BZOJ1003: [ZJOI2006]物流运输(最短路+DP)

题目：

1003: [ZJOI2006]物流运输

解析：

最短路+DP
我们用\(no[i][j]\)来表示\(i\)在第\(j\)天不可以经过
用\(cost[i][j]\)表示第\(i\)天到第\(j\)天的花费
在最短路的时候判断一下在第\(i\)天到第\(j\)天中哪些码头不可以走，在做最短路时跳过

最后设f[i]表示到第i天时的最小花费
转移方程
\(f[i] = min(f[i], f[j]+k+cost[j+1][i]*(i-j))\)

代码：

#include <bits/stdc++.h>

using namespace std;

const int N = 1010;
const int INF = 0x3f3f3f3f;

int n, m, k, E, num, t;
int head[N], dis[N];

long long f[N], cost[N][N];

bool vis[N], no[N][N], mark[N];

struct node {
	int v, nx, w;
} e[N];

struct edge {
	int id, dis;
	bool operator <(const edge &oth) const {
		return dis > oth.dis;
	}
};

inline void add(int u, int v, int w) {
	e[++num] = (node) {v, head[u], w}, head[u] = num;
}

priority_queue<edge>q;
void dijkstra(int s, int from, int to) {
	memset(dis, INF, sizeof dis);
	memset(vis, 0, sizeof vis);
	memset(mark, 0, sizeof mark);
	for (int i = 1; i <= m; ++i)
		for (int j = from; j <= to; ++j)
			if (no[i][j]) mark[i] = 1;
	dis[s] = 0;	
	q.push((edge) {s, 0});
	while (!q.empty()) {
		int u = q.top().id;
		q.pop();
		if (vis[u]) continue;
		vis[u] = 1;
		for (int i = head[u]; ~i; i = e[i].nx) {
			int v = e[i].v;
			if (mark[v]) continue;
			if (dis[v] > dis[u] + e[i].w) 
				q.push((edge) {v, dis[v] = dis[u] + e[i].w});
		}
	}
}

signed main() {
	memset(head, -1, sizeof head);
	cin >> n >> m >> k >> E;
	for (int i = 1, x, y, z; i <= E; ++i) {
		cin >> x >> y >> z;
		add(x, y, z), add(y, x, z);
	}
	cin >> t;
	for (int i = 1, x, y, z; i <= t; ++i) {
		cin >> x >> y >> z;
		for (int j = y; j <= z; ++j) no[x][j] = 1;
	}
	for (int i = 1; i <= n; ++i)
		for (int j = i; j <= n; ++j) {
			dijkstra(1, i, j);
			cost[i][j] = dis[m];
		}
	for (int i = 1; i <= n; ++i) ;
	for (int i = 1; i <= n; ++i) {
		f[i] = cost[1][i] * i;
		for (int j = 1; j <= i; ++j) {
			f[i] = min(f[i], f[j] + k + cost[j + 1][i] * (i - j));
		}
	}
	cout << f[n];
}