【HDU - 4725 The Shortest Path in Nya Graph】【最短路建图】【拆层】【好题】

http://acm.hdu.edu.cn/showproblem.php?pid=4725

【题意】

给你n个点，每个点有一个层的位置

有m条边，连接两点，并且相邻层之间可以通过c来到达

【思路】

将每个层拆出来作为一个点建图

点与点：原来的m条边建双向边

层与层：相邻层建c的双向边

点与层：层到层上的点的距离为0，点到相邻层代表的点为c

注意：相同层上的点的距离不为0

【代码】

#include<bits/stdc++.h>
const int inf = 0x3f3f3f3f;
using namespace std;
const int maxn = 200006;
const int maxm = 1006;
int dis[maxn],layer[maxn],have[maxn],vis[maxn];
int n;

struct edge {
	int v, w;
	edge(int _v = 0, int _w = 0) :v(_v), w(_w) {}
	bool operator < (const edge &r)const {
		return w>r.w;
	}
};

vector<edge>E[maxn];

void add(int u, int v, int w) {
	E[u].push_back(edge(v, w));
}

void dijkstra(int s, int t) {
	memset(vis, 0, sizeof(vis));
	for (int i = 1; i <= n * 2; i++)dis[i] = inf;
	priority_queue<edge>q;
	while (!q.empty())q.pop();
	q.push(edge(s, 0));
	dis[s] = 0;
	while (!q.empty()) {
		edge temp = q.top();
		q.pop();
		int u = temp.v;
		if (vis[u])continue;
		vis[u] = 1;
		for (int i = 0; i<E[u].size(); i++) {
			int v = E[u][i].v;
			int cost = E[u][i].w;
			if (!vis[v] && dis[v]>dis[u] + cost) {
				dis[v] = dis[u] + cost;
				q.push(edge(v, dis[v]));
			}
		}
	}
}

int main() {
	int t;
	int cas = 0;
	scanf("%d", &t);
	while (t--) {
		memset(have, 0, sizeof(have));
		for (int i = 0; i <= n * 2 + 1; i++)E[i].clear();
		int m, c;
		scanf("%d%d%d", &n, &m, &c);
		for (int i = 1; i <= n; i++) {
			scanf("%d", &layer[i]);
			have[layer[i]] = 1;
		}
		for (int i = 1; i <= m; i++) {//dd
			int u, v, w;
			scanf("%d%d%d", &u, &v, &w);
			add(u, v, w);
			add(v, u, w);
		}
		for (int i = 1; i<n; i++) {//bb
			if (have[i] && have[i + 1]) {
				add(i + n, n + i + 1, c);
				add(n + i + 1, n + i, c);
			}
		}
		for (int i = 1; i <= n; i++) {
			add(layer[i] + n, i, 0);
			if (layer[i]>1)add(i, layer[i] + n - 1, c);
			if (layer[i]<n)add(i, layer[i] + 1 + n, c);
		}
		dijkstra(1, n);
		printf("Case #%d: %d\n", ++cas, dis[n] == inf ? -1 : dis[n]);
	}
}