
std::string expected = "8-5-12-12-15 23-15-18-12-4";
std::string output = ciphers::a1z26::encrypt(input);
std::cout << "Input: " << input << std::endl;
std::cout << "Expected: " << expected << std::endl;
std::cout << "Output: " << output << std::endl;
assert(output == expected);
std::cout << "TEST PASSED";
// 2nd test
input = "12-15-23-5-18-3-1-19-5";
expected = "lowercase";
output = ciphers::a1z26::decrypt(input);
std::cout << "Input: " << input << std::endl;
std::cout << "Expected: " << expected << std::endl;
std::cout << "Output: " << output << std::endl;
assert(output == expected);
std::cout << "TEST PASSED";
// 3rd test
input = "21-16-16-5-18-3-1-19-5";
expected = "UPPERCASE";
output = ciphers::a1z26::decrypt(input, true);
std::cout << "Input: " << input << std::endl;
std::cout << "Expected: " << expected << std::endl;
std::cout << "Output: " << output << std::endl;
assert(output == expected);
std::cout << "TEST PASSED";
}
/**
* @brief Main function
* @returns 0 on exit
*/
int main() {
test(); // run self-test implementations
return 0;
}

5
ciphers/atbash_cipher.cpp
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@@ -22,7 +22,8 @@
*/
namespace ciphers {
/** \namespace atbash
* \brief Functions for the [Atbash Cipher](https://en.wikipedia.org/wiki/Atbash) implementation
* \brief Functions for the [Atbash
* Cipher](https://en.wikipedia.org/wiki/Atbash) implementation
*/
namespace atbash {
std::map<char, char> atbash_cipher_map = {
@@ -43,7 +44,7 @@ std::map<char, char> atbash_cipher_map = {
* @param text Plaintext to be encrypted
* @returns encoded or decoded string
*/
std::string atbash_cipher(std::string text) {
std::string atbash_cipher(const std::string& text) {
std::string result;
for (char letter : text) {
result += atbash_cipher_map[letter];

213
data_structures/dsu_path_compression.cpp Normal file
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@@ -0,0 +1,213 @@
/**
* @file
* @brief [DSU (Disjoint
* sets)](https://en.wikipedia.org/wiki/Disjoint-set-data_structure)
* @details
* It is a very powerful data structure that keeps track of different
* clusters(sets) of elements, these sets are disjoint(doesnot have a common
* element). Disjoint sets uses cases : for finding connected components in a
* graph, used in Kruskal's algorithm for finding Minimum Spanning tree.
* Operations that can be performed:
* 1) UnionSet(i,j): add(element i and j to the set)
* 2) findSet(i): returns the representative of the set to which i belogngs to.
* 3) get_max(i),get_min(i) : returns the maximum and minimum
* Below is the class-based approach which uses the heuristic of path
* compression. Using path compression in findSet(i),we are able to get to the
* representative of i in O(1) time.
* @author [AayushVyasKIIT](https://github.com/AayushVyasKIIT)
* @see dsu_union_rank.cpp
*/
#include <cassert> /// for assert
#include <iostream> /// for IO operations
#include <vector> /// for std::vector
using std::cout;
using std::endl;
using std::vector;
/**
* @brief Disjoint sets union data structure, class based representation.
* @param n number of elements
*/
class dsu {
private:
vector<uint64_t> p; ///< keeps track of the parent of ith element
vector<uint64_t> depth; ///< tracks the depth(rank) of i in the tree
vector<uint64_t> setSize; ///< size of each chunk(set)
vector<uint64_t> maxElement; ///< maximum of each set to which i belongs to
vector<uint64_t> minElement; ///< minimum of each set to which i belongs to
public:
/**
* @brief contructor for initialising all data members.
* @param n number of elements
*/
explicit dsu(uint64_t n) {
p.assign(n, 0);
/// initially, all of them are their own parents
for (uint64_t i = 0; i < n; i++) {
p[i] = i;
}
/// initially all have depth are equals to zero
depth.assign(n, 0);
maxElement.assign(n, 0);
minElement.assign(n, 0);
for (uint64_t i = 0; i < n; i++) {
depth[i] = 0;
maxElement[i] = i;
minElement[i] = i;
}
setSize.assign(n, 0);
/// initially set size will be equals to one
for (uint64_t i = 0; i < n; i++) {
setSize[i] = 1;
}
}
/**
* @brief Method to find the representative of the set to which i belongs
* to, T(n) = O(1)
* @param i element of some set
* @returns representative of the set to which i belongs to.
*/
uint64_t findSet(uint64_t i) {
/// using path compression
if (p[i] == i) {
return i;
}
return (p[i] = findSet(p[i]));
}
/**
* @brief Method that combines two disjoint sets to which i and j belongs to
* and make a single set having a common representative.
* @param i element of some set
* @param j element of some set
* @returns void
*/
void UnionSet(uint64_t i, uint64_t j) {
/// check if both belongs to the same set or not
if (isSame(i, j)) {
return;
}
// we find the representative of the i and j
uint64_t x = findSet(i);
uint64_t y = findSet(j);
/// always keeping the min as x
/// shallow tree
if (depth[x] > depth[y]) {
std::swap(x, y);
}
/// making the shallower root's parent the deeper root
p[x] = y;
/// if same depth, then increase one's depth
if (depth[x] == depth[y]) {
depth[y]++;
}
/// total size of the resultant set
setSize[y] += setSize[x];
/// changing the maximum elements
maxElement[y] = std::max(maxElement[x], maxElement[y]);
minElement[y] = std::min(minElement[x], minElement[y]);
}
/**
* @brief A utility function which check whether i and j belongs to
* same set or not
* @param i element of some set
* @param j element of some set
* @returns `true` if element `i` and `j` ARE in the same set
* @returns `false` if element `i` and `j` are NOT in same set
*/
bool isSame(uint64_t i, uint64_t j) {
if (findSet(i) == findSet(j)) {
return true;
}
return false;
}
/**
* @brief prints the minimum, maximum and size of the set to which i belongs
* to
* @param i element of some set
* @returns void
*/
vector<uint64_t> get(uint64_t i) {
vector<uint64_t> ans;
ans.push_back(get_min(i));
ans.push_back(get_max(i));
ans.push_back(size(i));
return ans;
}
/**
* @brief A utility function that returns the size of the set to which i
* belongs to
* @param i element of some set
* @returns size of the set to which i belongs to
*/
uint64_t size(uint64_t i) { return setSize[findSet(i)]; }
/**
* @brief A utility function that returns the max element of the set to
* which i belongs to
* @param i element of some set
* @returns maximum of the set to which i belongs to
*/
uint64_t get_max(uint64_t i) { return maxElement[findSet(i)]; }
/**
* @brief A utility function that returns the min element of the set to
* which i belongs to
* @param i element of some set
* @returns minimum of the set to which i belongs to
*/
uint64_t get_min(uint64_t i) { return minElement[findSet(i)]; }
};
/**
* @brief Self-test implementations, 1st test
* @returns void
*/
static void test1() {
// the minimum, maximum, and size of the set
uint64_t n = 10; ///< number of items
dsu d(n + 1); ///< object of class disjoint sets
// set 1
d.UnionSet(1, 2); // performs union operation on 1 and 2
d.UnionSet(1, 4); // performs union operation on 1 and 4
vector<uint64_t> ans = {1, 4, 3};
for (uint64_t i = 0; i < ans.size(); i++) {
assert(d.get(4).at(i) == ans[i]); // makes sure algorithm works fine
}
cout << "1st test passed!" << endl;
}
/**
* @brief Self-implementations, 2nd test
* @returns void
*/
static void test2() {
// the minimum, maximum, and size of the set
uint64_t n = 10; ///< number of items
dsu d(n + 1); ///< object of class disjoint sets
// set 1
d.UnionSet(3, 5);
d.UnionSet(5, 6);
d.UnionSet(5, 7);
vector<uint64_t> ans = {3, 7, 4};
for (uint64_t i = 0; i < ans.size(); i++) {
assert(d.get(3).at(i) == ans[i]); // makes sure algorithm works fine
}
cout << "2nd test passed!" << endl;
}
/**
* @brief Main function
* @returns 0 on exit
* */
int main() {
uint64_t n = 10; ///< number of items
dsu d(n + 1); ///< object of class disjoint sets
test1(); // run 1st test case
test2(); // run 2nd test case
return 0;
}

