I Wanna Go Home

本文介绍了一种解决特定条件下最短路径问题的方法。在该问题中,城市被分为两个阵营,要求从起点到终点的路径上最多只能有一次从一个阵营到另一个阵营的变化。通过调整图的连接方式,将问题转化为单向图中的最短路径问题,并使用Dijkstra算法求解。

摘要生成于 C知道 ,由 DeepSeek-R1 满血版支持, 前往体验 >

总时间限制:
1000ms
内存限制:
65536kB
描述

The country is facing a terrible civil war----cities in the country are divided into two parts supporting different leaders. As a merchant, Mr. M does not pay attention to politics but he actually knows the severe situation, and your task is to help him reach home as soon as possible.

"For the sake of safety,", said Mr.M, "your route should contain at most 1 road which connects two cities of different camp."

Would you please tell Mr. M at least how long will it take to reach his sweet home?

输入

The input contains multiple test cases.

The first line of each case is an integer N (2<=N<=600), representing the number of cities in the country.

The second line contains one integer M (0<=M<=10000), which is the number of roads.

The following M lines are the information of the roads. Each line contains three integersA, B and T, which means the road between city A and cityB will cost time T. T is in the range of [1,500].

Next part contains N integers, which are either 1 or 2. The i-th integer shows the supporting leader of cityi.

To simplify the problem, we assume that Mr. M starts from city 1 and his target is city 2. City 1 always supports leader 1 while city 2 is at the same side of leader 2.

Note that all roads are bidirectional and there is at most 1 road between two cities.

Input is ended with a case of N=0.

输出

For each test case, output one integer representing the minimum time to reach home.

If it is impossible to reach home according to Mr. M's demands, output -1 instead.

样例输入
2
1
1 2 100
1 2
3
3
1 2 100
1 3 40
2 3 50
1 2 1
5
5
3 1 200
5 3 150
2 5 160
4 3 170
4 2 170
1 2 2 2 1
0
样例输出
100
90
540



题解:就是找到回家的最短路,从城市1->城市2,但是有个条件,就是每个点有值1或2,为了安全,值只能变一次,也就是说从支持1的城市到支持2的城市后,不能再返回支持1的城市,也就是说从值为1->值为2这是个单向的,那么只要在基本赋值完成后,弄成单向图就行啦,我把从值为2的城市到值为1的城市的边置为INF,就不能走这条路,剩余的就是单源最短路径Dijksra了

#include<bits/stdc++.h>
using namespace std;

const int INF = 0x9f9f9f;
int n,m;
int maze[700][700];
int sup[10010];
int vis[700];
int dis[700];

void dijksra(int start)
{
	memset(vis,0,sizeof(vis));
	memset(dis,0,sizeof(dis));
	dis[1] = 0;
	for(int i = 2; i <= n; i++)
		dis[i] = maze[1][i];
	vis[start] = 1;	
	for(int i = 1; i <= n; i++){
		int tmp = INF;
		int k;
		
		for(int j = 1; j <= n; j++){
			if (vis[j] == 0 && dis[j] < tmp){
				tmp = dis[j];
				k = j;
			} 
		}
		
		vis[k] = 1;
		for(int j = 1; j <= n; j++){
			if (vis[j] == 0 && dis[j] > dis[k]+maze[k][j])
				dis[j] = dis[k]+maze[k][j];
		}
	}
}

int main()
{
	while(~scanf("%d",&n)){
		if (n == 0)
			break;
		
		for(int i = 0; i <= n; i++)
			for(int j = 0; j <= n; j++)
				if (i == j)
					maze[i][j] = 0;
				else	maze[i][j] = INF;
				
		memset(sup,0,sizeof(sup));
		cin >> m;
		for(int i = 0; i < m; i++){
			int s,e,v;
			cin >> s >> e >> v;
			maze[s][e] = maze[e][s] = v;
		}
		for(int i = 1; i <= n; i++)
			cin >> sup[i];
		
		for(int i = 1; i <= m; i++){
			for(int j = 1; j <= m; j++){
				if (i == j)
					continue;
				else{
					if (sup[i] == 1 && sup[j] == 2)
						maze[j][i] = INF;
					else if (sup[i] == 2 && sup[j] == 1)
						maze[i][j] = INF; 
				}
			}
		}
		dijksra(1);
		if (dis[2] == INF)
			printf("-1\n");
		else
			printf("%d\n",dis[2]);
	}	

	return 0;
}

评论
添加红包

请填写红包祝福语或标题

红包个数最小为10个

红包金额最低5元

当前余额3.43前往充值 >
需支付:10.00
成就一亿技术人!
领取后你会自动成为博主和红包主的粉丝 规则
hope_wisdom
发出的红包
实付
使用余额支付
点击重新获取
扫码支付
钱包余额 0

抵扣说明:

1.余额是钱包充值的虚拟货币,按照1:1的比例进行支付金额的抵扣。
2.余额无法直接购买下载,可以购买VIP、付费专栏及课程。

余额充值