【題解】LuoGu5201:[USACO19JAN]Shortcut G

2020-09-21 11:00:47

原題傳送門
先跑一遍最短路,求出 n x t u nxt_u nxtu表示我下一步走到哪裡,然後跑一個拓撲

Code:

#include <bits/stdc++.h>
#define maxn 100010
#define LL long long
using namespace std;
struct heap{
	int node;
	LL len;
	bool operator < (const heap &x) const{return x.len < len; }
};
priority_queue <heap> q;
queue <int> Q;
struct Edge{
	int to, next, len;
}edge[maxn << 1];
int num, head[maxn], n, m, vis[maxn], nxt[maxn], deg[maxn];
LL dis[maxn], c[maxn], T, ans;

inline int read(){
	int s = 0, w = 1;
	char c = getchar();
	for (; !isdigit(c); c = getchar()) if (c == '-') w = -1;
	for (; isdigit(c); c = getchar()) s = (s << 1) + (s << 3) + (c ^ 48);
	return s * w;
}

void addedge(int x, int y, int z){ edge[++num] = (Edge){y, head[x], z}, head[x] = num; }

int main(){
	freopen("pc.in", "r", stdin);
	freopen("pc.out", "w", stdout);
	n = read(), m = read(), T = read();
	for (int i = 1; i <= n; ++i) c[i] = read();
	for (int i = 1; i <= m; ++i){
		int x = read(), y = read(), z = read();
		addedge(x, y, z), addedge(y, x, z);
	}
	for (int i = 2; i <= n; ++i) dis[i] = 1e11, nxt[i] = n + 1;
	q.push((heap){1, 0});
	while (!q.empty()){
		heap tmp = q.top(); q.pop();
		int u = tmp.node;
		if (vis[u]) continue;
		vis[u] = 1;
		for (int i = head[u]; i; i = edge[i].next){
			int v = edge[i].to, l = edge[i].len;
			if (dis[v] > dis[u] + l){
				dis[v] = dis[u] + l, nxt[v] = u;
				if (!vis[v]) q.push((heap){v, dis[v]});
			} else
			if (dis[v] == dis[u] + l && u < nxt[v]){
				nxt[v] = u;
				if (!vis[v]) q.push((heap){v, dis[v]});
			}
		}
	}
	num = 0;
	memset(head, 0, sizeof(head));
	for (int i = n; i; --i) addedge(i, nxt[i], 0), ++deg[nxt[i]];
	for (int i = 1; i <= n; ++i)
		if (!deg[i]) Q.push(i);
	while (!Q.empty()){
		int u = Q.front(); Q.pop();
		if (dis[u] > T) ans = max(ans, (dis[u] - T) * c[u]);
		for (int i = head[u]; i; i = edge[i].next){
			int v = edge[i].to;
			--deg[v], c[v] += c[u];
			if (!deg[v]) Q.push(v);
		}
	}
	printf("%lld\n", ans);
	return 0;
}