[欧拉] poj 2513 Colored Sticks

主题链接：

http://poj.org/problem?

id=2513

Colored Sticks

Time Limit: 5000MS		Memory Limit: 128000K
Total Submissions: 30955		Accepted: 8159

Description

You are given a bunch of wooden sticks. Each endpoint of each stick is colored with some color. Is it possible to align the sticks in a straight line such that the colors of the endpoints that touch are of the same color?

Input

Input is a sequence of lines, each line contains two words, separated by spaces, giving the colors of the endpoints of one stick. A word is a sequence of lowercase letters no longer than 10 characters. There is no more than 250000 sticks.

Output

If the sticks can be aligned in the desired way, output a single line saying Possible, otherwise output Impossible.

Sample Input

blue red
red violet
cyan blue
blue magenta
magenta cyan

Sample Output

Possible

Hint

Huge input,scanf is recommended.

Source

The UofA Local 2000.10.14

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题目意思：

有n条木棒。每条木棒两端有两种颜色，求这些木棒是否能能在一起，使得前一个木棒的后端颜色和前一个木棒的前端颜色一样。

解题思路：

欧拉通路+字典树+并查集

注意是无向边。注意要推断连通性。直接用map映射会超时，自己写字典树。

代码：

//#include<CSpreadSheet.h>

#include<iostream>
#include<cmath>
#include<cstdio>
#include<sstream>
#include<cstdlib>
#include<string>
#include<string.h>
#include<cstring>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
#include<stack>
#include<list>
#include<queue>
#include<ctime>
#include<bitset>
#include<cmath>
#define eps 1e-6
#define INF 0x3f3f3f3f
#define PI acos(-1.0)
#define ll __int64
#define LL long long
#define lson l,m,(rt<<1)
#define rson m+1,r,(rt<<1)|1
#define M 1000000007
//#pragma comment(linker, "/STACK:1024000000,1024000000")
using namespace std;

#define Maxn 550000

int dei[Maxn],a[Maxn],cnt,la;

struct Node
{
    struct Node * next[30];
    int nu;
}node[Maxn*15],root;

int Insert(char *a)
{
    Node * p=&root;

    while(*a)
    {
        if(p->next[*a-'a'+1]==NULL)
        {
            node[++la].nu=0;
            memset(node[la].next,NULL,sizeof(node[la].next));
            p->next[*a-'a'+1]=&node[la];
        }
        p=p->next[*a-'a'+1];
        a++;
    }
    if(!p->nu)
        p->nu=++cnt;
    return p->nu;

}

int Find(int x)
{
    int temp=x;
    while(x!=fa[x])
        x=fa[x];
    while(fa[temp]!=x)
    {
        int cur=fa[temp];
        fa[temp]=x;
        temp=cur;
    }
    return x;
}
void Unio(int a,int b)
{
    a=Find(a),b=Find(b);
    if(a!=b)
        fa[a]=b;
}
int main()
{

   memset(dei,0,sizeof(dei));
   string a,b;
   char sa[15],sb[15];
   cnt=la=0;
   for(int i=1;i<=Maxn-5000;i++)
        fa[i]=i;

   memset(root.next,NULL,sizeof(root.next));
   root.nu=0;

   while(~scanf("%s%s",sa+1,sb+1))
   {
       int a=Insert(sa+1);
       int b=Insert(sb+1);

       dei[a]++,dei[b]++;
       Unio(a,b);
   }
   bool ans=true;
   int nui=0,nuo=0,la=-1;

   for(int i=1;i<=cnt;i++)
   {
       if(la==-1)
            la=Find(i);
       else if(la!=Find(i))
       {
           ans=false;
           break;
       }
       if(dei[i]&1)
            nui++;
   }
   if(!ans||nui>2||nui==1)
        printf("Impossible\n");
   else
        printf("Possible\n");
   //system("pause");

    return 0;
}

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