187
data_structures/dsu_union_rank.cpp Normal file
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@@ -0,0 +1,187 @@
/**
* @file
* @brief [DSU (Disjoint
* sets)](https://en.wikipedia.org/wiki/Disjoint-set-data_structure)
* @details
* dsu : It is a very powerful data structure which keeps track of different
* clusters(sets) of elements, these sets are disjoint(doesnot have a common
* element). Disjoint sets uses cases : for finding connected components in a
* graph, used in Kruskal's algorithm for finding Minimum Spanning tree.
* Operations that can be performed:
* 1) UnionSet(i,j): add(element i and j to the set)
* 2) findSet(i): returns the representative of the set to which i belogngs to.
* 3) getParents(i): prints the parent of i and so on and so forth.
* Below is the class-based approach which uses the heuristic of union-ranks.
* Using union-rank in findSet(i),we are able to get to the representative of i
* in slightly delayed O(logN) time but it allows us to keep tracks of the
* parent of i.
* @author [AayushVyasKIIT](https://github.com/AayushVyasKIIT)
* @see dsu_path_compression.cpp
*/
#include <cassert> /// for assert
#include <iostream> /// for IO operations
#include <vector> /// for std::vector
using std::cout;
using std::endl;
using std::vector;
/**
* @brief Disjoint sets union data structure, class based representation.
* @param n number of elements
*/
class dsu {
private:
vector<uint64_t> p; ///< keeps track of the parent of ith element
vector<uint64_t> depth; ///< tracks the depth(rank) of i in the tree
vector<uint64_t> setSize; ///< size of each chunk(set)
public:
/**
* @brief constructor for initialising all data members
* @param n number of elements
*/
explicit dsu(uint64_t n) {
p.assign(n, 0);
/// initially all of them are their own parents
depth.assign(n, 0);
setSize.assign(n, 0);
for (uint64_t i = 0; i < n; i++) {
p[i] = i;
depth[i] = 0;
setSize[i] = 1;
}
}
/**
* @brief Method to find the representative of the set to which i belongs
* to, T(n) = O(logN)
* @param i element of some set
* @returns representative of the set to which i belongs to
*/
uint64_t findSet(uint64_t i) {
/// using union-rank
while (i != p[i]) {
i = p[i];
}
return i;
}
/**
* @brief Method that combines two disjoint sets to which i and j belongs to
* and make a single set having a common representative.
* @param i element of some set
* @param j element of some set
* @returns void
*/
void unionSet(uint64_t i, uint64_t j) {
/// checks if both belongs to same set or not
if (isSame(i, j)) {
return;
}
/// we find representative of the i and j
uint64_t x = findSet(i);
uint64_t y = findSet(j);
/// always keeping the min as x
/// in order to create a shallow tree
if (depth[x] > depth[y]) {
std::swap(x, y);
}
/// making the shallower tree, root parent of the deeper root
p[x] = y;
/// if same depth, then increase one's depth
if (depth[x] == depth[y]) {
depth[y]++;
}
/// total size of the resultant set
setSize[y] += setSize[x];
}
/**
* @brief A utility function which check whether i and j belongs to same set
* or not
* @param i element of some set
* @param j element of some set
* @returns `true` if element i and j are in same set
* @returns `false` if element i and j are not in same set
*/
bool isSame(uint64_t i, uint64_t j) {
if (findSet(i) == findSet(j)) {
return true;
}
return false;
}
/**
* @brief Method to print all the parents of i, or the path from i to
* representative.
* @param i element of some set
* @returns void
*/
vector<uint64_t> getParents(uint64_t i) {
vector<uint64_t> ans;
while (p[i] != i) {
ans.push_back(i);
i = p[i];
}
ans.push_back(i);
return ans;
}
};
/**
* @brief Self-implementations, 1st test
* @returns void
*/
static void test1() {
/* checks the parents in the resultant structures */
uint64_t n = 10; ///< number of elements
dsu d(n + 1); ///< object of class disjoint sets
d.unionSet(2, 1); ///< performs union operation on 1 and 2
d.unionSet(1, 4);
d.unionSet(8, 1);
d.unionSet(3, 5);
d.unionSet(5, 6);
d.unionSet(5, 7);
d.unionSet(9, 10);
d.unionSet(2, 10);
// keeping track of the changes using parent pointers
vector<uint64_t> ans = {7, 5};
for (uint64_t i = 0; i < ans.size(); i++) {
assert(d.getParents(7).at(i) ==
ans[i]); // makes sure algorithm works fine
}
cout << "1st test passed!" << endl;
}
/**
* @brief Self-implementations, 2nd test
* @returns void
*/
static void test2() {
// checks the parents in the resultant structures
uint64_t n = 10; ///< number of elements
dsu d(n + 1); ///< object of class disjoint sets
d.unionSet(2, 1); /// performs union operation on 1 and 2
d.unionSet(1, 4);
d.unionSet(8, 1);
d.unionSet(3, 5);
d.unionSet(5, 6);
d.unionSet(5, 7);
d.unionSet(9, 10);
d.unionSet(2, 10);
/// keeping track of the changes using parent pointers
vector<uint64_t> ans = {2, 1, 10};
for (uint64_t i = 0; i < ans.size(); i++) {
assert(d.getParents(2).at(i) ==
ans[i]); /// makes sure algorithm works fine
}
cout << "2nd test passed!" << endl;
}
/**
* @brief Main function
* @returns 0 on exit
*/
int main() {
test1(); // run 1st test case
test2(); // run 2nd test case
return 0;
}

154
data_structures/stack_using_queue.cpp
View File

@@ -3,13 +3,14 @@
* @details
* Using 2 Queues inside the Stack class, we can easily implement Stack
* data structure with heavy computation in push function.
*
* References used: [StudyTonight](https://www.studytonight.com/data-structures/stack-using-queue)
*
* References used:
* [StudyTonight](https://www.studytonight.com/data-structures/stack-using-queue)
* @author [tushar2407](https://github.com/tushar2407)
*/
#include <iostream> /// for IO operations
#include <queue> /// for queue data structure
#include <cassert> /// for assert
#include <cassert> /// for assert
#include <iostream> /// for IO operations
#include <queue> /// for queue data structure
/**
* @namespace data_strcutres
@@ -18,66 +19,59 @@
namespace data_structures {
/**
* @namespace stack_using_queue
* @brief Functions for the [Stack Using Queue](https://www.studytonight.com/data-structures/stack-using-queue) implementation
* @brief Functions for the [Stack Using
* Queue](https://www.studytonight.com/data-structures/stack-using-queue)
* implementation
*/
namespace stack_using_queue {
/**
* @brief Stack Class implementation for basic methods of Stack Data Structure.
*/
struct Stack {
std::queue<int64_t> main_q; ///< stores the current state of the stack
std::queue<int64_t> auxiliary_q; ///< used to carry out intermediate
///< operations to implement stack
uint32_t current_size = 0; ///< stores the current size of the stack
/**
* @brief Stack Class implementation for basic methods of Stack Data Structure.
* Returns the top most element of the stack
* @returns top element of the queue
*/
struct Stack
{
std::queue<int64_t> main_q; ///< stores the current state of the stack
std::queue<int64_t> auxiliary_q; ///< used to carry out intermediate operations to implement stack
uint32_t current_size = 0; ///< stores the current size of the stack
/**
* Returns the top most element of the stack
* @returns top element of the queue
*/
int top()
{
return main_q.front();
}
int top() { return main_q.front(); }
/**
* @brief Inserts an element to the top of the stack.
* @param val the element that will be inserted into the stack
* @returns void
*/
void push(int val)
{
auxiliary_q.push(val);
while(!main_q.empty())
{
auxiliary_q.push(main_q.front());
main_q.pop();
}
swap(main_q, auxiliary_q);
current_size++;
}
/**
* @brief Removes the topmost element from the stack
* @returns void
*/
void pop()
{
if(main_q.empty()) {
return;
}
/**
* @brief Inserts an element to the top of the stack.
* @param val the element that will be inserted into the stack
* @returns void
*/
void push(int val) {
auxiliary_q.push(val);
while (!main_q.empty()) {
auxiliary_q.push(main_q.front());
main_q.pop();
current_size--;
}
swap(main_q, auxiliary_q);
current_size++;
}
/**
* @brief Utility function to return the current size of the stack
* @returns current size of stack
*/
int size()
{
return current_size;
/**
* @brief Removes the topmost element from the stack
* @returns void
*/
void pop() {
if (main_q.empty()) {
return;
}
};
main_q.pop();
current_size--;
}
/**
* @brief Utility function to return the current size of the stack
* @returns current size of stack
*/
int size() { return current_size; }
};
} // namespace stack_using_queue
} // namespace data_structures
@@ -85,30 +79,29 @@ namespace stack_using_queue {
* @brief Self-test implementations
* @returns void
*/
static void test()
{
static void test() {
data_structures::stack_using_queue::Stack s;
s.push(1); /// insert an element into the stack
s.push(2); /// insert an element into the stack
s.push(3); /// insert an element into the stack
assert(s.size()==3); /// size should be 3
assert(s.top()==3); /// topmost element in the stack should be 3
s.pop(); /// remove the topmost element from the stack
assert(s.top()==2); /// topmost element in the stack should now be 2
s.pop(); /// remove the topmost element from the stack
assert(s.top()==1);
s.push(5); /// insert an element into the stack
assert(s.top()==5); /// topmost element in the stack should now be 5
s.pop(); /// remove the topmost element from the stack
assert(s.top()==1); /// topmost element in the stack should now be 1
assert(s.size()==1); /// size should be 1
s.push(1); /// insert an element into the stack
s.push(2); /// insert an element into the stack
s.push(3); /// insert an element into the stack
assert(s.size() == 3); /// size should be 3
assert(s.top() == 3); /// topmost element in the stack should be 3
s.pop(); /// remove the topmost element from the stack
assert(s.top() == 2); /// topmost element in the stack should now be 2
s.pop(); /// remove the topmost element from the stack
assert(s.top() == 1);
s.push(5); /// insert an element into the stack
assert(s.top() == 5); /// topmost element in the stack should now be 5
s.pop(); /// remove the topmost element from the stack
assert(s.top() == 1); /// topmost element in the stack should now be 1
assert(s.size() == 1); /// size should be 1
}
/**
@@ -119,8 +112,7 @@ static void test()
* declared above.
* @returns 0 on exit
*/
int main()
{
int main() {
test(); // run self-test implementations
return 0;
}

