From b0a4d4bdbbac0ac3f4f4702579234956a154bb1f Mon Sep 17 00:00:00 2001
From: Ritik Nandwal <ritiknandwal021@gmail.com>
Date: Mon, 3 May 2021 19:17:03 +0530
Subject: [PATCH] Add kruskals implementation

---
 graph/kruskals.cpp | 67 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 67 insertions(+)
 create mode 100644 graph/kruskals.cpp

diff --git a/graph/kruskals.cpp b/graph/kruskals.cpp
new file mode 100644
index 0000000..d6fc748
--- /dev/null
+++ b/graph/kruskals.cpp
@@ -0,0 +1,67 @@
+#include<bits/stdc++.h>
+using namespace std;
+struct node{
+    int u,v,w;
+    node(int first,int second,int weight){
+        u=first;
+        v=second;
+        w=weight;
+    }
+};
+bool comp(node a,node b){
+    return a.w < b.w;
+}
+int findPar(int u,vector<int> &parent){
+    if(u == parent[u])
+        return u;
+    return findPar(parent[u],parent);
+}
+void Union(int u,int v,vector<int> &parent,vector<int> &size){
+    u = findPar(u,parent);
+    v = findPar(v,parent);
+    if(size[u] < size[v]){
+        parent[u] = v;
+        size[v] += size[u];
+    }else{
+        parent[v]=u;
+        size[u]+=size[v];
+    }
+}
+int main(){
+    int N,m;
+    cin>>N>>m;
+    vector<node> edges;
+    for(int i=0;i<m;i++){
+        int u,v,w;
+        cin>>u>>v>>w;
+        edges.push_back(node(u,v,w));
+    }
+    /*
+        sample testcase for trying
+        N=4,m=5
+        0 1 10
+        0 2 6
+        0 3 5
+        1 3 15
+        2 3 4
+    */
+    sort(edges.begin(),edges.end(),comp);
+    vector<int> parent(N);
+    for(int i=0;i<N;i++)
+        parent[i] = i;
+    vector<int> size(N,0);
+    int cost=0;
+    vector<pair<int,int>> mst;
+    for(auto it:edges){
+        if(findPar(it.v,parent) != findPar(it.u,parent)){
+            cost+=it.w;
+            mst.push_back({it.u,it.v});
+            Union(it.u,it.v,parent,size);
+        }
+    }
+    cout<<cost<<endl;
+    for(auto it:mst){
+        cout<<it.first<<" "<<it.second<<endl;
+    }
+    return 0;
+}