1003

  • Description

As an emergency rescue team leader of a city, you are given a special map of your country. The map shows several scattered cities connected by some roads. Amount of rescue teams in each city and the length of each road between any pair of cities are marked on the map. When there is an emergency call to you from some other city, your job is to lead your men to the place as quickly as possible, and at the mean time, call up as many hands on the way as possible.

  • Input

Each input file contains one test case. For each test case, the first line contains 4 positive integers: N (<= 500) - the number of cities (and the cities are numbered from 0 to N-1), M - the number of roads, C1 and C2 - the cities that you are currently in and that you must save, respectively. The next line contains N integers, where the i-th integer is the number of rescue teams in the i-th city. Then M lines follow, each describes a road with three integers c1, c2 and L, which are the pair of cities connected by a road and the length of that road, respectively. It is guaranteed that there exists at least one path from C1 to C2.

  • Output

For each test case, print in one line two numbers: the number of different shortest paths between C1 and C2, and the maximum amount of rescue teams you can possibly gather.
All the numbers in a line must be separated by exactly one space, and there is no extra space allowed at the end of a line.

  • Sample Input
5 6 0 2
1 2 1 5 3
0 1 1
0 2 2
0 3 1
1 2 1
2 4 1
3 4 1
  • Sample Output
2 4
时间限制 400 ms
内存限制 65536 kB
代码长度限制 16000 B
判题程序 Standard

 

  • 题解

这是一道单源最短路径问题

很明显使用Dijstra算法求解,在求最短路径条数和路径节点之和上,需要在Dijstra算法框架上改造。

  • 测试用例

设计了几个测试用例,希望能帮上有需要的你
https://github.com/jahentao/PAT/tree/master/PAT%E7%94%B2%E7%BA%A7(Advanced%20Level)/testData/1003

  • 代码
import java.util.Scanner;
public class Main {
    public static void main(String[] args) {
        final int N, M, C1, C2;
        Scanner scanner = new Scanner(System.in);
        N = scanner.nextInt();
        M = scanner.nextInt();
        C1 = scanner.nextInt();
        C2 = scanner.nextInt();
        int[] teams = new int[N];
        for(int i=0; i<N; i++) {
            teams[i] = scanner.nextInt();
        }
        int[][] w = new int[N][N];
        for(int i=0; i<N; i++) {
            for (int j=0; j<N; j++) {
                if(i==j)
                    w[i][i] = 0;
                else
                    w[i][j] = Integer.MAX_VALUE;
            }
        }
        for(int k=0; k<M; k++) {
            int i = scanner.nextInt();
            int j = scanner.nextInt();
            w[i][j] = w[j][i] =scanner.nextInt();
        }
        int[] S =  new int[N];
        int[] dist = new int[N];
        for (int i=0; i<N; i++)
            dist[i] = Integer.MAX_VALUE;
        int pathcount[] = new int[N];
        int maxteams[] = new int[N];
        dist[C1] = 0;
        pathcount[C1]=1;
        maxteams[C1] = teams[C1];
        int cnt = C1;
        for (int k=0; k<N; k++) {
            int min = Integer.MAX_VALUE;
            for (int i=0; i<N; i++)
                if (S[i]==0 && dist[i]<min)
                    min = dist[cnt = i];
            if (min==Integer.MAX_VALUE || cnt==C2) break;
            S[cnt] = 1;
            for (int i=0; i<N; i++)
                if (S[i]==0 && dist[cnt]!=Integer.MAX_VALUE && w[cnt][i]!=Integer.MAX_VALUE) {
                    int tmp = dist[cnt] + w[cnt][i];
                    if (tmp == dist[i]) {
                        pathcount[i] += pathcount[cnt];
                        if (maxteams[cnt] + teams[i] > maxteams[i])
                            maxteams[i] = maxteams[cnt] + teams[i];
                    }else if (tmp < dist[i]) {
                        dist[i] = tmp;
                        pathcount[i] = pathcount[cnt];
                        maxteams[i] = maxteams[cnt] + teams[i];
                    }
                }
        }
        System.out.print(pathcount[C2]+" "+maxteams[C2]);
    }
}

 

发布者

jahentao

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