279
math/area.cpp Normal file
View File

@@ -0,0 +1,279 @@
/**
* @file
* @brief Implementations for the [area](https://en.wikipedia.org/wiki/Area) of
* various shapes
* @details The area of a shape is the amount of 2D space it takes up.
* All shapes have a formula to get the area of any given shape.
* These implementations support multiple return types.
*
* @author [Focusucof](https://github.com/Focusucof)
*/
#define _USE_MATH_DEFINES
#include <cassert> /// for assert
#include <cmath> /// for M_PI definition and pow()
#include <cmath>
#include <cstdint> /// for uint16_t datatype
#include <iostream> /// for IO operations
/**
* @namespace math
* @brief Mathematical algorithms
*/
namespace math {
/**
* @brief area of a [square](https://en.wikipedia.org/wiki/Square) (l * l)
* @param length is the length of the square
* @returns area of square
*/
template <typename T>
T square_area(T length) {
return length * length;
}
/**
* @brief area of a [rectangle](https://en.wikipedia.org/wiki/Rectangle) (l * w)
* @param length is the length of the rectangle
* @param width is the width of the rectangle
* @returns area of the rectangle
*/
template <typename T>
T rect_area(T length, T width) {
return length * width;
}
/**
* @brief area of a [triangle](https://en.wikipedia.org/wiki/Triangle) (b * h /
* 2)
* @param base is the length of the bottom side of the triangle
* @param height is the length of the tallest point in the triangle
* @returns area of the triangle
*/
template <typename T>
T triangle_area(T base, T height) {
return base * height / 2;
}
/**
* @brief area of a [circle](https://en.wikipedia.org/wiki/Area_of_a_circle) (pi
* * r^2)
* @param radius is the radius of the circle
* @returns area of the circle
*/
template <typename T>
T circle_area(T radius) {
return M_PI * pow(radius, 2);
}
/**
* @brief area of a [parallelogram](https://en.wikipedia.org/wiki/Parallelogram)
* (b * h)
* @param base is the length of the bottom side of the parallelogram
* @param height is the length of the tallest point in the parallelogram
* @returns area of the parallelogram
*/
template <typename T>
T parallelogram_area(T base, T height) {
return base * height;
}
/**
* @brief surface area of a [cube](https://en.wikipedia.org/wiki/Cube) ( 6 * (l
* * l))
* @param length is the length of the cube
* @returns surface area of the cube
*/
template <typename T>
T cube_surface_area(T length) {
return 6 * length * length;
}
/**
* @brief surface area of a [sphere](https://en.wikipedia.org/wiki/Sphere) ( 4 *
* pi * r^2)
* @param radius is the radius of the sphere
* @returns surface area of the sphere
*/
template <typename T>
T sphere_surface_area(T radius) {
return 4 * M_PI * pow(radius, 2);
}
/**
* @brief surface area of a [cylinder](https://en.wikipedia.org/wiki/Cylinder)
* (2 * pi * r * h + 2 * pi * r^2)
* @param radius is the radius of the cylinder
* @param height is the height of the cylinder
* @returns surface area of the cylinder
*/
template <typename T>
T cylinder_surface_area(T radius, T height) {
return 2 * M_PI * radius * height + 2 * M_PI * pow(radius, 2);
}
} // namespace math
/**
* @brief Self-test implementations
* @returns void
*/
static void test() {
// I/O variables for testing
uint16_t int_length = 0; // 16 bit integer length input
uint16_t int_width = 0; // 16 bit integer width input
uint16_t int_base = 0; // 16 bit integer base input
uint16_t int_height = 0; // 16 bit integer height input
uint16_t int_expected = 0; // 16 bit integer expected output
uint16_t int_area = 0; // 16 bit integer output
float float_length = NAN; // float length input
float float_expected = NAN; // float expected output
float float_area = NAN; // float output
double double_length = NAN; // double length input
double double_width = NAN; // double width input
double double_radius = NAN; // double radius input
double double_height = NAN; // double height input
double double_expected = NAN; // double expected output
double double_area = NAN; // double output
// 1st test
int_length = 5;
int_expected = 25;
int_area = math::square_area(int_length);
std::cout << "AREA OF A SQUARE (int)" << std::endl;
std::cout << "Input Length: " << int_length << std::endl;
std::cout << "Expected Output: " << int_expected << std::endl;
std::cout << "Output: " << int_area << std::endl;
assert(int_area == int_expected);
std::cout << "TEST PASSED" << std::endl << std::endl;
// 2nd test
float_length = 2.5;
float_expected = 6.25;
float_area = math::square_area(float_length);
std::cout << "AREA OF A SQUARE (float)" << std::endl;
std::cout << "Input Length: " << float_length << std::endl;
std::cout << "Expected Output: " << float_expected << std::endl;
std::cout << "Output: " << float_area << std::endl;
assert(float_area == float_expected);
std::cout << "TEST PASSED" << std::endl << std::endl;
// 3rd test
int_length = 4;
int_width = 7;
int_expected = 28;
int_area = math::rect_area(int_length, int_width);
std::cout << "AREA OF A RECTANGLE (int)" << std::endl;
std::cout << "Input Length: " << int_length << std::endl;
std::cout << "Input Width: " << int_width << std::endl;
std::cout << "Expected Output: " << int_expected << std::endl;
std::cout << "Output: " << int_area << std::endl;
assert(int_area == int_expected);
std::cout << "TEST PASSED" << std::endl << std::endl;
// 4th test
double_length = 2.5;
double_width = 5.7;
double_expected = 14.25;
double_area = math::rect_area(double_length, double_width);
std::cout << "AREA OF A RECTANGLE (double)" << std::endl;
std::cout << "Input Length: " << double_length << std::endl;
std::cout << "Input Width: " << double_width << std::endl;
std::cout << "Expected Output: " << double_expected << std::endl;
std::cout << "Output: " << double_area << std::endl;
assert(double_area == double_expected);
std::cout << "TEST PASSED" << std::endl << std::endl;
// 5th test
int_base = 10;
int_height = 3;
int_expected = 15;
int_area = math::triangle_area(int_base, int_height);
std::cout << "AREA OF A TRIANGLE" << std::endl;
std::cout << "Input Base: " << int_base << std::endl;
std::cout << "Input Height: " << int_height << std::endl;
std::cout << "Expected Output: " << int_expected << std::endl;
std::cout << "Output: " << int_area << std::endl;
assert(int_area == int_expected);
std::cout << "TEST PASSED" << std::endl << std::endl;
// 6th test
double_radius = 6;
double_expected =
113.09733552923255; // rounded down because the double datatype
// truncates after 14 decimal places
double_area = math::circle_area(double_radius);
std::cout << "AREA OF A CIRCLE" << std::endl;
std::cout << "Input Radius: " << double_radius << std::endl;
std::cout << "Expected Output: " << double_expected << std::endl;
std::cout << "Output: " << double_area << std::endl;
assert(double_area == double_expected);
std::cout << "TEST PASSED" << std::endl << std::endl;
// 7th test
int_base = 6;
int_height = 7;
int_expected = 42;
int_area = math::parallelogram_area(int_base, int_height);
std::cout << "AREA OF A PARALLELOGRAM" << std::endl;
std::cout << "Input Base: " << int_base << std::endl;
std::cout << "Input Height: " << int_height << std::endl;
std::cout << "Expected Output: " << int_expected << std::endl;
std::cout << "Output: " << int_area << std::endl;
assert(int_area == int_expected);
std::cout << "TEST PASSED" << std::endl << std::endl;
// 8th test
double_length = 5.5;
double_expected = 181.5;
double_area = math::cube_surface_area(double_length);
std::cout << "SURFACE AREA OF A CUBE" << std::endl;
std::cout << "Input Length: " << double_length << std::endl;
std::cout << "Expected Output: " << double_expected << std::endl;
std::cout << "Output: " << double_area << std::endl;
assert(double_area == double_expected);
std::cout << "TEST PASSED" << std::endl << std::endl;
// 9th test
double_radius = 10.0;
double_expected = 1256.6370614359172; // rounded down because the whole
// value gets truncated
double_area = math::sphere_surface_area(double_radius);
std::cout << "SURFACE AREA OF A SPHERE" << std::endl;
std::cout << "Input Radius: " << double_radius << std::endl;
std::cout << "Expected Output: " << double_expected << std::endl;
std::cout << "Output: " << double_area << std::endl;
assert(double_area == double_expected);
std::cout << "TEST PASSED" << std::endl << std::endl;
// 10th test
double_radius = 4.0;
double_height = 7.0;
double_expected = 276.46015351590177;
double_area = math::cylinder_surface_area(double_radius, double_height);
std::cout << "SURFACE AREA OF A CYLINDER" << std::endl;
std::cout << "Input Radius: " << double_radius << std::endl;
std::cout << "Input Height: " << double_height << std::endl;
std::cout << "Expected Output: " << double_expected << std::endl;
std::cout << "Output: " << double_area << std::endl;
assert(double_area == double_expected);
std::cout << "TEST PASSED" << std::endl << std::endl;
}
/**
* @brief Main function
* @returns 0 on exit
*/
int main() {
test(); // run self-test implementations
return 0;
}

