Added Bellman ford and Koseraju Algorithm in C++ Section.

C++program/Bellman-Ford.cpp

@@ -0,0 +1,143 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+// a structure to represent a weighted edge in graph
+struct Edge
+{
+    int src, dest, weight;
+};
+
+// a structure to represent a connected, directed and
+// weighted graph
+struct Graph
+{
+    // V-> Number of vertices, E-> Number of edges
+    int V, E;
+
+    // graph is represented as an array of edges.
+    struct Edge *edge;
+};
+
+// Creates a graph with V vertices and E edges
+struct Graph *createGraph(int V, int E)
+{
+    struct Graph *graph = new Graph;
+    graph->V = V;
+    graph->E = E;
+    graph->edge = new Edge[E];
+    return graph;
+}
+
+// A utility function used to print the solution
+void printArr(int dist[], int n)
+{
+    printf("Vertex Distance from Source\n");
+    for (int i = 0; i < n; ++i)
+        printf("%d \t\t %d\n", i, dist[i]);
+}
+
+// The main function that finds shortest distances from src
+// to all other vertices using Bellman-Ford algorithm. The
+// function also detects negative weight cycle
+void BellmanFord(struct Graph *graph, int src)
+{
+    int V = graph->V;
+    int E = graph->E;
+    int dist[V];
+
+    // Step 1: Initialize distances from src to all other
+    // vertices as INFINITE
+    for (int i = 0; i < V; i++)
+        dist[i] = INT_MAX;
+    dist[src] = 0;
+
+    // Step 2: Relax all edges |V| - 1 times. A simple
+    // shortest path from src to any other vertex can have
+    // at-most |V| - 1 edges
+    for (int i = 1; i <= V - 1; i++)
+    {
+        for (int j = 0; j < E; j++)
+        {
+            int u = graph->edge[j].src;
+            int v = graph->edge[j].dest;
+            int weight = graph->edge[j].weight;
+            if (dist[u] != INT_MAX && dist[u] + weight < dist[v])
+                dist[v] = dist[u] + weight;
+        }
+    }
+
+    // Step 3: check for negative-weight cycles. The above
+    // step guarantees shortest distances if graph doesn't
+    // contain negative weight cycle. If we get a shorter
+    // path, then there is a cycle.
+    for (int i = 0; i < E; i++)
+    {
+        int u = graph->edge[i].src;
+        int v = graph->edge[i].dest;
+        int weight = graph->edge[i].weight;
+        if (dist[u] != INT_MAX && dist[u] + weight < dist[v])
+        {
+            printf("Graph contains negative weight cycle");
+            return; // If negative cycle is detected, simply
+                    // return
+        }
+    }
+
+    printArr(dist, V);
+
+    return;
+}
+
+// Driver's code
+int main()
+{
+    /* Let us create the graph given in above example */
+    int V = 5; // Number of vertices in graph
+    int E = 8; // Number of edges in graph
+    struct Graph *graph = createGraph(V, E);
+
+    // add edge 0-1 (or A-B in above figure)
+    graph->edge[0].src = 0;
+    graph->edge[0].dest = 1;
+    graph->edge[0].weight = -1;
+
+    // add edge 0-2 (or A-C in above figure)
+    graph->edge[1].src = 0;
+    graph->edge[1].dest = 2;
+    graph->edge[1].weight = 4;
+
+    // add edge 1-2 (or B-C in above figure)
+    graph->edge[2].src = 1;
+    graph->edge[2].dest = 2;
+    graph->edge[2].weight = 3;
+
+    // add edge 1-3 (or B-D in above figure)
+    graph->edge[3].src = 1;
+    graph->edge[3].dest = 3;
+    graph->edge[3].weight = 2;
+
+    // add edge 1-4 (or B-E in above figure)
+    graph->edge[4].src = 1;
+    graph->edge[4].dest = 4;
+    graph->edge[4].weight = 2;
+
+    // add edge 3-2 (or D-C in above figure)
+    graph->edge[5].src = 3;
+    graph->edge[5].dest = 2;
+    graph->edge[5].weight = 5;
+
+    // add edge 3-1 (or D-B in above figure)
+    graph->edge[6].src = 3;
+    graph->edge[6].dest = 1;
+    graph->edge[6].weight = 1;
+
+    // add edge 4-3 (or E-D in above figure)
+    graph->edge[7].src = 4;
+    graph->edge[7].dest = 3;
+    graph->edge[7].weight = -3;
+
+    // Function call
+    BellmanFord(graph, 0);
+
+    return 0;
+}

