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NC51345. John's trip

描述

Little Johnny has got a new car. He decided to drive around the town to visit his friends. Johnny wanted to visit all his friends, but there was many of them. In each street he had one friend. He started thinking how to make his trip as short as possible. Very soon he realized that the best way to do it was to travel through each street of town only once. Naturally, he wanted to finish his trip at the same place he started, at his parents' house.
The streets in Johnny's town were named by integer numbers from 1 to n, . The junctions were independently named by integer numbers from 1 to m, . No junction connects more than 44 streets. All junctions in the town had different numbers. Each street was connecting exactly two junctions. No two streets in the town had the same number. He immediately started to plan his round trip. If there was more than one such round trip, he would have chosen the one which, when written down as a sequence of street numbers is lexicographically the smallest. But Johnny was not able to find even one such round trip.
Help Johnny and write a program which finds the desired shortest round trip. If the round trip does not exist the program should write a message. Assume that Johnny lives at the junction ending the street appears first in the input with smaller number. All streets in the town are two way. There exists a way from each street to another street in the town. The streets in the town are very narrow and there is no possibility to turn back the car once he is in the street

输入描述

Input file consists of several blocks. Each block describes one town. Each line in the block contains three integers x; y; z, where  and  are the numbers of junctions which are connected by the street number z. The end of the block is marked by the line containing x = y = 0. At the end of the input file there is an empty block, x = y = 0.

输出描述

Output one line of each block contains the sequence of street numbers (single members of the sequence are separated by space) describing Johnny's round trip. If the round trip cannot be found the corresponding output block contains the message "Round trip does not exist."

示例1

输入:

1 2 1
2 3 2
3 1 6
1 2 5
2 3 3
3 1 4
0 0
1 2 1
2 3 2
1 3 3
2 4 4
0 0
0 0

输出:

1 2 3 5 4 6
Round trip does not exist.

原站题解

上次编辑到这里,代码来自缓存 点击恢复默认模板

C++(g++ 7.5.0) 解法, 执行用时: 58ms, 内存消耗: 856K, 提交时间: 2022-08-21 20:05:51

#include<bits/stdc++.h>
#define lowbit(x) x&(-x)
#define coff ios::sync_with_stdio(0)
const int inf=0x3f3f3f3f;
const int inn=-(1<<30);
using namespace std;
const int N=50;
const int M=2005;
int g[N][M];
int mark[M];
int d[N];
int n,m;
int ans[M],cnt;
int st;
void init()
{
    n=m=0;
    memset(g,0,sizeof g);
    memset(d,0,sizeof d);
}
bool input()
{
    init();
    int a,b,c;
    cin>>a>>b;
    if(!a&&!b) return 0;
    cin>>c;
    n=max(n,max(a,b));
    st=min(a,b);
    g[a][c]=b;
    g[b][c]=a;
    d[a]++;
    d[b]++;
    m++;
    while(cin>>a>>b)
    {
        if(!a&&!b) break;
        cin>>c;
        n=max(n,max(a,b));
        g[a][c]=b;
        g[b][c]=a;
        d[a]++;
        d[b]++;
        m++;
    }
    return 1;
}
void dfs(int x)
{
    for(int i=1;i<=m;i++)
    {
        if(g[x][i]&&!mark[i])
        {
            mark[i]=1;
            dfs(g[x][i]);
            ans[++cnt]=i;
        }
    }
}
void solve()
{
    for(int i=1;i<=n;i++)
    {
        if(d[i]%2)
        {
            puts("Round trip does not exist.");
            return;
        }
    }
    memset(mark,0,sizeof mark);
    cnt=0;
    dfs(st);
    for(int i=m;i>=1;i--)
    {
        cout<<ans[i]<<' ';
    }
    cout<<endl;
}
int main()
{
    while(input())
    {
        solve();
    }
    return 0;
}

C++14(g++5.4) 解法, 执行用时: 47ms, 内存消耗: 888K, 提交时间: 2019-09-11 23:12:03

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
const int M=45;
const int N=1995;
int gra[M][N]; //gra[i][j]=k表示点x经过边j到达点k
int ind[M]; //每个节点的度
int ans[N],cnt; //最佳方案
bool vis[N]; //标记每条街道是否被访问
int maxn; //纪录最大的街道编号
void dfs(int s)
{
    for(int i=1;i<=maxn;i++)
      if(gra[s][i]&&!vis[i])
      {
          vis[i]=true;
          dfs(gra[s][i]);
          ans[cnt++]=i;
      }
}
int main()
{
    int start;
    int u,v,w;
    while(scanf("%d%d",&u,&v))
    {
        if(u==0&&v==0) break;
        start=min(u,v);
        maxn=0;
        cnt=0;
        memset(gra,0,sizeof(gra));
        memset(ind,0,sizeof(ind));
        memset(vis,false,sizeof(vis));
        while(u!=0&&v!=0)
        {
            scanf("%d",&w);
            gra[u][w]=v;
            gra[v][w]=u;
            ind[u]=!ind[u]; //我们只需要纪录度数的奇偶性即可
            ind[v]=!ind[v];
            maxn=max(maxn,w);
            scanf("%d%d",&u,&v);
        }
        int k=1;
        for(;k<M;k++) //查找节点度数为偶数的点
          if(ind[k]) break;
        if(k<M)
        {
            puts("Round trip does not exist.");
            continue;
        }
        dfs(start);
        for(int i=cnt-1;i>=0;i--)
          printf("%d ",ans[i]);
        printf("\n");
    }
    return 0;
}

C++11(clang++ 3.9) 解法, 执行用时: 20ms, 内存消耗: 888K, 提交时间: 2019-12-11 15:53:26

#include<bits/stdc++.h>
using namespace std;
int Start,t,t1,t2,Top,Num[45],Step[1995],Map[45][1995],Edge[45][1995];
bool Mark[1995];
void DFS(int t) {
	for (int a=1; a<=Num[t]; a++) {
		int S=Edge[t][a];
		if (!Mark[S]) {
			int T=Map[t][S];
			Mark[S]=true;
			DFS(T);
			Step[++Top]=S;
		}
	}
}
int main() {
	while (scanf("%d%d",&t1,&t2)!=EOF) {
		if (!t1&&!t2)
			break;
		memset(Num,0,sizeof(Num));
		scanf("%d",&t);
		Start=min(t1,t2);
		Edge[t1][++Num[t1]]=t;
		Edge[t2][++Num[t2]]=t;
		Map[t1][t]=t2;
		Map[t2][t]=t1;
		while (scanf("%d%d",&t1,&t2)!=EOF) {
			if (!t1&&!t2)
				break;
			scanf("%d",&t);
			Edge[t1][++Num[t1]]=t;
			Edge[t2][++Num[t2]]=t;
			Map[t1][t]=t2;
			Map[t2][t]=t1;
		}
		int T;
		for (T=1;; T++)
			if (!Num[T]||Num[T]&1)
				break;
		if (Num[T]) {
			puts("Round trip does not exist.");
			continue;
		}
		int Max=T-1;
		for (T=1; T<=Max; T++)
			sort(Edge[T]+1,Edge[T]+Num[T]+1);
		memset(Mark,0,sizeof(Mark));
		Top=0;
		DFS(Start);
		for (T=Top; T>1; T--)
			printf("%d ",Step[T]);
		printf("%d\n",Step[T]);
	}
	return 0;
}

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