23
math/check_prime.cpp
View File

@@ -7,12 +7,14 @@
* @brief
* Reduced all possibilities of a number which cannot be prime.
* Eg: No even number, except 2 can be a prime number, hence we will increment
* our loop with i+2 jumping on all odd numbers only. If number is <= 1 or if it
* is even except 2, break the loop and return false telling number is not
* prime.
* our loop with i+6 jumping and check for i or i+2 to be a factor of the
* number; if it's a factor then we will return false otherwise true after the
* loop terminates at the terminating condition which is (i*i<=num)
*/
#include <cassert>
#include <iostream>
#include <cassert> /// for assert
#include <iostream> /// for IO operations
/**
* Function to check if the given number is prime or not.
* @param num number to be checked.
@@ -23,14 +25,13 @@ bool is_prime(T num) {
bool result = true;
if (num <= 1) {
return false;
} else if (num == 2) {
} else if (num == 2 || num == 3) {
return true;
} else if ((num & 1) == 0) {
} else if ((num % 2) == 0 || num % 3 == 0) {
return false;
}
if (num >= 3) {
for (T i = 3; (i * i) <= (num); i = (i + 2)) {
if ((num % i) == 0) {
} else {
for (T i = 5; (i * i) <= (num); i = (i + 6)) {
if ((num % i) == 0 || (num % (i + 2) == 0)) {
result = false;
break;
}

