Merge branch 'master' into directory-update

dynamic_programming/Unbounded_0_1_Knapsack.cpp

@@ -0,0 +1,151 @@
+/**
+ * @file
+ * @brief Implementation of the Unbounded 0/1 Knapsack Problem
+ * 
+ * @details 
+ * The Unbounded 0/1 Knapsack problem allows taking unlimited quantities of each item. 
+ * The goal is to maximize the total value without exceeding the given knapsack capacity. 
+ * Unlike the 0/1 knapsack, where each item can be taken only once, in this variation, 
+ * any item can be picked any number of times as long as the total weight stays within 
+ * the knapsack's capacity.
+ * 
+ * Given a set of N items, each with a weight and a value, represented by the arrays 
+ * `wt` and `val` respectively, and a knapsack with a weight limit W, the task is to 
+ * fill the knapsack to maximize the total value.
+ *
+ * @note weight and value of items is greater than zero 
+ *
+ * ### Algorithm
+ * The approach uses dynamic programming to build a solution iteratively. 
+ * A 2D array is used for memoization to store intermediate results, allowing 
+ * the function to avoid redundant calculations.
+ * 
+ * @author [Sanskruti Yeole](https://github.com/yeolesanskruti)
+ * @see dynamic_programming/0_1_knapsack.cpp
+ */
+
+#include <iostream>  // Standard input-output stream
+#include <vector>   // Standard library for using dynamic arrays (vectors)
+#include <cassert>  // For using assert function to validate test cases
+#include <cstdint>  // For fixed-width integer types like std::uint16_t
+
+/**
+ * @namespace dynamic_programming
+ * @brief Namespace for dynamic programming algorithms
+ */
+namespace dynamic_programming {
+
+/**
+ * @namespace Knapsack
+ * @brief Implementation of unbounded 0-1 knapsack problem
+ */
+namespace unbounded_knapsack {
+
+/**
+ * @brief Recursive function to calculate the maximum value obtainable using 
+ *        an unbounded knapsack approach.
+ *
+ * @param i Current index in the value and weight vectors.
+ * @param W Remaining capacity of the knapsack.
+ * @param val Vector of values corresponding to the items.
+ * @note "val" data type can be changed according to the size of the input.
+ * @param wt Vector of weights corresponding to the items.
+ * @note "wt" data type can be changed according to the size of the input.
+ * @param dp 2D vector for memoization to avoid redundant calculations.
+ * @return The maximum value that can be obtained for the given index and capacity.
+ */
+std::uint16_t KnapSackFilling(std::uint16_t i, std::uint16_t W, 
+                    const std::vector<std::uint16_t>& val, 
+                    const std::vector<std::uint16_t>& wt, 
+                    std::vector<std::vector<int>>& dp) {
+    if (i == 0) {
+        if (wt[0] <= W) {
+            return (W / wt[0]) * val[0]; // Take as many of the first item as possible
+        } else {
+            return 0; // Can't take the first item
+        }
+    }
+    if (dp[i][W] != -1) return dp[i][W]; // Return result if available
+
+    int nottake = KnapSackFilling(i - 1, W, val, wt, dp); // Value without taking item i
+    int take = 0;
+    if (W >= wt[i]) {
+        take = val[i] + KnapSackFilling(i, W - wt[i], val, wt, dp); // Value taking item i
