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 c
1
, c
2
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
Sample Output:
2 4
code
#include <iostream>
#include <algorithm>
using namespace std;
int main()
{
int dis[500],num[500],weight[500],w[500];
int adj[500][500];
int visit[500];
const int inf = 999999;
int n,m,origin,dest;
scanf("%d%d%d%d",&n,&m,&origin,&dest);
for(int i=0;i<n;i++)
{
scanf("%d",&weight[i]);
}
fill(adj[0],adj[0]+500*500,inf);
fill(dis,dis+500,inf);
fill(num,num+500,0);
int a,b,c;
for(int i=0;i<m;i++)
{
scanf("%d%d%d",&a,&b,&c);
adj[a][b] = adj[b][a] = c;
}
dis[origin] = 0;
w[origin] = weight[origin];
num[origin] = 1;
for(int i=0;i<n;i++)
{
int x=-1, minn=inf;
for(int j=0;j<n;j++)
{
if(!visit[j] && dis[j]<minn) {
minn = dis[j];
x = j;
}
}
visit[x] = 1;
for(int y=0;y<n;y++)
{
if(dis[y]>dis[x]+adj[x][y]) {
dis[y] = dis[x] + adj[x][y];
num[y] = num[x];
w[y] = weight[y]+w[x];
}else if(dis[y] == dis[x]+adj[x][y] && dis[x]!=0) {
num[y] = num[y] + num[x];
if(w[x]+weight[y]>w[y]) {
w[y] = w[x] + weight[y];
}
}
}
// printf("%d\n",i);
// printf("num:");
// for(int k=0;k<n;k++) printf("%d ",num[k]);
// printf("\n");
// printf("dis:");
// for(int k=0;k<n;k++) printf("%d ",dis[k]);
// printf("\n");
// printf("w:");
// for(int k=0;k<n;k++) printf("%d ",w[k]);
// printf("\n");
}
// for(int i=0;i<n;i++)
// {
// for(int j=0;j<n;j++)
// {
// printf("%d ",adj[i][j]);
// }
// printf("\n");
// }
printf("%d %d", num[dest],w[dest]);
return 0;
}
note
- Dijkstra 算法
假设我们要求从A到F的最短路个数和最短路上最大的点权和
example
上图的邻接矩阵表示：
点权数组
每次迭代找到数组中最小值，并对与该节点相连的边进行松弛
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| w | 1 | 0 | 0 | 0 | 0 | 0 |
| dis | 0 | inf | inf | inf | inf | inf |
| num | 1 | 0 | 0 | 0 | 0 | 0 |
| visit | 0 | 0 | 0 | 0 | 0 | 0 |
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| w | 1 | 3 | 4 | 5 | 6 | 0 |
| dis | 0 | 1 | 2 | 3 | 4 | inf |
| num | 1 | 1 | 1 | 1 | 1 | 0 |
| visit | 1 | 0 | 0 | 0 | 0 | 0 |
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| w | 1 | 3 | 4 | 5 | 6 | 9 |
| dis | 0 | 1 | 2 | 3 | 4 | 4 |
| num | 1 | 1 | 1 | 1 | 1 | 1 |
| visit | 1 | 1 | 0 | 0 | 0 | 0 |
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| w | 1 | 3 | 4 | 8 | 6 | 10 |
| dis | 0 | 1 | 2 | 3 | 4 | 4 |
| num | 1 | 1 | 1 | 2 | 1 | 2 |
| visit | 1 | 1 | 1 | 0 | 0 | 0 |
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| w | 1 | 3 | 4 | 8 | 6 | 14 |
| dis | 0 | 1 | 2 | 3 | 4 | 4 |
| num | 1 | 1 | 1 | 2 | 1 | 4 |
| visit | 1 | 1 | 1 | 1 | 0 | 0 |
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| w | 1 | 3 | 4 | 8 | 6 | 14 |
| dis | 0 | 1 | 2 | 3 | 4 | 4 |
| num | 1 | 1 | 1 | 2 | 1 | 4 |
| visit | 1 | 1 | 1 | 1 | 1 | 0 |
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| w | 1 | 3 | 4 | 8 | 6 | 14 |
| dis | 0 | 1 | 2 | 3 | 4 | 4 |
| num | 1 | 1 | 1 | 2 | 1 | 4 |
| visit | 1 | 1 | 1 | 1 | 1 | 1 |
-
fill 和 memset
fill 可以填充任何值，包含在<algorithm>中
对vector：fill(v.begin(), v.end(), -1)
对一维数组：fill(arr, arr + 10, 2)
对二维数组：fill(adj[0],adj[0]+500*500,inf);
memset按照字节进行填充，一般用来填充char型数组，也经常用于填充int型的全0或全-1操作，包含在<cstring>中
对数组：memset(a, 0, sizeof(a))
