Test/yukicoder/yuki2780.test.cpp

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• Last update: 2024-06-08 17:31:17+09:00
• Problem: https://yukicoder.me/problems/no/2780

Depends on

• 強連結成分分解 (SCC, Strongly Connected Component) (Graph/scc.hpp)

Code

#define PROBLEM "https://yukicoder.me/problems/no/2780"

#include <bits/stdc++.h>

#include "Graph/scc.hpp"

using namespace std;

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n;
    cin >> n;
    vector<vector<int>> g(n);
    for(int i = 0; i < n; i++){
        int m;
        cin >> m;
        g[i].resize(m);
        for(auto &&v : g[i]){
            cin >> v;
            v--;
        }
    }
    SCC scc(g);
    auto G = scc.groups();
    if(find(G[0].begin(), G[0].end(), 0) == G[0].end()){
        cout << "No\n";
        return 0;
    }
    vector<int> dp(G.size());
    for(int i = 0; i < G.size(); i++){
        if(dp[i] != i){
            cout << "No\n";
            return 0;
        }
        for(auto &&v : G[i]){
            for(auto &&u : g[v]){
                if(scc[u] == i) continue;
                dp[scc[u]] = max(dp[scc[u]], dp[i] + 1);
            }
        }
    }
    cout << "Yes\n";
}

#line 1 "Test/yukicoder/yuki2780.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/2780"

#include <bits/stdc++.h>

#line 1 "Graph/scc.hpp"
struct SCC {
    int n, group_num;
    std::vector<std::vector<int>> &g;
    std::vector<int> ids;
    SCC(std::vector<std::vector<int>> &_g) : n(_g.size()), g(_g), ids(n), group_num(0) {
        int now_ord = 0;
        std::vector<int> visited, low(n), ord(n, -1);
        visited.reserve(n);
        auto dfs = [&](auto self, int v) -> void {
            low[v] = ord[v] = now_ord++;
            visited.emplace_back(v);
            for(auto to : g[v]) {
                if (ord[to] == -1) {
                    self(self, to);
                    low[v] = std::min(low[v], low[to]);
                } else {
                    low[v] = std::min(low[v], ord[to]);
                }
            }
            if (low[v] == ord[v]) {
                while (true) {
                    int u = visited.back();
                    visited.pop_back();
                    ord[u] = n;
                    ids[u] = group_num;
                    if (u == v) break;
                }
                group_num++;
            }
        };
        for (int i = 0; i < n; i++) {
            if (ord[i] == -1) dfs(dfs, i);
        }
        for (auto& x : ids) {
            x = group_num - 1 - x;
        }
    }
    const int operator[](int p) const {
        assert(0 <= p && p < n);
        return ids[p];
    }
    int operator[](int p) { 
        assert(0 <= p && p < n);
        return ids[p];
    }
    std::vector<std::vector<int>> groups(){
        std::vector<int> counts(group_num);
        for (auto x : ids) counts[x]++;
        std::vector<std::vector<int>> groups(group_num);
        for (int i = 0; i < group_num; i++) {
            groups[i].reserve(counts[i]);
        }
        for (int i = 0; i < n; i++) {
            groups[ids[i]].emplace_back(i);
        }
        return groups;
    }
};
#line 5 "Test/yukicoder/yuki2780.test.cpp"
using namespace std;

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n;
    cin >> n;
    vector<vector<int>> g(n);
    for(int i = 0; i < n; i++){
        int m;
        cin >> m;
        g[i].resize(m);
        for(auto &&v : g[i]){
            cin >> v;
            v--;
        }
    }
    SCC scc(g);
    auto G = scc.groups();
    if(find(G[0].begin(), G[0].end(), 0) == G[0].end()){
        cout << "No\n";
        return 0;
    }
    vector<int> dp(G.size());
    for(int i = 0; i < G.size(); i++){
        if(dp[i] != i){
            cout << "No\n";
            return 0;
        }
        for(auto &&v : G[i]){
            for(auto &&u : g[v]){
                if(scc[u] == i) continue;
                dp[scc[u]] = max(dp[scc[u]], dp[i] + 1);
            }
        }
    }
    cout << "Yes\n";
}

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