PAT (Advanced Level) 1003 Emergency （Dijkstra算法）

1003 Emergency (25 分)

 

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 Specification:

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 Specification:

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

 

結尾無空行

Sample Output:

2 4

 

結尾無空行

 

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        String s = reader.readLine();
        String[] s1 = s.split(" ");
        int N = Integer.parseInt(s1[0]);      //城市數
        int M = Integer.parseInt(s1[1]);      //道路數
        int C1 = Integer.parseInt(s1[2]);     //所在城市
        int C2 = Integer.parseInt(s1[3]);     //目的城市
        int[] dis = new int[N];            //dis[i]表示節點i距離起始點得最短距離
        int[] weight = new int[N];         //weight[i]表示節點i中的急救隊數
        int[] w = new int[N];             //w[i]表示從起始點到i能聚集的最大急救隊數量
        int[] num = new int[N];           //num[i]表示起始點到i最短路徑數
        boolean[] visited = new boolean[N];//標記被訪問過的節點
        int[][] edgs = new int[N][N];    //edges[i][j]表示從城市i 到 j的路徑長度
        Arrays.fill(dis, Integer.MAX_VALUE);
        Arrays.fill(w, Integer.MIN_VALUE);
        dis[C1] = 0;
        num[C1] = 1;

        String s2 = reader.readLine();
        String[] s3 = s2.split(" ");
        for (int i = 0; i < N; i++) {
            weight[i] = Integer.parseInt(s3[i]);
            Arrays.fill(edgs[i], Integer.MAX_VALUE);
        }

        w[C1] = weight[C1];

        for (int i = 0; i < M; i++){
            String s4 = reader.readLine();
            String[] s5 = s4.split(" ");
            int u = Integer.parseInt(s5[0]);
            int v = Integer.parseInt(s5[1]);
            int len = Integer.parseInt(s5[2]);
            edgs[u][v] = len;
            edgs[v][u] = len;
        }

        for (int i = 0; i < N; i++) {
　　　　　　　　//查找離起點距離最小且未被訪問過的節點
            int u = -1, minDis = Integer.MAX_VALUE;
            for (int j = 0; j < N; j++) {
                if (!visited[j] && dis[j] < minDis){
                    u = j;
                    minDis = dis[j];
                }
            }
            if (u == -1) break;
            visited[u] = true;
            for (int j = 0; j < N; j++) {
                //遍歷當前訪問節點的鄰居節點
                if (!visited[j] && edgs[u][j] != Integer.MAX_VALUE){
                    if (dis[u] + edgs[u][j] < dis[j]){
                        dis[j] = dis[u] + edgs[u][j];
                        w[j] = w[u] + weight[j];
                        num[j] = num[u];
                    }else if (dis[u] + edgs[u][j] == dis[j]){
                        num[j] = num[u] + num[j];
                        if (w[j] < w[u] + weight[j]){
                            w[j] = w[j] = w[u] + weight[j];
                        }
                    }
                }
            }
        }
        System.out.println(num[C2] + " " + w[C2]);
    }

}