+    }
+    return dp[i][W] = std::max(take, nottake); // Store and return the maximum value
+}
+
+/**
+ * @brief Wrapper function to initiate the unbounded knapsack calculation.
+ *
+ * @param N Number of items.
+ * @param W Maximum weight capacity of the knapsack.
+ * @param val Vector of values corresponding to the items.
+ * @param wt Vector of weights corresponding to the items.
+ * @return The maximum value that can be obtained for the given capacity.
+ */
+std::uint16_t unboundedKnapsack(std::uint16_t N, std::uint16_t W, 
+                      const std::vector<std::uint16_t>& val, 
+                      const std::vector<std::uint16_t>& wt) {
+    if(N==0)return 0; // Expect 0 since no items
+    std::vector<std::vector<int>> dp(N, std::vector<int>(W + 1, -1)); // Initialize memoization table
+    return KnapSackFilling(N - 1, W, val, wt, dp); // Start the calculation
+}
+
+} // unbounded_knapsack
+
+} // dynamic_programming
+
+/**
+ * @brief self test implementation
+ * @return void
+ */
+static void tests() {
+    // Test Case 1
+    std::uint16_t N1 = 4;  // Number of items
+    std::vector<std::uint16_t> wt1 = {1, 3, 4, 5}; // Weights of the items
+    std::vector<std::uint16_t> val1 = {6, 1, 7, 7}; // Values of the items
+    std::uint16_t W1 = 8; // Maximum capacity of the knapsack
+    // Test the function and assert the expected output
+    assert(unboundedKnapsack(N1, W1, val1, wt1) == 48);
+    std::cout << "Maximum Knapsack value " << unboundedKnapsack(N1, W1, val1, wt1) << std::endl;
+
+    // Test Case 2
+    std::uint16_t N2 = 3; // Number of items
+    std::vector<std::uint16_t> wt2 = {10, 20, 30}; // Weights of the items
+    std::vector<std::uint16_t> val2 = {60, 100, 120}; // Values of the items
+    std::uint16_t W2 = 5; // Maximum capacity of the knapsack
+    // Test the function and assert the expected output
+    assert(unboundedKnapsack(N2, W2, val2, wt2) == 0);
+    std::cout << "Maximum Knapsack value " << unboundedKnapsack(N2, W2, val2, wt2) << std::endl;
+
+    // Test Case 3
+    std::uint16_t N3 = 3; // Number of items
+    std::vector<std::uint16_t> wt3 = {2, 4, 6}; // Weights of the items
+    std::vector<std::uint16_t> val3 = {5, 11, 13};// Values of the items 
+    std::uint16_t W3 = 27;// Maximum capacity of the knapsack 
+    // Test the function and assert the expected output
+    assert(unboundedKnapsack(N3, W3, val3, wt3) == 27);
+    std::cout << "Maximum Knapsack value " << unboundedKnapsack(N3, W3, val3, wt3) << std::endl;
+
+    // Test Case 4
+    std::uint16_t N4 = 0; // Number of items
+    std::vector<std::uint16_t> wt4 = {}; // Weights of the items
+    std::vector<std::uint16_t> val4 = {}; // Values of the items 
+    std::uint16_t W4 = 10; // Maximum capacity of the knapsack
+    assert(unboundedKnapsack(N4, W4, val4, wt4) == 0); 
+    std::cout << "Maximum Knapsack value for empty arrays: " << unboundedKnapsack(N4, W4, val4, wt4) << std::endl;
+  
+    std::cout << "All test cases passed!" << std::endl;
+
+}
+
+/**
+ * @brief main function
+ * @return 0 on successful exit
+ */
+int main() {
+    tests(); // Run self test implementation 
+    return 0;
+}
+

