POJ 2513 Colored Sticks

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 redred violetcyan blueblue magentamagenta cyan

Sample Output

Possible

Hint

Huge input,scanf is recommended.

题解

trie树+并查集+欧拉路。

字符串哈希我从没写过感觉比较麻烦，所以用trie，不过据说hash会T。并查集是为了确定只练成一条线。否则欧拉路是简单的判定是否不重复地用了所有的棍子。

#include<cstdio>#include<cstring>#include<cstdlib>#include<iostream>#include<cmath>#include<algorithm>using namespace std;char a[15],b[15];int trie[500005][26],num[500005],size,ct;int fa[500005],e[500005];int search(char ch[]){int w=0,p=0,l=strlen(ch),k;while(p<=l)   {k=ch[p]-'a';    if(!trie[w][k]) return 0;    w=trie[w][k]; p++;   }return num[w];}void insert(char ch[]){int w=0,p=0,l=strlen(ch),k;while(p<=l)   {k=ch[p]-'a';    if(!trie[w][k]) trie[w][k]=++size;    w=trie[w][k]; p++;   }num[w]=++ct;}int find(int x){if(fa[x]!=x) fa[x]=find(fa[x]);return fa[x];}void init(){int i,x,y,r1,r2;for(i=1;i<=500001;i++) fa[i]=i;while(scanf("%s%s",a,b)!=EOF)   {x=search(a);    y=search(b);    if(x==0) {insert(a); x=ct;}    if(y==0) {insert(b); y=ct;}    e[x]++; e[y]++;    r1=find(x),r2=find(y);    if(r1!=r2) fa[r1]=r2;   }}void work(){int i,s=0,j,k;for(i=1;i<=ct;i++)   {if(e[i]&1) s++;}if(s!=0&&s!=2) {printf("Impossible\n"); return;}j=find(1);for(i=2;i<=ct;i++)   {k=find(i);    if(j!=k) {printf("Impossible\n"); return;}   }printf("Possible\n");}int main(){init(); work();return 0;}