Added question - Product_of_lengths_all_cycles_undirected_graph

Product_of_lengths_all_cycles_undirected_graph/question.txt

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+Given an undirected and unweighted graph. The task is to find the product of the lengths of all cycles formed in it.

Product_of_lengths_all_cycles_undirected_graph/solution.cpp

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+//solution source  - geeksforgeeks
+#include <bits/stdc++.h> 
+using namespace std; 
+const int N = 100000; 
+
+// variables to be used 
+// in both functions 
+vector<int> graph[N]; 
+
+// Function to mark the vertex with 
+// different colors for different cycles 
+void dfs_cycle(int u, int p, int color[], 
+            int mark[], int par[], int& cyclenumber) 
+{ 
+
+    // already (completely) visited vertex. 
+    if (color[u] == 2) { 
+        return; 
+    } 
+
+    // seen vertex, but was not completely  
+    // visited -> cycle detected. 
+    // backtrack based on parents to find 
+    // the complete cycle. 
+    if (color[u] == 1) { 
+
+        cyclenumber++; 
+        int cur = p; 
+        mark[cur] = cyclenumber; 
+
+        // backtrack the vertex which are 
+        // in the current cycle thats found 
+        while (cur != u) { 
+            cur = par[cur]; 
+            mark[cur] = cyclenumber; 
+        } 
+        return; 
+    } 
+    par[u] = p; 
+
+    // partially visited. 
+    color[u] = 1; 
+
+    // simple dfs on graph 
+    for (int v : graph[u]) { 
+
+        // if it has not been visited previously 
+        if (v == par[u]) { 
+            continue; 
+        } 
+        dfs_cycle(v, u, color, mark, par, cyclenumber); 
+    } 
+
+    // completely visited. 
+    color[u] = 2; 
+} 
+
+// add the edges to the graph 
+void addEdge(int u, int v) 
+{ 
+    graph[u].push_back(v); 
+    graph[v].push_back(u); 
+} 
+
+// Function to print the cycles 
+int productLength(int edges, int mark[], int& cyclenumber) 
+{ 
+    unordered_map<int, int> mp; 
+
+    // push the edges that into the 
+    // cycle adjacency list 
+    for (int i = 1; i <= edges; i++) { 
+        if (mark[i] != 0) 
+            mp[mark[i]]++; 
+    } 
+    int cnt = 1; 
+
+    // prodcut all the length of cycles 
+    for (int i = 1; i <= cyclenumber; i++) { 
+        cnt = cnt * mp[i]; 
+    } 
+    if (cyclenumber == 0) 
+        cnt = 0; 
+
+    return cnt; 
+} 
+
+// Driver Code 
+int main() 
+{ 
+
+    // add edges 
+    addEdge(1, 2); 
+    addEdge(2, 3); 
+    addEdge(3, 4); 
+    addEdge(4, 6); 
+    addEdge(4, 7); 
+    addEdge(5, 6); 
+    addEdge(3, 5); 
+    addEdge(7, 8); 
+    addEdge(6, 10); 
+    addEdge(5, 9); 
+    addEdge(10, 11); 
+    addEdge(11, 12); 
+    addEdge(11, 13); 
+    addEdge(12, 13); 
+
+    // arrays required to color the 
+    // graph, store the parent of node 
+    int color[N]; 
+    int par[N]; 
+
+    // mark with unique numbers 
+    int mark[N]; 
+
+    // store the numbers of cycle 
+    int cyclenumber = 0; 
+    int edges = 13; 
+
+    // call DFS to mark the cycles 
+    dfs_cycle(1, 0, color, mark, par, cyclenumber); 
+
+    // function to print the cycles 
+    cout << productLength(edges, mark, cyclenumber); 
+
+    return 0; 
+}