128
math/integral_approximation2.cpp
View File

@@ -1,29 +1,34 @@
/**
* @file
* @brief [Monte Carlo Integration](https://en.wikipedia.org/wiki/Monte_Carlo_integration)
* @brief [Monte Carlo
* Integration](https://en.wikipedia.org/wiki/Monte_Carlo_integration)
*
* @details
* In mathematics, Monte Carlo integration is a technique for numerical integration using random numbers.
* It is a particular Monte Carlo method that numerically computes a definite integral.
* While other algorithms usually evaluate the integrand at a regular grid, Monte Carlo randomly chooses points at which the integrand is evaluated.
* This method is particularly useful for higher-dimensional integrals.
* In mathematics, Monte Carlo integration is a technique for numerical
* integration using random numbers. It is a particular Monte Carlo method that
* numerically computes a definite integral. While other algorithms usually
* evaluate the integrand at a regular grid, Monte Carlo randomly chooses points
* at which the integrand is evaluated. This method is particularly useful for
* higher-dimensional integrals.
*
* This implementation supports arbitrary pdfs.
* These pdfs are sampled using the [Metropolis-Hastings algorithm](https://en.wikipedia.org/wiki/Metropolis–Hastings_algorithm).
* This can be swapped out by every other sampling techniques for example the inverse method.
* Metropolis-Hastings was chosen because it is the most general and can also be extended for a higher dimensional sampling space.
* These pdfs are sampled using the [Metropolis-Hastings
* algorithm](https://en.wikipedia.org/wiki/Metropolis–Hastings_algorithm). This
* can be swapped out by every other sampling techniques for example the inverse
* method. Metropolis-Hastings was chosen because it is the most general and can
* also be extended for a higher dimensional sampling space.
*
* @author [Domenic Zingsheim](https://github.com/DerAndereDomenic)
*/
#define _USE_MATH_DEFINES /// for M_PI on windows
#include <cmath> /// for math functions
#include <cstdint> /// for fixed size data types
#include <ctime> /// for time to initialize rng
#include <functional> /// for function pointers
#include <iostream> /// for std::cout
#include <random> /// for random number generation
#include <vector> /// for std::vector
#define _USE_MATH_DEFINES /// for M_PI on windows
#include <cmath> /// for math functions
#include <cstdint> /// for fixed size data types
#include <ctime> /// for time to initialize rng
#include <functional> /// for function pointers
#include <iostream> /// for std::cout
#include <random> /// for random number generation
#include <vector> /// for std::vector
/**
* @namespace math
@@ -32,25 +37,34 @@
namespace math {
/**
* @namespace monte_carlo
* @brief Functions for the [Monte Carlo Integration](https://en.wikipedia.org/wiki/Monte_Carlo_integration) implementation
* @brief Functions for the [Monte Carlo
* Integration](https://en.wikipedia.org/wiki/Monte_Carlo_integration)
* implementation
*/
namespace monte_carlo {
using Function = std::function<double(double&)>; /// short-hand for std::functions used in this implementation
using Function = std::function<double(
double&)>; /// short-hand for std::functions used in this implementation
/**
* @brief Generate samples according to some pdf
* @details This function uses Metropolis-Hastings to generate random numbers. It generates a sequence of random numbers by using a markov chain.
* Therefore, we need to define a start_point and the number of samples we want to generate.
* Because the first samples generated by the markov chain may not be distributed according to the given pdf, one can specify how many samples
* @details This function uses Metropolis-Hastings to generate random numbers.
* It generates a sequence of random numbers by using a markov chain. Therefore,
* we need to define a start_point and the number of samples we want to
* generate. Because the first samples generated by the markov chain may not be
* distributed according to the given pdf, one can specify how many samples
* should be discarded before storing samples.
* @param start_point The starting point of the markov chain
* @param pdf The pdf to sample
* @param num_samples The number of samples to generate
* @param discard How many samples should be discarded at the start
* @returns A vector of size num_samples with samples distributed according to the pdf
* @returns A vector of size num_samples with samples distributed according to
* the pdf
*/
std::vector<double> generate_samples(const double& start_point, const Function& pdf, const uint32_t& num_samples, const uint32_t& discard = 100000) {
std::vector<double> generate_samples(const double& start_point,
const Function& pdf,
const uint32_t& num_samples,
const uint32_t& discard = 100000) {
std::vector<double> samples;
samples.reserve(num_samples);
@@ -61,19 +75,19 @@ std::vector<double> generate_samples(const double& start_point, const Function&
std::normal_distribution<double> normal(0.0, 1.0);
generator.seed(time(nullptr));
for(uint32_t t = 0; t < num_samples + discard; ++t) {
for (uint32_t t = 0; t < num_samples + discard; ++t) {
// Generate a new proposal according to some mutation strategy.
// This is arbitrary and can be swapped.
double x_dash = normal(generator) + x_t;
double acceptance_probability = std::min(pdf(x_dash)/pdf(x_t), 1.0);
double acceptance_probability = std::min(pdf(x_dash) / pdf(x_t), 1.0);
double u = uniform(generator);
// Accept "new state" according to the acceptance_probability
if(u <= acceptance_probability) {
if (u <= acceptance_probability) {
x_t = x_dash;
}
if(t >= discard) {
if (t >= discard) {
samples.push_back(x_t);
}
}
@@ -92,13 +106,17 @@ std::vector<double> generate_samples(const double& start_point, const Function&
* @param function The function to integrate
* @param pdf The pdf to sample
* @param num_samples The number of samples used to approximate the integral
* @returns The approximation of the integral according to 1/N \sum_{i}^N f(x_i) / p(x_i)
* @returns The approximation of the integral according to 1/N \sum_{i}^N f(x_i)
* / p(x_i)
*/
double integral_monte_carlo(const double& start_point, const Function& function, const Function& pdf, const uint32_t& num_samples = 1000000) {
double integral_monte_carlo(const double& start_point, const Function& function,
const Function& pdf,
const uint32_t& num_samples = 1000000) {
double integral = 0.0;
std::vector<double> samples = generate_samples(start_point, pdf, num_samples);
std::vector<double> samples =
generate_samples(start_point, pdf, num_samples);
for(double sample : samples) {
for (double sample : samples) {
integral += function(sample) / pdf(sample);
}
@@ -113,8 +131,13 @@ double integral_monte_carlo(const double& start_point, const Function& function,
* @returns void
*/
static void test() {
std::cout << "Disclaimer: Because this is a randomized algorithm," << std::endl;
std::cout << "it may happen that singular samples deviate from the true result." << std::endl << std::endl;;
std::cout << "Disclaimer: Because this is a randomized algorithm,"
<< std::endl;
std::cout
<< "it may happen that singular samples deviate from the true result."
<< std::endl
<< std::endl;
;
math::monte_carlo::Function f;
math::monte_carlo::Function pdf;
@@ -122,60 +145,58 @@ static void test() {
double lower_bound = 0, upper_bound = 0;
/* \int_{-2}^{2} -x^2 + 4 dx */
f = [&](double& x) {
return -x*x + 4.0;
};
f = [&](double& x) { return -x * x + 4.0; };
lower_bound = -2.0;
upper_bound = 2.0;
pdf = [&](double& x) {
if(x >= lower_bound && x <= -1.0) {
if (x >= lower_bound && x <= -1.0) {
return 0.1;
}
if(x <= upper_bound && x >= 1.0) {
if (x <= upper_bound && x >= 1.0) {
return 0.1;
}
if(x > -1.0 && x < 1.0) {
if (x > -1.0 && x < 1.0) {
return 0.4;
}
return 0.0;
};
integral = math::monte_carlo::integral_monte_carlo((upper_bound - lower_bound) / 2.0, f, pdf);
integral = math::monte_carlo::integral_monte_carlo(
(upper_bound - lower_bound) / 2.0, f, pdf);
std::cout << "This number should be close to 10.666666: " << integral << std::endl;
std::cout << "This number should be close to 10.666666: " << integral
<< std::endl;
/* \int_{0}^{1} e^x dx */
f = [&](double& x) {
return std::exp(x);
};
f = [&](double& x) { return std::exp(x); };
lower_bound = 0.0;
upper_bound = 1.0;
pdf = [&](double& x) {
if(x >= lower_bound && x <= 0.2) {
if (x >= lower_bound && x <= 0.2) {
return 0.1;
}
if(x > 0.2 && x <= 0.4) {
if (x > 0.2 && x <= 0.4) {
return 0.4;
}
if(x > 0.4 && x < upper_bound) {
if (x > 0.4 && x < upper_bound) {
return 1.5;
}
return 0.0;
};
integral = math::monte_carlo::integral_monte_carlo((upper_bound - lower_bound) / 2.0, f, pdf);
integral = math::monte_carlo::integral_monte_carlo(
(upper_bound - lower_bound) / 2.0, f, pdf);
std::cout << "This number should be close to 1.7182818: " << integral << std::endl;
std::cout << "This number should be close to 1.7182818: " << integral
<< std::endl;
/* \int_{-\infty}^{\infty} sinc(x) dx, sinc(x) = sin(pi * x) / (pi * x)
This is a difficult integral because of its infinite domain.
Therefore, it may deviate largely from the expected result.
*/
f = [&](double& x) {
return std::sin(M_PI * x) / (M_PI * x);
};
f = [&](double& x) { return std::sin(M_PI * x) / (M_PI * x); };
pdf = [&](double& x) {
return 1.0 / std::sqrt(2.0 * M_PI) * std::exp(-x * x / 2.0);
@@ -183,7 +204,8 @@ static void test() {
integral = math::monte_carlo::integral_monte_carlo(0.0, f, pdf, 10000000);
std::cout << "This number should be close to 1.0: " << integral << std::endl;
std::cout << "This number should be close to 1.0: " << integral
<< std::endl;
}
/**

198
operations_on_datastructures/array_right_rotation.cpp
View File

@@ -1,27 +1,175 @@
#include <iostream>
using namespace std;
int main() {
int n, k;
cout << "Enter size of array=\t";
cin >> n;
cout << "Enter Number of indices u want to rotate the array to right=\t";
cin >> k;
int a[n];
cout << "Enter elements of array=\t";
for (int i = 0; i < n; i++) cin >> a[i];
int temp = 0;
for (int i = 0; i < k; i++) {
temp = a[n - 1];
for (int j = n - 1; j >= 0; j--) {
if (j == 0) {
a[j] = temp;
} else {
a[j] = a[j - 1];
}
}
}
cout << "Your rotated array is=\t";
for (int i = 0; i < n; i++) {
cout << a[i] << " ";
/**
* @file
* @brief Implementation for the [Array right
* Rotation](https://www.javatpoint.com/program-to-right-rotate-the-elements-of-an-array)
* algorithm.
* @details Shifting an array to the right involves moving each element of the
* array so that it occupies a position of a certain shift value after its
* current one. This implementation uses a result vector and does not mutate the
* input.
* @see array_left_rotation.cpp
* @author [Alvin](https://github.com/polarvoid)
*/
#include <cassert> /// for assert
#include <iostream> /// for IO operations
#include <vector> /// for std::vector
/**
* @namespace operations_on_datastructures
* @brief Operations on Data Structures
*/
namespace operations_on_datastructures {
/**
* @brief Prints the values of a vector sequentially, ending with a newline
* character.
* @param array Reference to the array to be printed
* @returns void
*/
void print(const std::vector<int32_t> &array) {
for (int32_t i : array) {
std::cout << i << " "; /// Print each value in the array
}
std::cout << "\n"; /// Print newline
}
/**
* @brief Shifts the given vector to the right by the shift amount and returns a
* new vector with the result. The original vector is not mutated.
* @details Shifts the values of the vector, by creating a new vector and adding
* values from the shift index to the end, then appending the rest of the
* elements to the start of the vector.
* @param array A reference to the input std::vector
* @param shift The amount to be shifted to the right
* @returns A std::vector with the shifted values
*/
std::vector<int32_t> shift_right(const std::vector<int32_t> &array,
size_t shift) {
if (array.size() <= shift) {
return {}; ///< We got an invalid shift, return empty array
}
std::vector<int32_t> res(array.size()); ///< Result array
for (size_t i = shift; i < array.size(); i++) {
res[i] = array[i - shift]; ///< Add values after the shift index
}
for (size_t i = 0; i < shift; i++) {
res[i] =
array[array.size() - shift + i]; ///< Add the values from the start
}
return res;
}
} // namespace operations_on_datastructures
/**
* @namespace tests
* @brief Testcases to check Union of Two Arrays.
*/
namespace tests {
using operations_on_datastructures::print;
using operations_on_datastructures::shift_right;
/**
* @brief A Test to check an simple case
* @returns void
*/
void test1() {
std::cout << "TEST CASE 1\n";
std::cout << "Initialized arr = {1, 2, 3, 4, 5}\n";
std::cout << "Expected result: {4, 5, 1, 2, 3}\n";
std::vector<int32_t> arr = {1, 2, 3, 4, 5};
std::vector<int32_t> res = shift_right(arr, 2);
std::vector<int32_t> expected = {4, 5, 1, 2, 3};
assert(res == expected);
print(res); ///< Should print 4 5 1 2 3
std::cout << "TEST PASSED!\n\n";
}
/**
* @brief A Test to check an empty vector
* @returns void
*/
void test2() {
std::cout << "TEST CASE 2\n";
std::cout << "Initialized arr = {}\n";
std::cout << "Expected result: {}\n";
std::vector<int32_t> arr = {};
std::vector<int32_t> res = shift_right(arr, 2);
std::vector<int32_t> expected = {};
assert(res == expected);
print(res); ///< Should print empty newline
std::cout << "TEST PASSED!\n\n";
}
/**
* @brief A Test to check an invalid shift value
* @returns void
*/
void test3() {
std::cout << "TEST CASE 3\n";
std::cout << "Initialized arr = {1, 2, 3, 4, 5}\n";
std::cout << "Expected result: {}\n";
std::vector<int32_t> arr = {1, 2, 3, 4, 5};
std::vector<int32_t> res = shift_right(arr, 7); ///< 7 > 5
std::vector<int32_t> expected = {};
assert(res == expected);
print(res); ///< Should print empty newline
std::cout << "TEST PASSED!\n\n";
}
/**
* @brief A Test to check a very large input
* @returns void
*/
void test4() {
std::cout << "TEST CASE 4\n";
std::cout << "Initialized arr = {2, 4, ..., 420}\n";
std::cout << "Expected result: {420, 2, 4, ..., 418}\n";
std::vector<int32_t> arr;
for (int i = 1; i <= 210; i++) {
arr.push_back(i * 2);
}
print(arr);
std::vector<int32_t> res = shift_right(arr, 1);
std::vector<int32_t> expected;
expected.push_back(420);
for (int i = 0; i < 209; i++) {
expected.push_back(arr[i]);
}
assert(res == expected);
print(res); ///< Should print {420, 2, 4, ..., 418}
std::cout << "TEST PASSED!\n\n";
}
/**
* @brief A Test to check a shift of zero
* @returns void
*/
void test5() {
std::cout << "TEST CASE 5\n";
std::cout << "Initialized arr = {1, 2, 3, 4, 5}\n";
std::cout << "Expected result: {1, 2, 3, 4, 5}\n";
std::vector<int32_t> arr = {1, 2, 3, 4, 5};
std::vector<int32_t> res = shift_right(arr, 0);
assert(res == arr);
print(res); ///< Should print 1 2 3 4 5
std::cout << "TEST PASSED!\n\n";
}
} // namespace tests
/**
* @brief Function to test the correctness of shift_right() function
* @returns void
*/
static void test() {
tests::test1();
tests::test2();
tests::test3();
tests::test4();
tests::test5();
}
/**
* @brief main function
* @returns 0 on exit
*/
int main() {
test(); // run self-test implementations
return 0;
}

