[算法笔记]PAT A1003 Emergency

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[算法笔记]PAT A1003 Emergency

题目链接：https://pintia/problem-sets/994805342720868352/problems/994805523835109376

题目

1003 Emergency

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

Sample Output:

2 4

代码长度限制 16 KB

时间限制 400 ms

内存限制 64 MB

分析

1. 求最短路径->Dijkstra算法
2. 排序->判断

代码

基于《算法笔记》

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

const int MAXV = 510;
const int INF = 10000000;

int n,m,st,ed,G[MAXV][MAXV],weight[MAXV];
int d[MAXV],w[MAXV],num[MAXV];
bool vis[MAXV] = {false}; 



//对于最短路径可以默写的D

void D(int s)
{
	fill(d,d+MAXV,INF);
	
	memset(num,0,sizeof(num));
	memset(w,0,sizeof(w));
	
	d[s] = 0;
	w[s] = weight[s];
	num[s] = 1;
	
	
	for(int i=0;i<n;i++)
	{
		int u = -1,MIN = INF;
		for(int j=0;j<n;j++)
		{
			if(vis[j]==false && d[j]<MIN)
			{
				u=j;
				MIN = d[j];
			}
		}
		if(u==-1) return;
		vis[u] = true;
		for(int v=0;v<n;v++)
		{
			if(vis[v]==false && G[u][v] != INF)
			{
				if(d[u]+G[u][v]<d[v])
				{
					//raolu
					d[v] = d[u] + G[u][v];
					w[v] = w[u] + weight[v];
					num[v] = num[u];
					
				}
				else if(d[u]+G[u][v]==d[v])
				{
					
					if(w[u]+weight[v]>w[v])
					{
						//注意不要把uv看错 
						w[v] = w[u] + weight[v];
					}
					num[v] += num[u];
				}
			}
		}
	}
} 

int main()
{
	scanf("%d%d%d%d",&n,&m,&st,&ed); 
	for(int i=0;i<n;i++)
	{
		scanf("%d",&weight[i]);
	}
	int u,v;
	fill(G[0],G[0]+MAXV*MAXV,INF);
	for(int i=0;i<m;i++)
	{
		scanf("%d%d",&u,&v);
		scanf("%d",&G[u][v]);
		G[v][u] = G[u][v];
	}
	D(st);
	printf("%d %d\n",num[ed],w[ed]);
	return 0;
}

小结

对于求最短路径的题目，Dijkstra算法可以当作一个模板背下来。

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