pku 2513 Colored Sticks（字典树+并查集）

Colored Sticks

Time Limit: 5000MS Memory Limit: 128000KTotal Submissions: 27266 Accepted: 7211

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.

Source

The UofA Local 2000.10.14

题意：给n条棍，每条棍2边有颜色，若2条棍的一边颜色相同则可以连起来，问是否能将所有棍连在一起

题解：可以把没种颜色看作一个点，然后这就是一个欧拉路问题（一笔画问题）。用字典树来分配并对应其颜色的下标，用并查集来判是否连通图，然后易知有奇数条边相连的点不能超过2个则存在欧拉路

#include<stdio.h>#include<string.h>struct tree{    int next[26],data;}tire[1000005];int v[1000005],cnt[1000005];int cou=0,cou2=1;int fin(int x){    if(x==v[x]) return x;    return v[x]=fin(v[x]);}int inter(char *s){    int p=0;    while(*s)    {        if(tire[p].next[*s-'a']==-1)        {            tire[p].next[*s-'a']=cou;            p=cou++;        }        else p=tire[p].next[*s-'a'];        s++;    }    if(tire[p].data!=-1) return tire[p].data;    v[cou2]=cou2;    return tire[p].data=cou2++;}int main(){    char a[13],b[13];    int x,y,i;    memset(tire,-1,sizeof(tire));    memset(cnt,0,sizeof(cnt));    while(scanf("%s%s",a,b)>0)    {        x=inter(a),y=inter(b);        cnt[x]++,cnt[y]++;        x=fin(x),y=fin(y);        if(x!=y) v[x]=y;    }    x=y=0;    for(i=1;i<cou2;i++)    {        if(cnt[i]&1) x++;        if(fin(i)==i) y++;        if(y>1||x>2) break;    }    if(y<=1&&x<=2) printf("Possible\n");    else printf("Impossible\n");    return 0;}