Create LCA_Binary_Lifting.cpp

Competitive programming/C++/LCA_Binary_Lifting.cpp

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+// Problem Link : https://cses.fi/problemset/task/1688
+
+// Lowest Common Ancestor | Binary Lifting - O(Log(N)) time complexity using a sparse table.
+
+#include <bits/stdc++.h>
+using namespace std;
+
+typedef long long ll;
+#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
+#define endl "\n"
+
+const ll N=2e5+5 ;
+vector<ll> v[N] ;
+int level[N]={},par[N][20] ;
+
+void DFS(ll x,ll p,ll cnt){
+    level[x]=cnt ; 
+    if (p!=-1) par[x][0] = p ;     
+    for(auto i : v[x]){
+        if (i!=p){
+            DFS(i,x,cnt+1) ;
+        }
+    }
+}
+
+int getLCA(int n1, int n2) {
+    if (level[n1]>level[n2]) swap(n1,n2) ;
+    ll d = level[n2]-level[n1] ;    // Equalise the level of both nodes.
+    while(d>0){
+        int x = log2(d) ;
+        n2 = par[n2][x] ;
+        d-=(1<<x) ;
+    }
+    if (n1==n2)    // n1 is either Ancestor or Descendant of n2.
+        return n1 ;
+    d = level[n1] ;
+    d = log2(d)+1 ;
+    for(ll i=d ; i>=0 ; i--){
+        if (par[n2][i]!=-1 && par[n2][i]!=par[n1][i]){   
+            n2 = par[n2][i] ;
+            n1 = par[n1][i] ;
+        }
+    }
+    return par[n2][0] ;  // LCA is just one node above n1 & n2.
+}
+
+int main() {
+    IOS ;
+    ll n,q,x,y ;
+    cin>>n>>q ;
+    memset(par,-1,sizeof(par)) ;
+    for(ll i=1 ; i<n ; i++){
+        cin>>x>>y ;
+        v[x].push_back(y) ;
+        v[y].push_back(x) ;
+    }
+
+    DFS(1,-1,0) ;
+    for(ll j=1 ; j<20 ; j++){          //  O(logN)
+        for(ll i=1 ; i<=n ; i++){      //  O(N)
+            int x = par[i][j-1] ;
+            if (x!=-1)
+                par[i][j]=par[x][j-1] ;
+        }
+    }
+    while(q--){
+        cin>>x>>y ;
+        int z=getLCA(x,y) ;  // Taking difference of level from LCA node
+        cout<< abs(level[x]-level[z]) + abs(level[y]-level[z]) <<endl ;
+    }
+
+	return 0;
+}