C++program/Koseraju.cpp

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+/* Implementation of Kosaraju's Algorithm to find out the strongly connected
+   components (SCCs) in a graph. Author:Anirban166
+*/
+
+#include <iostream>
+#include <stack>
+#include <vector>
+
+/**
+ * Iterative function/method to print graph:
+ * @param a adjacency list representation of the graph
+ * @param V number of vertices
+ * @return void
+ **/
+void print(const std::vector<std::vector<int>> &a, int V)
+{
+    for (int i = 0; i < V; i++)
+    {
+        if (!a[i].empty())
+        {
+            std::cout << "i=" << i << "-->";
+        }
+        for (int j : a[i])
+        {
+            std::cout << j << " ";
+        }
+        if (!a[i].empty())
+        {
+            std::cout << std::endl;
+        }
+    }
+}
+
+/**
+ * //Recursive function/method to push vertices into stack passed as parameter:
+ * @param v vertices
+ * @param st stack passed by reference
+ * @param vis array to keep track of visited nodes (boolean type)
+ * @param adj adjacency list representation of the graph
+ * @return void
+ **/
+void push_vertex(int v, std::stack<int> *st, std::vector<bool> *vis,
+                 const std::vector<std::vector<int>> &adj)
+{
+    (*vis)[v] = true;
+    for (auto i = adj[v].begin(); i != adj[v].end(); i++)
+    {
+        if ((*vis)[*i] == false)
+        {
+            push_vertex(*i, st, vis, adj);
+        }
+    }
+    st->push(v);
+}
+
+/**
+ * //Recursive function/method to implement depth first traversal(dfs):
+ * @param v vertices
+ * @param vis array to keep track of visited nodes (boolean type)
+ * @param grev graph with reversed edges
+ * @return void
+ **/
+void dfs(int v, std::vector<bool> *vis,
+         const std::vector<std::vector<int>> &grev)
+{
+    (*vis)[v] = true;
+    // cout<<v<<" ";
+    for (auto i = grev[v].begin(); i != grev[v].end(); i++)
+    {
+        if ((*vis)[*i] == false)
+        {
+            dfs(*i, vis, grev);
+        }
+    }
+}
+
+// function/method to implement Kosaraju's Algorithm:
+/**
+* Info about the method
+* @param V vertices in graph
+* @param adj array of vectors that represent a graph (adjacency list/array)
+* @return int ( 0, 1, 2..and so on, only unsigned values as either there can be
+no SCCs i.e. none(0) or there will be x no. of SCCs (x>0)) i.e. it returns the
+count of (number of) strongly connected components (SCCs) in the graph.
+(variable 'count_scc' within function)
+**/
+int kosaraju(int V, const std::vector<std::vector<int>> &adj)
+{
+    std::vector<bool> vis(V, false);
+    std::stack<int> st;
+    for (int v = 0; v < V; v++)
+    {
+        if (vis[v] == false)
+        {
+            push_vertex(v, &st, &vis, adj);
+        }
+    }
+    // making new graph (grev) with reverse edges as in adj[]:
+    std::vector<std::vector<int>> grev(V);
+    for (int i = 0; i < V + 1; i++)
+    {
+        for (auto j = adj[i].begin(); j != adj[i].end(); j++)
+        {
+            grev[*j].push_back(i);
+        }
+    }
+    // cout<<"grev="<<endl; ->debug statement
+    // print(grev,V);       ->debug statement
+    // reinitialise visited to 0
+    for (int i = 0; i < V; i++)
+        vis[i] = false;
+    int count_scc = 0;
+    while (!st.empty())
+    {
+        int t = st.top();
+        st.pop();
+        if (vis[t] == false)
+        {
+            dfs(t, &vis, grev);
+            count_scc++;
+        }
+    }
+    // cout<<"count_scc="<<count_scc<<endl; //in case you want to print here
+    // itself, uncomment & change return type of function to void.
+    return count_scc;
+}
+
+// All critical/corner cases have been taken care of.
+// Input your required values: (not hardcoded)
+int main()
+{
+    int t = 0;
+    std::cin >> t;
+    while (t--)
+    {
+        int a = 0, b = 0; // a->number of nodes, b->directed edges.
+        std::cin >> a >> b;
+        int m = 0, n = 0;
+        std::vector<std::vector<int>> adj(a + 1);
+        for (int i = 0; i < b; i++) // take total b inputs of 2 vertices each
+                                    // required to form an edge.
+        {
+            std::cin >> m >> n; // take input m,n denoting edge from m->n.
+            adj[m].push_back(n);
+        }
+        // pass number of nodes and adjacency array as parameters to function:
+        std::cout << kosaraju(a, adj) << std::endl;
+    }
+    return 0;
+}