1003. Emergency (25)

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本文介绍了一个基于Dijkstra算法的应急救援路线规划问题。任务是在给定的城市地图中找到从当前位置到目标位置的所有最短路径，并计算能集结的最大救援队伍数量。

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1003. Emergency (25)

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

作者

CHEN, Yue

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

Sample Output

2 4

有权单源最短径问题使用DIJKSTRA算法，增加一个数组记录最短路径的条数，一开始将救援人数理解错了，以为是所有最短路径上的人，实际是人数最多的一条径的人数。#include<stdio.h>
#include<stdlib.h>
#define inf 1000000
int Findmin(int* dis,int* record,int N)
{
	int index = -1, min = inf;
	int i;
	for (i = 0; i < N; i++)
	{
		if (dis[i] < min&&record[i] == 0)
		{
			min = dis[i];
			index = i;
		}
	}
	return index;
}
int main()
{
	
	int N, M, C1, C2;
	int i, j, k,temp;
	int rocn, pecn;
	scanf( "%d %d %d %d", &N, &M, &C1, &C2);
	int *rescue = (int *)malloc(sizeof(int)*N);
	for (i = 0; i < N; i++)
	{
		scanf( "%d", &rescue[i]);

	}
        //建立图
	int** map = (int**)malloc(sizeof(int *)*N);
	for (i = 0; i < N; i++)
	{
		map[i] = (int*)malloc(sizeof(int)*N);
		for (j = 0; j < N; j++)
			map[i][j] = inf;
		map[i][i] = 0;
	}
	for (i = 0; i < M; i++)
	{
		scanf("%d %d %d", &j, &k, &temp);
		map[j][k] = temp;
		map[k][j] = temp;
	}
	int* dis = (int*)malloc(sizeof(int)*N);
	int*record = (int*)malloc(sizeof(int)*N);
	int* people = (int*)malloc(sizeof(int)*N);
	int* path = (int*)malloc(sizeof(int)*N);
	/*初始化三个记录数组*/
	for (i = 0; i < N; i++) 
	{
		dis[i] = inf;//距离
		record[i] = 0;//访问标志
		people[i] = 0;//救援人数
		path[i] = 0;//最短路径条数
	}
	/*dijkstra*/
	dis[C1] = 0;
	people[C1] = rescue[C1];
	path[C1] = 1;
	while (1)
	{
		k = Findmin(dis,record,N);
		if (k == -1)break;
		record[k] = 1;
		for (i = 0; i < N; i++)
		{
			if (map[k][i] < inf && record[i]==0)
			{
				if (dis[k] + map[k][i] < dis[i])
				{
					dis[i] = dis[k] + map[k][i];
					people[i] = people[k] + rescue[i];
					path[i] = path[k];
				}
				else if (dis[k] + map[k][i] == dis[i])
				{
					if(people[k]+rescue[i]>people[i])people[i] = people[k] + rescue[i];
					path[i] = path[i] + path[k];
				}
			}
		}
		
	}
	printf("%d %d", path[C2], people[C2]);
	
	return 0;
}