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Binary Lifting Trees Adv #90

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99 changes: 99 additions & 0 deletions Dynamic Programming/binary_lifting.cpp
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// PLEASE READ README.TXT BEFORE USING



#include<bits/stdc++.h>
#define ll long long
#define ull unsigned long long
#define MOD 1000000007
#define FOR(i, a, b) for(ll i=a; i<=b; ++i)
#define FORR(i, a, b) for(ll i=a; i>=b; --i)

using namespace std;


int ROOT;

void lift( int root, vector<vector<int>> &tree, vector<int>&parent, int up[][35] , vector<bool>&visited )
{
if( root == ROOT ){
FOR(k, 0 , 35-1) {
up[root][k] = -1;
}
}else{
up[root][0]= parent[root];
FOR(k, 1, 35-1) {
if(up[root][k-1] == -1) up[root][k] = -1;
else
up[root][k] = up[up[root][k-1]][k-1];
}
}

FOR(i, 0, tree[root].size()-1){
if(!visited[tree[root][i]]) {
parent[tree[root][i]] = root;
visited[tree[root][i]] = 1;

lift(tree[root][i], tree, parent, up, visited);
}
}
}




int node_at_height(int node, int up[][35], int h ){
if( node <= -1 ) return node;
if( h == 0 ) return node;

int k =0 ; int temp = h;
while( temp%2 == 0)
{
temp = (temp/2); ++k;
}
// cout<<"$"<<k<<"$";
return node_at_height( up[node][k] , up , h - (long)(1<<k) );
}



int main () {


int total_nodes; cin>>total_nodes;

vector<vector<int>> tree(total_nodes+1);
FOR(i , 1, total_nodes-1){
int u, v ; cin>> u>> v;
tree[u].push_back(v);
tree[v].push_back(u);
}


ROOT = 1; // rooting tree at node 1 (global variable)

vector<int> parent(total_nodes+1 , -1 ); // vector for storing parent of each node

int up[total_nodes+1][35]; memset(up , -1, sizeof(int) * (total_nodes+1) * 35); // up[][] used for precomputation and storing dp values


vector<bool> visited(total_nodes+1, 0);
visited[1]=true;


lift(ROOT, tree, parent , up , visited ); // finally lifting


int queries; cin >> queries;

while(queries -- )
{
int node; cin >> node;
int height; cin >> height;

cout <<"node at give height from "<<node<< " is "<< node_at_height ( node, up , height )<<endl;
}

return 0;
}