Added a new Algorithm Weighted Quick Union

Author: Mcbook

Graph/Weighted_Quick_Union/weighted_quick_union.cpp

@@ -0,0 +1,86 @@
+/*
+ *  This is a weighted quick union algorithm.
+*/
+#include<iostream>
+#include<vector> 
+
+using namespace std;
+
+#define whatis(x) cout<<#x<<": "<<x<<endl
+#define MAX 10000007
+
+//For storing the root element
+//For storing the size of the root element
+int id[MAX];
+int sz[MAX];
+
+// initializing all the values of id[i] to i.
+// initializing all the values of sz[i] to 1;
+void initiate(){
+    for(int i = 0; i<MAX; i++ ) {
+        id[i] = i;
+        sz[i] = 1;
+    }
+}
+
+// joining two nodes
+void join(int p, int q) {
+    
+    while(id[p] != p ) p = id[p];
+    while(id[q] != q)  q = id[q];
+        
+    if( p == q ) return ;
+
+    if(sz[p] < sz[q]) { id[p] = q ; sz[q] += sz[p]; }
+    else {              id[q] = p;  sz[p] += sz[q]; 
+    }
+
+}
+
+//Checking if the pair of nodes is already joined or not
+bool check_join( int p, int q) {
+    
+    
+    while(id[p] != p ) p = id[p];
+    while(id[q] != q ) q = id[q];
+    
+    
+    if(p == q) return true;
+    else return false;
+}
+
+//Example to show how it works
+void example() {
+    
+    int p[][2] = { 
+        {1, 2}, 
+        {2, 3}, 
+
+    };
+
+    int check[][2] = {
+        {1, 3}, {1, 7}
+    };
+    
+    for(int i = 0; i<2; i++){
+        join(p[i][0], p[i][1]);
+    }
+
+    for(int i = 0 ; i<2; i++ ) {
+        cout<<check_join(check[i][0], check[i][1])<<endl;
+    }
+
+}
+
+/*
+1  as 1 and 3 are already joined.
+0  as 1 and 7 are not joined.
+*/
+
+int main() {
+    initiate(); //initiating id ans sz array above
+
+    example(); // Taking an example
+
+    return 0;
+}