graph #6

graphs/cyclicity_in_graph.cpp

@@ -0,0 +1,77 @@
+/*DISJOINT SET UNION*/
+/*Algorithm for finding if an undirected graph is cyclic or acyclic*/
+/*prerequisites
+    -basic knowledge about graphs
+    -should know traversing in graph(BFS, DFS)
+*/
+
+/*SCENARIO
+    There are n cities. They are connected by roads. If city 1 is connected directly with city 2,
+    and city 2 is connected directly with city 3,...., city k is connected with city 1. then we say that 
+    roads form a cycle. i.e.
+
+    1---2---4                               1---2---4---5
+    |  /\                                   |   |    \
+    | /  \                                  |   |     \
+    3     5---6                             6---3      7---8
+    |
+    |
+    7
+
+    in first case we see that roads connecting city 1,2,3 form a cycle.
+    in second case we see that roads connecting ctiy 1,2,3,6 form a cycle.
+*/
+
+/*ALGORITHM
+    1) first label each node as its parent node. i.e. each node is parent node of itself.
+    2) then traverse across the graph and find parent of each node.
+    3) if they have different parent do union of those 2, i.e. make thier parents same.
+    4) if two node have same parent then it must be a cycle.
+*/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+int find(int node,vector<int>&parent){
+    //finding the parent node
+    while(parent[node]!=node){
+        node=parent[node];
+    }
+    return node;
+}
+
+void Union(int i,int j,vector<int>&parent){
+    // union of node, i.e, setting parent as same.
+    int iroot=find(i,parent);
+    int jroot=find(j,parent);
+    if(iroot!=jroot){
+        parent[jroot]=iroot;
+    }
+}
+
+bool dsu(vector<vector<int>>& edges) {
+    //setting parent of each node
+    vector<int>parent(edges.size()+1);
+    for(int i=0;i<edges.size()+1;i++)parent[i]=i;
+
+    //appyling dsu
+    for(auto edge:edges){
+        if(find(edge[0],parent)==find(edge[1],parent))return true;
+        Union(edge[0],edge[1],parent);
+    }
+    return false;
+}
+
+int main(){
+    vector<vector<int>>graph={{1,2},{2,3},{3,4},{1,5},{1,4}};
+    /*
+        graph is:
+        2--1--5
+        |  |
+        3--4
+    */
+    bool ans= dsu(graph);
+
+    if(ans)cout<<"graph is cyclic!"<<endl;
+    else cout<<"graph is acyclic!"<<endl;
+}