26
operations_on_datastructures/intersection_of_2_arrays.cpp
View File

@@ -1,26 +0,0 @@
#include <iostream>
int main() {
int i, j, m, n;
cout << "Enter size of array 1:";
cin >> m;
cout << "Enter size of array 2:";
cin >> n;
int a[m];
int b[n];
cout << "Enter elements of array 1:";
for (i = 0; i < m; i++) cin >> a[i];
for (i = 0; i < n; i++) cin >> b[i];
i = 0;
j = 0;
while ((i < m) && (j < n)) {
if (a[i] < b[j])
i++;
else if (a[i] > b[j])
j++;
else {
cout << a[i++] << " ";
j++;
}
}
return 0;
}

203
operations_on_datastructures/intersection_of_two_arrays.cpp Normal file
View File

@@ -0,0 +1,203 @@
/**
* @file
* @brief Implementation for the [Intersection of two sorted
* Arrays](https://en.wikipedia.org/wiki/Intersection_(set_theory))
* algorithm.
* @details The intersection of two arrays is the collection of all the elements
* that are common in both the first and second arrays. This implementation uses
* ordered arrays, and an algorithm to correctly order them and return the
* result as a new array (vector).
* @see union_of_two_arrays.cpp
* @author [Alvin](https://github.com/polarvoid)
*/
#include <algorithm> /// for std::sort
#include <cassert> /// for assert
#include <iostream> /// for IO operations
#include <vector> /// for std::vector
/**
* @namespace operations_on_datastructures
* @brief Operations on Data Structures
*/
namespace operations_on_datastructures {
/**
* @brief Prints the values of a vector sequentially, ending with a newline
* character.
* @param array Reference to the array to be printed
* @returns void
*/
void print(const std::vector<int32_t> &array) {
for (int32_t i : array) {
std::cout << i << " "; /// Print each value in the array
}
std::cout << "\n"; /// Print newline
}
/**
* @brief Gets the intersection of two sorted arrays, and returns them in a
* vector.
* @details An algorithm is used that compares the elements of the two vectors,
* incrementing the index of the smaller of the two. If the elements are the
* same, the element is appended to the result array to be returned.
* @param first A std::vector of sorted integer values
* @param second A std::vector of sorted integer values
* @returns A std::vector of the intersection of the two arrays, in ascending
* order
*/
std::vector<int32_t> get_intersection(const std::vector<int32_t> &first,
const std::vector<int32_t> &second) {
std::vector<int32_t> res; ///< Vector to hold the intersection
size_t f_index = 0; ///< Index for the first array
size_t s_index = 0; ///< Index for the second array
size_t f_length = first.size(); ///< Length of first array
size_t s_length = second.size(); ///< Length of second array
while (f_index < f_length && s_index < s_length) {
if (first[f_index] < second[s_index]) {
f_index++; ///< Increment index of second array
} else if (first[f_index] > second[s_index]) {
s_index++; ///< Increment index of second array
} else {
if ((res.size() == 0) || (first[f_index] != res.back())) {
res.push_back(
first[f_index]); ///< Add the element if it is unique
}
f_index++; ///< Increment index of first array
s_index++; ///< Increment index of second array too
}
}
return res;
}
} // namespace operations_on_datastructures
/**
* @namespace tests
* @brief Testcases to check intersection of Two Arrays.
*/
namespace tests {
using operations_on_datastructures::get_intersection;
using operations_on_datastructures::print;
/**
* @brief A Test to check an edge case (two empty arrays)
* @returns void
*/
void test1() {
std::cout << "TEST CASE 1\n";
std::cout << "Intialized a = {} b = {}\n";
std::cout << "Expected result: {}\n";
std::vector<int32_t> a = {};
std::vector<int32_t> b = {};
std::vector<int32_t> result = get_intersection(a, b);
assert(result == a); ///< Check if result is empty
print(result); ///< Should only print newline
std::cout << "TEST PASSED!\n\n";
}
/**
* @brief A Test to check an edge case (one empty array)
* @returns void
*/
void test2() {
std::cout << "TEST CASE 2\n";
std::cout << "Intialized a = {} b = {2, 3}\n";
std::cout << "Expected result: {}\n";
std::vector<int32_t> a = {};
std::vector<int32_t> b = {2, 3};
std::vector<int32_t> result = get_intersection(a, b);
assert(result == a); ///< Check if result is equal to a
print(result); ///< Should only print newline
std::cout << "TEST PASSED!\n\n";
}
/**
* @brief A Test to check correct functionality with a simple test case
* @returns void
*/
void test3() {
std::cout << "TEST CASE 3\n";
std::cout << "Intialized a = {4, 6} b = {3, 6}\n";
std::cout << "Expected result: {6}\n";
std::vector<int32_t> a = {4, 6};
std::vector<int32_t> b = {3, 6};
std::vector<int32_t> result = get_intersection(a, b);
std::vector<int32_t> expected = {6};
assert(result == expected); ///< Check if result is correct
print(result); ///< Should print 6
std::cout << "TEST PASSED!\n\n";
}
/**
* @brief A Test to check correct functionality with duplicate values
* @returns void
*/
void test4() {
std::cout << "TEST CASE 4\n";
std::cout << "Intialized a = {4, 6, 6, 6} b = {2, 4, 4, 6}\n";
std::cout << "Expected result: {4, 6}\n";
std::vector<int32_t> a = {4, 6, 6, 6};
std::vector<int32_t> b = {2, 4, 4, 6};
std::vector<int32_t> result = get_intersection(a, b);
std::vector<int32_t> expected = {4, 6};
assert(result == expected); ///< Check if result is correct
print(result); ///< Should print 4 6
std::cout << "TEST PASSED!\n\n";
}
/**
* @brief A Test to check correct functionality with a harder test case
* @returns void
*/
void test5() {
std::cout << "TEST CASE 5\n";
std::cout << "Intialized a = {1, 2, 3, 4, 6, 7, 9} b = {2, 3, 4, 5}\n";
std::cout << "Expected result: {2, 3, 4}\n";
std::vector<int32_t> a = {1, 2, 3, 4, 6, 7, 9};
std::vector<int32_t> b = {2, 3, 4, 5};
std::vector<int32_t> result = get_intersection(a, b);
std::vector<int32_t> expected = {2, 3, 4};
assert(result == expected); ///< Check if result is correct
print(result); ///< Should print 2 3 4
std::cout << "TEST PASSED!\n\n";
}
/**
* @brief A Test to check correct functionality with an array sorted using
* std::sort
* @returns void
*/
void test6() {
std::cout << "TEST CASE 6\n";
std::cout << "Intialized a = {1, 3, 3, 2, 5, 9, 4, 7, 3, 2} ";
std::cout << "b = {11, 3, 7, 8, 6}\n";
std::cout << "Expected result: {3, 7}\n";
std::vector<int32_t> a = {1, 3, 3, 2, 5, 9, 4, 7, 3, 2};
std::vector<int32_t> b = {11, 3, 7, 8, 6};
std::sort(a.begin(), a.end()); ///< Sort vector a
std::sort(b.begin(), b.end()); ///< Sort vector b
std::vector<int32_t> result = get_intersection(a, b);
std::vector<int32_t> expected = {3, 7};
assert(result == expected); ///< Check if result is correct
print(result); ///< Should print 3 7
std::cout << "TEST PASSED!\n\n";
}
} // namespace tests
/**
* @brief Function to test the correctness of get_intersection() function
* @returns void
*/
static void test() {
tests::test1();
tests::test2();
tests::test3();
tests::test4();
tests::test5();
tests::test6();
}
/**
* @brief main function
* @returns 0 on exit
*/
int main() {
test(); // run self-test implementations
return 0;
}

