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10.find Lowest Common Ancestor(LCA)

 #include <bits/stdc++.h>

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template <class type1>
#define ll long long int
#define endl "\n"
#define ordered_set tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update>
using ordered_multiset = tree <type1, null_type, less_equal <type1>, rb_tree_tag, tree_order_statistics_node_update>;
 //ordered_multiset <ll> kek;(declaration for multiorder set)
// ordered_set o_set;(declaration)
//kek.order_of_key(i);(strictly less then i for multi order set)
//o_set.order_of_key(5) ;(strictly less then i for multi order set)
#define yes cout << "YES\n"
#define no cout << "NO\n"
#define N 100000
vector<ll>adj[N];
ll parent[N];
void dfs(ll node,ll par=-1)
{
     parent[node]=par;
     for(auto u:adj[node])
     {
        if(u==par)continue;
        dfs(u,node);
     }
}
vector<ll>path(ll node)
{
     vector<ll>v;
     while(node!=-1)
     {
         v.push_back(node);
         node=parent[node];
     }
     reverse(v.begin(),v.end());
     return v;
}
int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
   
     ll n,i;
     cin>>n;
     for(i=1;i<n;i++)
     {
         ll u,v;
         cin>>u>>v;
         adj[u].push_back(v);
         adj[v].push_back(u);
     }
     vector<ll>v1;
     vector<ll>v2;
     dfs(1);
     ll x,y;
     cin>>x>>y;
     v1=path(x);
     v2=path(y);
     ll ans;
   
     for(i=0;i<min(v1.size(),v2.size());i++)
     {
         if(v1[i]==v2[i])
         {
             ans=v1[i];
         }
         else break;
     }
      cout<<ans<<endl;
    return 0;
}

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