euler性质直接判断是否组成路径 uva10129

最新推荐文章于 2024-01-04 10:27:36 发布

xsthunder

最新推荐文章于 2024-01-04 10:27:36 发布

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分类专栏： cpp 并查集 euler uva 文章标签： uva10129

本文链接：https://blog.youkuaiyun.com/xsthunder/article/details/52056044

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本文介绍UVA10129题目的一种解法，通过并查集判断连通性和欧拉路径的存在性，确保图的每条边恰好被经过一次。详细解析了代码实现，并解释了如何验证图的连通性和欧拉路径的形成条件。

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#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstdlib>
#include<vector>
#include<map>
#include<queue>
#include<set>
#include<stack>
#include<cctype>
#include<cstring>
#include<utility>
using namespace std;
const int inf=0x7fffffff;
const int N_UN=300;
const int N_S=1e3+10;
int p[N_UN];
int ieul[N_UN];
int oeul[N_UN];
int eul[N_UN];
int t;
char s [N_S];
const int un_s ='a';
const int un_e='z';
const char ans[][100]={
    "The door cannot be opened.",
    "Ordering is possible."};
void init(){
    memset (eul,0,sizeof(eul));
    memset (ieul,0,sizeof(oeul));
    memset (oeul,0,sizeof(oeul));
    for(int i=un_s;i<=un_e;i++){
        p[i]=i;
    }
}
int un_find(int x){
    if(p[x]==x)return x;
    else return un_find(p[x]);
}
void un_set(int x,int y){
    int xfa,yfa;
    xfa=un_find(x);
    yfa=un_find(y);
    if(xfa==yfa){
        return ;
    }
    else {
        p[xfa]=yfa;
        return ;
    }
}
bool check_un(){
    int head=0;
    for(int i=un_s;i<=un_e;i++){
        if(eul[i])head=un_find(i);
    }
    if(!head)cout<<"wrong head";
    else {
        for(int i=un_s;i<=un_e;i++){
            if(eul[i])if(head!=un_find(i))return 0;
        }
    }
    return 1;
}
bool check_eul(){
    int flag=0;
    int cntodd=0;
    for(int i=un_s;i<=un_e;i++)if(eul[i]){
        if(ieul[i]!=oeul[i]){
            cntodd++;
            if(abs(ieul[i]-oeul[i])!=1)return 0;
            flag+=ieul[i]-oeul[i];
        }
    }
    if(cntodd==0)return 1;
    else if(cntodd==2){if(flag==0)return 1;}
    else return 0;
}

int main()
{

#ifdef DEBUG
    freopen("in", "r", stdin);
//  freopen("out", "w", stdout);
#endif
    int T;
    int n;
    scanf("%d",&T);
    while(T--){
        scanf("%d", &n);
        init();
        t=n;
        while(n--){
            scanf("%s" , s);
            int x,y;
            x=s[0];
            y=s[strlen(s)-1];
            eul[x]++;
            eul[y]++;
            ieul[x]++;
            oeul[y]++;
            un_set(x,y);
//          for(int i=un_s;i<=un_e;i++)if(eul[i]){cout<<(char)i<<"eul "<<eul[i]<<" p "<<(char)p[i]<<" ieul "<<ieul[i]<<" oeul "<<oeul[i]<<endl;}
        }
        printf("%s\n", ans[check_un()&&check_eul()]);
    }


    //insert code
    return 0;
}
//uva10129.cc