27
operations_on_datastructures/union_of_2_arrays.cpp
View File

@@ -1,27 +0,0 @@
#include <iostream>
int main() {
int m, n, i = 0, j = 0;
cout << "Enter size of both arrays:";
cin >> m >> n;
int a[m];
int b[n];
cout << "Enter elements of array 1:";
for (i = 0; i < m; i++) cin >> a[i];
cout << "Enter elements of array 2:";
for (i = 0; i < n; i++) cin >> b[i];
i = 0;
j = 0;
while ((i < m) && (j < n)) {
if (a[i] < b[j])
cout << a[i++] << " ";
else if (a[i] > b[j])
cout << b[j++] << " ";
else {
cout << a[i++];
j++;
}
}
while (i < m) cout << a[i++] << " ";
while (j < n) cout << b[j++] << " ";
return 0;
}

220
operations_on_datastructures/union_of_two_arrays.cpp Normal file
View File

@@ -0,0 +1,220 @@
/**
* @file
* @brief Implementation for the [Union of two sorted
* Arrays](https://en.wikipedia.org/wiki/Union_(set_theory))
* algorithm.
* @details The Union of two arrays is the collection of all the unique elements
* in the first array, combined with all of the unique elements of a second
* array. This implementation uses ordered arrays, and an algorithm to correctly
* order them and return the result as a new array (vector).
* @see intersection_of_two_arrays.cpp
* @author [Alvin](https://github.com/polarvoid)
*/
#include <algorithm> /// for std::sort
#include <cassert> /// for assert
#include <iostream> /// for IO operations
#include <vector> /// for std::vector
/**
* @namespace operations_on_datastructures
* @brief Operations on Data Structures
*/
namespace operations_on_datastructures {
/**
* @brief Prints the values of a vector sequentially, ending with a newline
* character.
* @param array Reference to the array to be printed
* @returns void
*/
void print(const std::vector<int32_t> &array) {
for (int32_t i : array) {
std::cout << i << " "; /// Print each value in the array
}
std::cout << "\n"; /// Print newline
}
/**
* @brief Gets the union of two sorted arrays, and returns them in a
* vector.
* @details An algorithm is used that compares the elements of the two vectors,
* appending the one that has a lower value, and incrementing the index for that
* array. If one of the arrays reaches its end, all the elements of the other
* are appended to the resultant vector.
* @param first A std::vector of sorted integer values
* @param second A std::vector of sorted integer values
* @returns A std::vector of the union of the two arrays, in ascending order
*/
std::vector<int32_t> get_union(const std::vector<int32_t> &first,
const std::vector<int32_t> &second) {
std::vector<int32_t> res; ///< Vector to hold the union
size_t f_index = 0; ///< Index for the first array
size_t s_index = 0; ///< Index for the second array
size_t f_length = first.size(); ///< Length of first array
size_t s_length = second.size(); ///< Length of second array
int32_t next = 0; ///< Integer to store value of the next element
while (f_index < f_length && s_index < s_length) {
if (first[f_index] < second[s_index]) {
next = first[f_index]; ///< Append from first array
f_index++; ///< Increment index of second array
} else if (first[f_index] > second[s_index]) {
next = second[s_index]; ///< Append from second array
s_index++; ///< Increment index of second array
} else {
next = first[f_index]; ///< Element is the same in both
f_index++; ///< Increment index of first array
s_index++; ///< Increment index of second array too
}
if ((res.size() == 0) || (next != res.back())) {
res.push_back(next); ///< Add the element if it is unique
}
}
while (f_index < f_length) {
next = first[f_index]; ///< Add remaining elements
if ((res.size() == 0) || (next != res.back())) {
res.push_back(next); ///< Add the element if it is unique
}
f_index++;
}
while (s_index < s_length) {
next = second[s_index]; ///< Add remaining elements
if ((res.size() == 0) || (next != res.back())) {
res.push_back(next); ///< Add the element if it is unique
}
s_index++;
}
return res;
}
} // namespace operations_on_datastructures
/**
* @namespace tests
* @brief Testcases to check Union of Two Arrays.
*/
namespace tests {
using operations_on_datastructures::get_union;
using operations_on_datastructures::print;
/**
* @brief A Test to check an edge case (two empty arrays)
* @returns void
*/
void test1() {
std::cout << "TEST CASE 1\n";
std::cout << "Intialized a = {} b = {}\n";
std::cout << "Expected result: {}\n";
std::vector<int32_t> a = {};
std::vector<int32_t> b = {};
std::vector<int32_t> result = get_union(a, b);
assert(result == a); ///< Check if result is empty
print(result); ///< Should only print newline
std::cout << "TEST PASSED!\n\n";
}
/**
* @brief A Test to check an edge case (one empty array)
* @returns void
*/
void test2() {
std::cout << "TEST CASE 2\n";
std::cout << "Intialized a = {} b = {2, 3}\n";
std::cout << "Expected result: {2, 3}\n";
std::vector<int32_t> a = {};
std::vector<int32_t> b = {2, 3};
std::vector<int32_t> result = get_union(a, b);
assert(result == b); ///< Check if result is equal to b
print(result); ///< Should print 2 3
std::cout << "TEST PASSED!\n\n";
}
/**
* @brief A Test to check correct functionality with a simple test case
* @returns void
*/
void test3() {
std::cout << "TEST CASE 3\n";
std::cout << "Intialized a = {4, 6} b = {2, 3}\n";
std::cout << "Expected result: {2, 3, 4, 6}\n";
std::vector<int32_t> a = {4, 6};
std::vector<int32_t> b = {2, 3};
std::vector<int32_t> result = get_union(a, b);
std::vector<int32_t> expected = {2, 3, 4, 6};
assert(result == expected); ///< Check if result is correct
print(result); ///< Should print 2 3 4 6
std::cout << "TEST PASSED!\n\n";
}
/**
* @brief A Test to check correct functionality with duplicate values
* @returns void
*/
void test4() {
std::cout << "TEST CASE 4\n";
std::cout << "Intialized a = {4, 6, 6, 7} b = {2, 3, 4}\n";
std::cout << "Expected result: {2, 3, 4, 6, 7}\n";
std::vector<int32_t> a = {4, 6, 6, 7};
std::vector<int32_t> b = {2, 3, 4};
std::vector<int32_t> result = get_union(a, b);
std::vector<int32_t> expected = {2, 3, 4, 6, 7};
assert(result == expected); ///< Check if result is correct
print(result); ///< Should print 2 3 4 6 7
std::cout << "TEST PASSED!\n\n";
}
/**
* @brief A Test to check correct functionality with a harder test case
* @returns void
*/
void test5() {
std::cout << "TEST CASE 5\n";
std::cout << "Intialized a = {1, 4, 6, 7, 9} b = {2, 3, 5}\n";
std::cout << "Expected result: {1, 2, 3, 4, 5, 6, 7, 9}\n";
std::vector<int32_t> a = {1, 4, 6, 7, 9};
std::vector<int32_t> b = {2, 3, 5};
std::vector<int32_t> result = get_union(a, b);
std::vector<int32_t> expected = {1, 2, 3, 4, 5, 6, 7, 9};
assert(result == expected); ///< Check if result is correct
print(result); ///< Should print 1 2 3 4 5 6 7 9
std::cout << "TEST PASSED!\n\n";
}
/**
* @brief A Test to check correct functionality with an array sorted using
* std::sort
* @returns void
*/
void test6() {
std::cout << "TEST CASE 6\n";
std::cout << "Intialized a = {1, 3, 3, 2, 5, 9, 4, 3, 2} ";
std::cout << "b = {11, 3, 7, 8, 6}\n";
std::cout << "Expected result: {1, 2, 3, 4, 5, 6, 7, 8, 9, 11}\n";
std::vector<int32_t> a = {1, 3, 3, 2, 5, 9, 4, 3, 2};
std::vector<int32_t> b = {11, 3, 7, 8, 6};
std::sort(a.begin(), a.end()); ///< Sort vector a
std::sort(b.begin(), b.end()); ///< Sort vector b
std::vector<int32_t> result = get_union(a, b);
std::vector<int32_t> expected = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11};
assert(result == expected); ///< Check if result is correct
print(result); ///< Should print 1 2 3 4 5 6 7 8 9 11
std::cout << "TEST PASSED!\n\n";
}
} // namespace tests
/**
* @brief Function to test the correctness of get_union() function
* @returns void
*/
static void test() {
tests::test1();
tests::test2();
tests::test3();
tests::test4();
tests::test5();
tests::test6();
}
/**
* @brief main function
* @returns 0 on exit
*/
int main() {
test(); // run self-test implementations
return 0;
}

