CF Round#791 D - Toss a Coin to Your Graph...

D - Toss a Coin to Your Graph...

二分 + 判环 + DAGDP

1. 最大值最小化可以想到二分答案
2. check过程为只给小于等于答案的点之间连边，虽然 k 很大，但如果存在环则一定可以，不存在环就求当前图的最长路，如果最长路 <= k - 1 则可以
3. 判环和求最长路都可用拓扑排序完成
4. 注意 k == 1 时要特判

#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
#include <cmath>
#include <stack>
#include <queue>
using namespace std;
typedef long long ll;
typedef pair<int, int> PII;
const int N = 2e5 + 10;

int n, m;
ll k;
int a[N], din[N];
pair<int, int> Edge[N];
vector<int> G[N];

int dist[N];

void init()
{
	for (int i = 1; i <= n; i++)
		G[i].clear();
	memset(dist, 0, sizeof dist);
	memset(din, 0, sizeof din);
}
void add(int a, int b)
{
	G[a].push_back(b);
	din[b]++;
}
bool topsort()
{
	queue<int> q;
	for (int i = 1; i <= n; i++)
		if (!din[i]) q.push(i);
	vector<int> ans;
	while(!q.empty())
	{
		int u = q.front();
		q.pop();
		ans.push_back(u);
		for (int v : G[u])
		{
			din[v]--;
			dist[v] = max(dist[v], dist[u] + 1);
			if (!din[v])
				q.push(v);
		}
	}
	return ans.size() < n || *max_element(dist + 1, dist + n + 1) >= k - 1;
}
bool check(int x)
{
	init();
	for (int i = 1; i <= m; i++)
		 if (a[Edge[i].first] <= x && a[Edge[i].second] <= x)
            add(Edge[i].first, Edge[i].second);
    return topsort();
}
int main()
{
	ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
	cin >> n >> m >> k;
	for (int i = 1; i <= n; i++)
		cin >> a[i];
	for (int i = 1; i <= m; i++)
		cin >> Edge[i].first >> Edge[i].second;
	if (k == 1)
	{
		cout << *max_element(a + 1, a + n + 1) << endl;
		return 0;
	}
	int l = 0, r = 1e9 + 1;
	while(l + 1 != r)
	{
		int mid = l + r >> 1;
		if (check(mid))
			r = mid;
		else
			l = mid;
	}
	cout << (r == (int)1e9 + 1 ? -1 : r) << endl;
	return 0;
}