graph/topological_sort.cpp

@@ -1,50 +1,189 @@
-#include <algorithm>
+/**
-#include <iostream>
+ * @file
-#include <vector>
+ * @brief [Topological Sort
+ * Algorithm](https://en.wikipedia.org/wiki/Topological_sorting)
+ * @details
+ * Topological sorting of a directed graph is a linear ordering or its vertices
+ * such that for every directed edge (u,v) from vertex u to vertex v, u comes
+ * before v in the oredering.
+ *
+ * A topological sort is possible only in a directed acyclic graph (DAG).
+ * This file contains code of finding topological sort using Kahn's Algorithm
+ * which involves using Depth First Search technique
+ */
 
-int number_of_vertices,
+#include <algorithm>  // For std::reverse
-    number_of_edges;  // For number of Vertices (V) and number of edges (E)
+#include <cassert>    // For assert
-std::vector<std::vector<int>> graph;
+#include <iostream>   // For IO operations
-std::vector<bool> visited;
+#include <stack>      // For std::stack
-std::vector<int> topological_order;
+#include <stdexcept>  // For std::invalid_argument
+#include <vector>     // For std::vector
 
-void dfs(int v) {
+/**
-    visited[v] = true;
+ * @namespace graph
-    for (int u : graph[v]) {
+ * @brief Graph algorithms
-        if (!visited[u]) {
+ */
-            dfs(u);
+namespace graph {
+
+/**
+ * @namespace topological_sort
+ * @brief Topological Sort Algorithm
+ */
+namespace topological_sort {
+/**
+ * @class Graph
+ * @brief Class that represents a directed graph and provides methods for
+ * manipulating the graph
+ */
+class Graph {
+ private:
+    int n;                              // Number of nodes
+    std::vector<std::vector<int>> adj;  // Adjacency list representation
+
+ public:
+    /**
+     * @brief Constructor for the Graph class
+     * @param nodes Number of nodes in the graph
+     */
+    Graph(int nodes) : n(nodes), adj(nodes) {}
+
+    /**
+     * @brief Function that adds an edge between two nodes or vertices of graph
+     * @param u Start node of the edge
+     * @param v End node of the edge
+     */
+    void addEdge(int u, int v) { adj[u].push_back(v); }
+
+    /**
+     * @brief Get the adjacency list of the graph
+     * @returns A reference to the adjacency list
+     */
+    const std::vector<std::vector<int>>& getAdjacencyList() const {
+        return adj;
+    }
+
+    /**
+     * @brief Get the number of nodes in the graph
+     * @returns The number of nodes
+     */
+    int getNumNodes() const { return n; }
+};
+
+/**
+ * @brief Function to perform Depth First Search on the graph
+ * @param v Starting vertex for depth-first search
+ * @param visited Array representing whether each node has been visited
+ * @param graph Adjacency list of the graph
+ * @param s Stack containing the vertices for topological sorting
+ */
+void dfs(int v, std::vector<int>& visited,
+         const std::vector<std::vector<int>>& graph, std::stack<int>& s) {
+    visited[v] = 1;
+    for (int neighbour : graph[v]) {
+        if (!visited[neighbour]) {
+            dfs(neighbour, visited, graph, s);
         }
     }
-    topological_order.push_back(v);
+    s.push(v);
 }
 