4
range_queries/segtree.cpp
View File

@@ -144,7 +144,7 @@ void update(std::vector<int64_t> *segtree, std::vector<int64_t> *lazy,
* @returns void
*/
static void test() {
int64_t max = static_cast<int64_t>(2 * pow(2, ceil(log2(7))) - 1);
auto max = static_cast<int64_t>(2 * pow(2, ceil(log2(7))) - 1);
assert(max == 15);
std::vector<int64_t> arr{1, 2, 3, 4, 5, 6, 7}, lazy(max), segtree(max);
@@ -172,7 +172,7 @@ int main() {
uint64_t n = 0;
std::cin >> n;
uint64_t max = static_cast<uint64_t>(2 * pow(2, ceil(log2(n))) - 1);
auto max = static_cast<uint64_t>(2 * pow(2, ceil(log2(n))) - 1);
std::vector<int64_t> arr(n), lazy(max), segtree(max);
int choice = 0;

33
sorting/selection_sort.cpp
View File

@@ -1,33 +0,0 @@
// Selection Sort
#include <iostream>
using namespace std;
int main() {
int Array[6];
cout << "\nEnter any 6 Numbers for Unsorted Array : ";
// Input
for (int i = 0; i < 6; i++) {
cin >> Array[i];
}
// Selection Sorting
for (int i = 0; i < 6; i++) {
int min = i;
for (int j = i + 1; j < 6; j++) {
if (Array[j] < Array[min]) {
min = j; // Finding the smallest number in Array
}
}
int temp = Array[i];
Array[i] = Array[min];
Array[min] = temp;
}
// Output
cout << "\nSorted Array : ";
for (int i = 0; i < 6; i++) {
cout << Array[i] << "\t";
}
}

126
sorting/selection_sort_iterative.cpp Normal file
View File

@@ -0,0 +1,126 @@
/******************************************************************************
* @file
* @brief Implementation of the [Selection
* sort](https://en.wikipedia.org/wiki/Selection_sort) implementation using
* swapping
* @details
* The selection sort algorithm divides the input vector into two parts: a
* sorted subvector of items which is built up from left to right at the front
* (left) of the vector, and a subvector of the remaining unsorted items that
* occupy the rest of the vector. Initially, the sorted subvector is empty, and
* the unsorted subvector is the entire input vector. The algorithm proceeds by
* finding the smallest (or largest, depending on the sorting order) element in
* the unsorted subvector, exchanging (swapping) it with the leftmost unsorted
* element (putting it in sorted order), and moving the subvector boundaries one
* element to the right.
*
* ### Implementation
*
* SelectionSort
* The algorithm divides the input vector into two parts: the subvector of items
* already sorted, which is built up from left to right. Initially, the sorted
* subvector is empty and the unsorted subvector is the entire input vector. The
* algorithm proceeds by finding the smallest element in the unsorted subvector,
* exchanging (swapping) it with the leftmost unsorted element (putting it in
* sorted order), and moving the subvector boundaries one element to the right.
*
* @author [Lajat Manekar](https://github.com/Lazeeez)
* @author Unknown author
*******************************************************************************/
#include <algorithm> /// for std::is_sorted
#include <cassert> /// for std::assert
#include <iostream> /// for IO operations
#include <vector> /// for std::vector
/******************************************************************************
* @namespace sorting
* @brief Sorting algorithms
*******************************************************************************/
namespace sorting {
/******************************************************************************
* @brief The main function which implements Selection sort
* @param arr vector to be sorted
* @param len length of vector to be sorted
* @returns @param array resultant sorted vector
*******************************************************************************/
std::vector<uint64_t> selectionSort(const std::vector<uint64_t> &arr,
uint64_t len) {
std::vector<uint64_t> array(
arr.begin(),
arr.end()); // declare a vector in which result will be stored
for (uint64_t it = 0; it < len; ++it) {
uint64_t min = it; // set min value
for (uint64_t it2 = it + 1; it2 < len; ++it2) {
if (array[it2] < array[min]) { // check which element is smaller
min = it2; // store index of smallest element to min
}
}
if (min != it) { // swap if min does not match to i
uint64_t tmp = array[min];
array[min] = array[it];
array[it] = tmp;
}
}
return array; // return sorted vector
}
} // namespace sorting
/*******************************************************************************
* @brief Self-test implementations
* @returns void
*******************************************************************************/
static void test() {
// testcase #1
// [1, 0, 0, 1, 1, 0, 2, 1] returns [0, 0, 0, 1, 1, 1, 1, 2]
std::vector<uint64_t> vector1 = {1, 0, 0, 1, 1, 0, 2, 1};
uint64_t vector1size = vector1.size();
std::cout << "1st test... ";
std::vector<uint64_t> result_test1;
result_test1 = sorting::selectionSort(vector1, vector1size);
assert(std::is_sorted(result_test1.begin(), result_test1.end()));
std::cout << "Passed" << std::endl;
// testcase #2
// [19, 22, 540, 241, 156, 140, 12, 1] returns [1, 12, 19, 22, 140, 156,
// 241,540]
std::vector<uint64_t> vector2 = {19, 22, 540, 241, 156, 140, 12, 1};
uint64_t vector2size = vector2.size();
std::cout << "2nd test... ";
std::vector<uint64_t> result_test2;
result_test2 = sorting::selectionSort(vector2, vector2size);
assert(std::is_sorted(result_test2.begin(), result_test2.end()));
std::cout << "Passed" << std::endl;
// testcase #3
// [11, 20, 30, 41, 15, 60, 82, 15] returns [11, 15, 15, 20, 30, 41, 60, 82]
std::vector<uint64_t> vector3 = {11, 20, 30, 41, 15, 60, 82, 15};
uint64_t vector3size = vector3.size();
std::cout << "3rd test... ";
std::vector<uint64_t> result_test3;
result_test3 = sorting::selectionSort(vector3, vector3size);
assert(std::is_sorted(result_test3.begin(), result_test3.end()));
std::cout << "Passed" << std::endl;
// testcase #4
// [1, 9, 11, 546, 26, 65, 212, 14, -11] returns [-11, 1, 9, 11, 14, 26, 65,
// 212, 546]
std::vector<uint64_t> vector4 = {1, 9, 11, 546, 26, 65, 212, 14};
uint64_t vector4size = vector2.size();
std::cout << "4th test... ";
std::vector<uint64_t> result_test4;
result_test4 = sorting::selectionSort(vector4, vector4size);
assert(std::is_sorted(result_test4.begin(), result_test4.end()));
std::cout << "Passed" << std::endl;
}
/*******************************************************************************
* @brief Main function
* @returns 0 on exit
*******************************************************************************/
int main() {
test(); // run self-test implementations
return 0;
}