Create LCA_binary_lifting.cpp

adding a sample problem of finding distance between two nodes in a tree for eg, if nodes are A and B then dist(A,B) = depth(A) + depth(B) - 2*LCA(A,B) here calculating LCA in efficient time is crucial. so there is a technique called binary lifting which calculates LCA in log(n) time

Author: harshpac

C++/Data-Structures/Tree/LCA_binary_lifting.cpp

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+
+/* find least common ancestor
+ 
+ time complexity O(logn)
+ 
+ using binary lifting
+ 
+*/
+
+
+#include<iostream>
+using namespace std;
+#include<queue>
+#include<map>
+#include<math.h>
+#define lli long long int
+#include<vector>
+#define vi vector<int>
+#define fo(i,n) for(int i=1;i<=n;i++)
+#define maxN 10
+#include <bits/stdc++.h>
+
+//ques--- find the dist bw two nodes in a tree
+
+
+vi adj[1001];
+vi level(1001);
+
+int LCA[1001][maxN+1];
+
+void dfs(int node, int lvl, int parent){
+
+level[node]=lvl;
+LCA[node][0]=parent;
+//cout<<node<<"jiji";
+
+for(int child: adj[node]){
+if(child!=parent)
+dfs(child,lvl+1,node);
+}
+
+}
+
+void init(int n){
+dfs(1,0,-1);
+
+for(int j=1;j<=maxN;j++){
+for(int i=1;i<=n;i++){
+if(LCA[i][j-1]!=-1){
+int temp=LCA[i][j-1];
+LCA[i][j] = LCA[temp][j-1];
+}
+else LCA[i][j] = -1;
+}
+}
+}
+
+
+
+
+// this returns the least common ancestor of two nodes a and b
+
+
+int getLCA(int a, int b){
+
+int diff;
+
+if(level[b]<level[a]) swap(a,b);
+
+diff = level[b] - level[a];
+
+while(diff>0){
+int i = log2(diff);
+
+b = LCA[b][i];
+
+diff -= (1<<i);
+}
+
+if(a == b) return a;
+
+for(int i=maxN;i>=0;i--){
+if(LCA[a][i]!=-1 && (LCA[a][i]!=LCA[b][i]))
+a = LCA[a][i], b = LCA[b][i];
+}
+
+return LCA[a][0];
+}
+
+int getDist(int a, int b){
+
+int lca=getLCA(a,b);
+//if(level[a]>level[b])
+return level[a] + level[b] - 2*level[lca];
+
+}
+
+int main(){
+ // now working fine :)))
+ 
+// it was throwing running time error from 2 hours 
+ // bcoz in for loop there was i = 0; i<=maxN i.e, maxN+1 times
+ // while I declared LCA as LCA[1001][maxN] should be maxN+1 or bigg....
+ // so remember while assigning sizes globally.
+int n,a,b; cin>>n;
+
+fo(i,n-1)
+cin>>a>>b, adj[a].push_back(b), adj[b].push_back(a);
+
+init(n);
+
+
+
+int q; cin>>q;
+
+while(q--){
+cin>>a>>b;
+int d= getDist(a,b);
+cout<<d<<endl;
+}
+
+}