Merge branch 'master' into lazeeez

This commit is contained in:
Lajat5
2021-10-24 21:55:07 +05:30
committed by GitHub
5 changed files with 606 additions and 27 deletions

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@@ -46,6 +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)
@@ -241,7 +243,7 @@
* [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)

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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;
}

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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;
}

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#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;
}

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/**
* @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;
}