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binary-lifting-lca.cpp
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binary-lifting-lca.cpp
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#include <bits/stdc++.h>
using namespace std;
const int MX = 1e5+5, LOG = 17; // LOG = ceil(log2(n))
int N, M, Q, depth[MX], ancestor[LOG][MX];
vector<int> adj[MX];
void dfs(int u, int par) {
ancestor[0][u] = par;
for(int k=1; k<LOG; k++)
ancestor[k][u] = ancestor[k-1][ancestor[k-1][u]];
for(auto v: adj[u]) {
if(v == par) continue;
depth[v] = depth[u] + 1;
dfs(v, u);
}
}
int lca(int u, int v) {
if(depth[u] < depth[v])
swap(u, v);
for(int k=LOG-1; k>=0; k--)
if(ancestor[k][u] != -1 && depth[ancestor[k][u]] >= depth[v])
u = ancestor[k][u];
/*
alternative to the above
for(int k=LOG-1; k>=0; k--)
if ((depth[u] - pow(2, k)) >= depth[v])
u = ancestor[k][u];
*/
// the lca is one the query nodes themselves
if(u == v)
return u;
for(int k=LOG-1; k>=0; k--)
if(ancestor[k][u] != -1 && ancestor[k][u] != ancestor[k][v])
u = ancestor[k][u], v = ancestor[k][v];
return ancestor[0][u];
}
int main() {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
cin >> N >> M >> Q;
// construct tree
for(int i=0, u, v; i<M; i++) {
cin >> u >> v;
adj[u].push_back(v);
adj[v].push_back(u);
}
// initialise ancestor table
dfs(0, -1);
// queries
for(int i=0, u, v; i<Q; i++) {
cin >> u >> v;
cout << lca(u, v) << '\n';
}
return 0;
}
/*
test case
17 16 4
0 1
0 2
2 3
2 4
2 5
3 13
3 14
14 15
15 16
1 6
1 7
7 8
8 9
8 10
6 11
6 12
4 15
10 12
5 16
9 16
expected output
2
1
2
0
*/