PAT甲级 1030

Travel Plan

A traveler’s map gives the distances between cities along the highways, together with the cost of each highway. Now you are supposed to write a program to help a traveler to decide the shortest path between his/her starting city and the destination. If such a shortest path is not unique, you are supposed to output the one with the minimum cost, which is guaranteed to be unique.

Input Specification:

Each input file contains one test case. Each case starts with a line containing 4 positive integers N, M, S, and D, where N (<=500) is the number of cities (and hence the cities are numbered from 0 to N-1); M is the number of highways; S and D are the starting and the destination cities, respectively. Then M lines follow, each provides the information of a highway, in the format:

City1 City2 Distance Cost

where the numbers are all integers no more than 500, and are separated by a space.

Output Specification:

For each test case, print in one line the cities along the shortest path from the starting point to the destination, followed by the total distance and the total cost of the path. The numbers must be separated by a space and there must be no extra space at the end of output.

Sample Input
4 5 0 3
0 1 1 20
1 3 2 30
0 3 4 10
0 2 2 20
2 3 1 20
Sample Output
0 2 3 3 40

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1. 考点

   1. 求最短路径

2. 题解

   1. 使用dfs找到最短路径

3. 笔记

   1. 不知道为什么dfs在这里可以过？如果是完全图的话，dfs的时间复杂度是n!。

#include<iostream>
#include<stdio.h>
#include<vector>
#include<limits.h>
#include<algorithm>
using namespace std;

const int maxn=500+1;

struct node{
    int vertex;
    int dist;
    int cost;
    node(){};
    node(int vertex,int dist,int cost){
        this->vertex=vertex,this->dist=dist,this->cost=cost;
    }
};
vector<node >vp[maxn];
vector<int> rst,tempRst;
bool visit[maxn];
int minTotalDist=INT_MAX,minTotalCost=INT_MAX;

void input_data(int edge){
    int u,v,d,c;
    for(int i=0;i<edge;i++){
        scanf("%d %d %d %d",&u,&v,&d,&c);
        vp[u].push_back(node(v,d,c));
        vp[v].push_back(node(u,d,c));
    }
}
void dfs(int cur,int finalEnd,int dist,int cost){
    if(cur==finalEnd && dist<=minTotalDist){
        if(dist<minTotalDist || (dist==minTotalDist && cost<minTotalCost)){
            minTotalDist=dist;  
            minTotalCost=cost;
            rst.resize(tempRst.size());
            copy(tempRst.begin(),tempRst.end(),rst.begin());
        }
    }else{
        for(auto it=vp[cur].begin();it!=vp[cur].end();it++){
            if(!visit[it->vertex]){
                tempRst.push_back(it->vertex);
                visit[it->vertex]=true;
                dfs(it->vertex,finalEnd,dist+it->dist,cost+it->cost);
                tempRst.pop_back();
                visit[it->vertex]=false;
            }
        }
    }
}
void output_data(){
    for(auto it=rst.begin();it!=rst.end();it++){
        printf("%d ",*it);
    }
    printf("%d %d",minTotalDist,minTotalCost);
}

int main(){
    freopen("./in","r",stdin);
    int N,M,S,D;
    scanf("%d %d %d %d",&N,&M,&S,&D);
    input_data(M);
    tempRst.push_back(S);
    visit[S]=true;
    dfs(S,D,0,0);
    output_data();
    return 0;
}