Out of all shortest path I am finding min of maximum distance I have to travel for every level.





#include<bits/stdc++.h>
using namespace std;

void bfs(int u,vector<int> &d,const vector<vector<int>> adj){
    d[u] = 0;
    queue<int> q;
    q.push(u);

    while(!q.empty()){
        int u = q.front();
        q.pop();

        for(auto v:adj[u]){
            if(d[v]>d[u]+1){
                d[v]=d[u]+1;
                q.push(v);
            }
        }
    }
}

int main(){
    int n,m;
    cin>>n>>m;
    vector<vector<int>> adj(n);

    for(int i=0;i<m;i++){
        int u,v;
        cin>>u>>v;
        adj[u-1].push_back(v-1);
        adj[v-1].push_back(u-1);
    }

    vector<int> ds(n,1e9),df(n,1e9),dr(n,1e9);
    int s,f,r;
    cin>>s>>f>>r;
    s--,f--,r--;
    bfs(s,ds,adj);
    bfs(f,df,adj);
    bfs(r,dr,adj);

    vector<vector<int>> l(ds[f]+1);

    for(int i=0;i<n;i++){
        if(ds[i]+df[i]==ds[f]){
            l[ds[i]].push_back(i);
        }
    }
    int ans = INT_MAX;
    for(int i=0;i<=ds[f];i++){
        int a = INT_MIN;
        for(auto x: l[i]){
            a = max(a,dr[x]);
        }
        ans = min(a,ans);
    }

    cout<<ans;

    return 0;
}

This is wrong because you're assuming that the answer is the minimum distance to the robbers in its unique optimal path, which is not always true.

Edited by author 17.08.2022 04:41

Edited by author 17.08.2022 04:41

Consider this test:

9 12
1 2
1 3
2 4
2 5
3 6
3 7
4 6
4 9
5 6
6 8
7 8
7 9
1 9 6

Correct answer: 1
(shortest path is either 1-2-4-9 or 1-3-7-9, so robbers can move 6-4 or 6-3)