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 }