(Analysis by Benjamin Qi)

Say that two cows are in the same connected component if all cows on the path between them are of the same type. We can generate these components with a DFS.

For each friend's path, if the endpoints of the path are in different components then he is clearly satisfied since both types of cows must appear on the path. Otherwise, all cows in the path have the same type, so it suffices to check whether the cow at the starting point of the path is of the type which the friend prefers.

It follows that this problem is solvable in $O(N+M)$ time. My code is below:

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

typedef vector<int> vi;

#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)

#define pb push_back

void setIO(string name) {
ios_base::sync_with_stdio(0); cin.tie(0);
freopen((name+".in").c_str(),"r",stdin);
freopen((name+".out").c_str(),"w",stdout);
}

const int MX = 100005;

int N,M,comp[MX],num;
char col[MX];

void dfs(int x) {
if (comp[x]) return;
comp[x] = num;
trav(t,adj[x]) if (col[t] == col[x]) dfs(t);
}

int main() {
setIO("milkvisits"); cin >> N >> M;
string s; cin >> s;
FOR(i,1,N+1) col[i] = s[i-1];
F0R(i,N-1) {
int A,B; cin >> A >> B;