F_Graph_Without_Long_Directed_Paths.cpp

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

int32_t main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);

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

    vector<int> color(n + 1, -1);

    function<bool(int)> dfs = [&](int node) {
        for(auto &j : adj[node]) {
            if(color[j] == -1) {
                color[j] = (1 ^ color[node]);
                if(!dfs(j)) return false;
            }
            else if(color[j] == color[node]) {
                return false;
            }
        }
        return true;
    };


    for(int i=1;i<=n;i++) {
        if(color[i] == -1) {
            color[i] = 0;
            if(!dfs(i)) {
                cout << "NO\n";
                return 0;
            }
        }
    }
    cout << "YES\n";
    for(int i=0;i<m;i++) {
        if(color[from[i]] == 0 && color[to[i]] == 1) {
            cout << 1;
        }
        else cout << 0;
    }
    cout << "\n";


    return 0;
}