九度 OJ1162 I wanna go home

在一场内战撕裂的国家中,商人Mr.M必须穿越对立阵营的城市回到家乡。任务是在遵守特定规则下找到最快回家路线。此问题转化为带有限制条件的最短路径算法,需考虑不同阵营间的连接限制。

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题目描述:
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 integers A, B and T, which means the road between city A and city B 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 city i.
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

思路:

  1. 跨阵营路只存储单向边
  2. 只允许1->2 1->1 2->2
#include<stdio.h>
#include<vector>
using namespace std;
struct E{
	int next;
	int t;
};
vector<E> edge[10001];
int Dis[601];
int Camp[601];
bool mark[601];
int main(){
	int n,m;
	while(scanf("%d",&n)!=EOF){
		if(n==0) break;
		scanf("%d",&m);
		for(int i=1;i<=n;i++){
			edge[i].clear();
			Dis[i]=-1;
			mark[i]=false;
		}
		for(int i=0;i<m;i++){
			int a,b,c;
			scanf("%d%d%d",&a,&b,&c);
			E tmp;
			tmp.next=b;
			tmp.t=c;
			edge[a].push_back(tmp);
			tmp.next=a;
			edge[b].push_back(tmp);
		}	
		for(int i=1;i<=n;i++){
			scanf("%d",&Camp[i]);
		}
		for(int i=1;i<=n;i++){
			if(Camp[i]==2){
				for(int j=0;j<edge[i].size();j++){
					if(Camp[edge[i][j].next]==1){
						edge[i][j].t=99999999;//跨阵营路径之存储单向边
						                      //,把另一个方向设置成一个较大的数
						                      //因此这条路不会出现在最短路径中 
					}
				}
			}
		}
		Dis[1]=0;
		mark[1]=true;
		int newP=1;
		for(int i=1;i<n;i++){
			for(int j=0;j<edge[newP].size();j++){
				int t=edge[newP][j].next;
				int c=edge[newP][j].t;
				if(mark[t]==true) continue;
				if(Dis[t]==-1||Dis[t]>Dis[newP]+c){
					Dis[t]=Dis[newP]+c;
				}
			}
			int min=123123123;
			for(int j=1;j<=n;j++){
				if(mark[j]==true) continue;
				if(Dis[j]==-1) continue;
				if(Dis[j]<min){
					min=Dis[j];
					newP=j;
				}
			}
			mark[newP]=true;
		}
		if(mark[2]==false){
			printf("-1\n");
		}else{
			printf("%d\n",Dis[2]);
		}
	}
}
#include<stdio.h>
#include<vector>
using namespace std;
struct E{
	int next;
	int t;
};
vector<E> edge[10001];
int Dis[601];
int Camp[601];
bool mark[601];
int main(){
	int n,m;
	while(scanf("%d",&n)!=EOF){
		if(n==0) break;
		scanf("%d",&m);
		for(int i=1;i<=n;i++){
			edge[i].clear();
			Dis[i]=-1;
			mark[i]=false;
		}
		for(int i=0;i<m;i++){
			int a,b,c;
			scanf("%d%d%d",&a,&b,&c);
			E tmp;
			tmp.next=b;
			tmp.t=c;
			edge[a].push_back(tmp);
			tmp.next=a;
			edge[b].push_back(tmp);
		}	
		for(int i=1;i<=n;i++){
			scanf("%d",&Camp[i]);
		}
		Dis[1]=0;
		mark[1]=true;
		int newP=1;
		for(int i=1;i<n;i++){
			for(int j=0;j<edge[newP].size();j++){
				int t=edge[newP][j].next;
				int c=edge[newP][j].t;
				if(mark[t]==true) continue;
				if((Dis[t]==-1||Dis[t]>Dis[newP]+c)&&!(Camp[newP]==2&&Camp[t]==1)){//只允许1->2 1->1 2->2 
					Dis[t]=Dis[newP]+c;
				}
			}
			int min=123123123;
			for(int j=1;j<=n;j++){
				if(mark[j]==true) continue;
				if(Dis[j]==-1) continue;
				if(Dis[j]<min){
					min=Dis[j];
					newP=j;
				}
			}
			mark[newP]=true;
		}
		if(mark[2]==false){
			printf("-1\n");
		}else{
			printf("%d\n",Dis[2]);
		}
	}
}
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