1003. Emergency

Posted 2020-06-30 Will Wu的学习笔记

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

 使用变形的dijkstra算法  并且随时更新最短路径的数目以及能够搜集到的队伍数目。

 1 #include <iostream>
 2 #include <vector>
 3 #include <cstdlib>
 4 using namespace std;
 5 
 6 #define MaxDistance 10000
 7 vector< vector <int>> GMatrix;
 8 vector<int> dist;
 9 vector<int> teams;
10 
11 int N,M,start,en;
12 
13 void dijkstra()
14 {
15     vector<int> flag(N, 0);
16     vector<int> pathcount(N, 0);
17     vector<int> amount(N, 0);
18     for (size_t i = 0; i < N; i++)//initial the dist
19     {
20         if (GMatrix[start][i] != -1)
21             dist.push_back(GMatrix[start][i]);
22     }
23     amount[start] = teams[start];
24     pathcount[start] = 1;
25     
26     while(1) 
27     {
28         int min = MaxDistance;
29         int k;
30         for (size_t j = 0; j < N; j++)
31         {
32             if ((flag[j] == 0) && (dist[j] < min))
33             {
34                 min = dist[j];
35                 k = j;
36             }
37         }
38         if (k == en|| min==MaxDistance) break; //can not find the mini or find the end node, then break the iterative while(1) 
39         flag[k] = 1;
40         for (size_t j = 0; j < N; j++)
41         {
42             int temp = dist[k] + GMatrix[k][j];
43             if ((flag[j] == 0) && (temp < dist[j]))
44             {
45                 dist[j] = temp;
46                 amount[j] = amount[k] + teams[j]; //update the teams you can gather
47                 pathcount[j] = pathcount[k];// update the shortest road sums
48             }
49             else if ((flag[j] == 0) && (temp == dist[j]))
50             {
51                 pathcount[j] += pathcount[k]; //update 
52                 if (amount[k] + teams[j]>amount[j]) 
53                     amount[j] = amount[k] + teams[j]; //update
54             }
55         }
56     }
57     //for (size_t i = 0; i < N; i++)//output the dist for check
58     //{
59     //    cout << dist[i] << " ";
60     //}
61     //cout << endl;
62     cout << pathcount[en] << " " << amount[en] << endl;
63 
64 }
65 int main()
66 {
67     cin >> N >> M >> start >> en;
68     for (size_t i = 0; i < N; i++)//input the teams
69     {
70         int t; cin >> t;
71         teams.push_back(t);
72     }
73     for (size_t i = 0; i < N; i++)//initial the GMtraix
74     {
75         vector<int> arr(N, MaxDistance);
76         GMatrix.push_back(arr);
77         GMatrix[i][i] = 0;//for the same start and end, the dist=0; 
78     }
79     for (size_t i = 0; i < M; i++)//input the road to the graph
80     {
81         int left, right, road;
82         cin >> left >> right >> road;
83         GMatrix[left][right] = road; GMatrix[right][left] = road;
84     }
85     dijkstra();
86 
87 
88     return 0;
89 }