-void topological_sort() {
+/**
-    visited.assign(number_of_vertices, false);
+ * @brief Function to get the topological sort of the graph
-    topological_order.clear();
+ * @param g Graph object
-    for (int i = 0; i < number_of_vertices; ++i) {
+ * @returns A vector containing the topological order of nodes
+ */
+std::vector<int> topologicalSort(const Graph& g) {
+    int n = g.getNumNodes();
+    const auto& adj = g.getAdjacencyList();
+    std::vector<int> visited(n, 0);
+    std::stack<int> s;
+
+    for (int i = 0; i < n; i++) {
         if (!visited[i]) {
-            dfs(i);
+            dfs(i, visited, adj, s);
         }
     }
-    reverse(topological_order.begin(), topological_order.end());
+
-}
+    std::vector<int> ans;
-int main() {
+    while (!s.empty()) {
-    std::cout
+        int elem = s.top();
-        << "Enter the number of vertices and the number of directed edges\n";
+        s.pop();
-    std::cin >> number_of_vertices >> number_of_edges;
+        ans.push_back(elem);
-    int x = 0, y = 0;
-    graph.resize(number_of_vertices, std::vector<int>());
-    for (int i = 0; i < number_of_edges; ++i) {
-        std::cin >> x >> y;
-        x--, y--;  // to convert 1-indexed to 0-indexed
-        graph[x].push_back(y);
     }
-    topological_sort();
+
-    std::cout << "Topological Order : \n";
+    if (ans.size() < n) {  // Cycle detected
-    for (int v : topological_order) {
+        throw std::invalid_argument("cycle detected in graph");
-        std::cout << v + 1
+    }
-                  << ' ';  // converting zero based indexing back to one based.
+    return ans;
+}
+}  // namespace topological_sort
+}  // namespace graph
+
+/**
+ * @brief Self-test implementation
+ * @returns void
+ */
+static void test() {
+    // Test 1
+    std::cout << "Testing for graph 1\n";
+    int n_1 = 6;
+    graph::topological_sort::Graph graph1(n_1);
+    graph1.addEdge(4, 0);
+    graph1.addEdge(5, 0);
+    graph1.addEdge(5, 2);
+    graph1.addEdge(2, 3);
+    graph1.addEdge(3, 1);
+    graph1.addEdge(4, 1);
+    std::vector<int> ans_1 = graph::topological_sort::topologicalSort(graph1);
+    std::vector<int> expected_1 = {5, 4, 2, 3, 1, 0};
+    std::cout << "Topological Sorting Order: ";
+    for (int i : ans_1) {
+        std::cout << i << " ";
     }
     std::cout << '\n';
+    assert(ans_1 == expected_1);
+    std::cout << "Test Passed\n\n";
+
+    // Test 2
+    std::cout << "Testing for graph 2\n";
+    int n_2 = 5;
+    graph::topological_sort::Graph graph2(n_2);
+    graph2.addEdge(0, 1);
+    graph2.addEdge(0, 2);
+    graph2.addEdge(1, 2);
+    graph2.addEdge(2, 3);
+    graph2.addEdge(1, 3);
+    graph2.addEdge(2, 4);
+    std::vector<int> ans_2 = graph::topological_sort::topologicalSort(graph2);
+    std::vector<int> expected_2 = {0, 1, 2, 4, 3};
+    std::cout << "Topological Sorting Order: ";
+    for (int i : ans_2) {
+        std::cout << i << " ";
+    }
+    std::cout << '\n';
+    assert(ans_2 == expected_2);
+    std::cout << "Test Passed\n\n";
+
+    // Test 3 - Graph with cycle
+    std::cout << "Testing for graph 3\n";
+    int n_3 = 3;
+    graph::topological_sort::Graph graph3(n_3);
+    graph3.addEdge(0, 1);
+    graph3.addEdge(1, 2);
+    graph3.addEdge(2, 0);
+    try {
+        graph::topological_sort::topologicalSort(graph3);
+    } catch (std::invalid_argument& err) {
+        assert(std::string(err.what()) == "cycle detected in graph");
+    }
+    std::cout << "Test Passed\n";
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // run self test implementations
     return 0;
 }

math/sieve_of_eratosthenes.cpp

@@ -1,6 +1,7 @@
 /**
  * @file
- * @brief Get list of prime numbers using Sieve of Eratosthenes
+ * @brief Prime Numbers using [Sieve of
+ * Eratosthenes](https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes)
  * @details
  * Sieve of Eratosthenes is an algorithm that finds all the primes
  * between 2 and N.
@@ -11,21 +12,39 @@
  * @see primes_up_to_billion.cpp prime_numbers.cpp
  */
 
-#include <cassert>
+#include <cassert>   /// for assert
-#include <iostream>
+#include <iostream>  /// for IO operations
-#include <vector>
+#include <vector>    /// for std::vector
 
