Riding the Fences(欧拉回路)

本文探讨了一位懒惰的农夫如何通过一次遍历所有围栏来最小化他的劳动。利用图论中的概念,文章提供了一个算法解决方案,确保农夫能够只沿每条围栏走一次,从而找到最短的路径。此问题涉及到图的遍历和路径优化,对于理解图论和算法设计原则具有教育意义。

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描述

Farmer John owns a large number of fences that must be repaired annually. He traverses the fences by riding a horse along each and every one of them (and nowhere else) and fixing the broken parts.

Farmer John is as lazy as the next farmer and hates to ride the same fence twice. Your program must read in a description of a network of fences and tell Farmer John a path to traverse each fence length exactly once, if possible. Farmer J can, if he wishes, start and finish at any fence intersection.

Every fence connects two fence intersections, which are numbered inclusively from 1 through 500 (though some farms have far fewer than 500 intersections). Any number of fences (>=1) can meet at a fence intersection. It is always possible to ride from any fence to any other fence (i.e., all fences are “connected”).

Your program must output the path of intersections that, if interpreted as a base 500 number, would have the smallest magnitude.

There will always be at least one solution for each set of input data supplied to your program for testing.

输入

Line 1: The number of fences, F (1 <= F <= 1024)

Line 2…F+1: A pair of integers (1 <= i,j <= 500) that tell which pair of intersections this fence connects.

输出

The output consists of F+1 lines, each containing a single integer. Print the number of the starting intersection on the first line, the next intersection’s number on the next line, and so on, until the final intersection on the last line. There might be many possible answers to any given input set, but only one is ordered correctly.

样例输入

9
1 2
2 3
3 4
4 2
4 5
2 5
5 6
5 7
4 6

样例输出

1
2
3
4
2
5
4
6
5
7
这题主要是要注意输入可能会有重边,会有很多的边,所以存边的数组要开的稍微大一点,主要是经验不足吧

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=505;
int degree[N],G[N][N];
int k,ans[100005];
void f(int u){
    int v;
    for(v=1;v<=500;v++){
        if(G[u][v]){
            G[u][v]--;
            G[v][u]--;
            f(v);
            ans[k++]=v;
        }
    }
}
int main(){
    int n;
    while(~scanf("%d",&n)){
        k=0;
        memset(degree,0,sizeof(degree));
        memset(G,0,sizeof(G));
        int x,y,ma=0,flag=1;
        for(int i=0;i<n;i++){
            scanf("%d%d",&x,&y);
            degree[x]++;
            degree[y]++;
            G[x][y]++;
            G[y][x]++;
            ma=max(max(ma,x),y);
        }
        for(int i=1;i<=ma;i++){
            if(degree[i]%2){
                f(i);
                flag=0;
                printf("%d\n",i);
                break;
            }
        }
        if(flag){
            for(int i=1;i<=ma;i++){
                if(degree[i]!=0){
                    f(i);
                    printf("%d\n",i);
                    break;
                }
            }
        }
        for(int i=k-1;i>=0;i--){
            printf("%d\n",ans[i]);
        }
    }
}
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