 /**
- * This is the function that finds the primes and eliminates the multiples.
+ * @namespace math
+ * @brief Mathematical algorithms
+ */
+namespace math {
+/**
+ * @namespace sieve_of_eratosthenes
+ * @brief Functions for finding Prime Numbers using Sieve of Eratosthenes
+ */
+namespace sieve_of_eratosthenes {
+/**
+ * @brief Function to sieve out the primes
+ * @details
+ * This function finds all the primes between 2 and N using the Sieve of
+ * Eratosthenes algorithm. It starts by assuming all numbers (except zero and
+ * one) are prime and then iteratively marks the multiples of each prime as
+ * non-prime.
+ *
  * Contains a common optimization to start eliminating multiples of
  * a prime p starting from p * p since all of the lower multiples
  * have been already eliminated.
- * @param N number of primes to check
+ * @param N number till which primes are to be found
- * @return is_prime a vector of `N + 1` booleans identifying if `i`^th number is a prime or not
+ * @return is_prime a vector of `N + 1` booleans identifying if `i`^th number is
+ * a prime or not
  */
 std::vector<bool> sieve(uint32_t N) {
-    std::vector<bool> is_prime(N + 1, true);
+    std::vector<bool> is_prime(N + 1, true);  // Initialize all as prime numbers
-    is_prime[0] = is_prime[1] = false;
+    is_prime[0] = is_prime[1] = false;        // 0 and 1 are not prime numbers
+
     for (uint32_t i = 2; i * i <= N; i++) {
         if (is_prime[i]) {
             for (uint32_t j = i * i; j <= N; j += i) {
@@ -37,9 +56,10 @@ std::vector<bool> sieve(uint32_t N) {
 }
 
 /**
- * This function prints out the primes to STDOUT
+ * @brief Function to print the prime numbers
- * @param N number of primes to check
+ * @param N number till which primes are to be found
- * @param is_prime a vector of `N + 1` booleans identifying if `i`^th number is a prime or not
+ * @param is_prime a vector of `N + 1` booleans identifying if `i`^th number is
+ * a prime or not
  */
 void print(uint32_t N, const std::vector<bool> &is_prime) {
     for (uint32_t i = 2; i <= N; i++) {
@@ -50,23 +70,53 @@ void print(uint32_t N, const std::vector<bool> &is_prime) {
     std::cout << std::endl;
 }
 
+}  // namespace sieve_of_eratosthenes
+}  // namespace math
+
 /**
- * Test implementations
+ * @brief Self-test implementations
+ * @return void
  */
-void tests() {
+static void tests() {
-  //                    0      1      2     3     4      5     6      7     8      9      10
+    std::vector<bool> is_prime_1 =
-  std::vector<bool> ans{false, false, true, true, false, true, false, true, false, false, false};
+        math::sieve_of_eratosthenes::sieve(static_cast<uint32_t>(10));
-  assert(sieve(10) == ans);
+    std::vector<bool> is_prime_2 =
+        math::sieve_of_eratosthenes::sieve(static_cast<uint32_t>(20));
+    std::vector<bool> is_prime_3 =
+        math::sieve_of_eratosthenes::sieve(static_cast<uint32_t>(100));
+
+    std::vector<bool> expected_1{false, false, true,  true,  false, true,
+                                 false, true,  false, false, false};
+    assert(is_prime_1 == expected_1);
+
+    std::vector<bool> expected_2{false, false, true,  true,  false, true,
+                                 false, true,  false, false, false, true,
+                                 false, true,  false, false, false, true,
+                                 false, true,  false};
+    assert(is_prime_2 == expected_2);
+
+    std::vector<bool> expected_3{
+        false, false, true,  true,  false, true,  false, true,  false, false,
+        false, true,  false, true,  false, false, false, true,  false, true,
+        false, false, false, true,  false, false, false, false, false, true,
+        false, true,  false, false, false, false, false, true,  false, false,
+        false, true,  false, true,  false, false, false, true,  false, false,
+        false, false, false, true,  false, false, false, false, false, true,
+        false, true,  false, false, false, false, false, true,  false, false,
+        false, true,  false, true,  false, false, false, false, false, true,
+        false, false, false, true,  false, false, false, false, false, true,
+        false, false, false, false, false, false, false, true,  false, false,
+        false};
+    assert(is_prime_3 == expected_3);
+
+    std::cout << "All tests have passed successfully!\n";
 }
 
 /**
- * Main function
+ * @brief Main function
+ * @returns 0 on exit
  */
 int main() {
     tests();
-
-    uint32_t N = 100;
-    std::vector<bool> is_prime = sieve(N);
-    print(N, is_prime);
     return 0;
 }