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 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

 

有一端颜色相同的可以接到一块，那么就默认颜色相同的拼到一起了，然后每行给出两个颜色，对两个颜色进行合并，看看最后是否是一个连通图，如果是连通图了，还得拍成一行，也就是一笔走完所有点，就是判断欧拉图，奇数度的点最多两个，注意有坑，如果一行数据也没有，也是Possible。

这里用字典树，记录每种颜色，返回对应的下标，然后进行并查集合并，以此判断是否为连通图。记录每种颜色出现次数，判断他的度数的奇偶性。

代码：

#include <iostream>
#include <cstdio>
#include <sstream>
#include <cstring>
#define MAX 2000005
using namespace std;
int pos,pos1;
int trie[MAX][26],num[MAX],to[MAX];
int f[MAX];
int odd,root;
int Insert(char *s) {
    int i = 0,c = 0;
    while(s[i]) {
        int d = s[i] - 'a';
        if(!trie[c][d]) trie[c][d] = ++ pos;
        c = trie[c][d];
        i ++;
    }
    if(!to[c]) {
        to[c] = ++ pos1;
        f[pos1] = pos1;
    }
    num[to[c]] ++;
    return to[c];
}
int getf(int x) {
    return f[x] == x ? f[x] : f[x] = getf(f[x]);
}
void Union(int x,int y) {
    int xx = getf(x);
    int yy = getf(y);
    if(xx != yy) {
        f[xx] = yy;
    }
}
int main() {
    char s[20],t[20];
    while(~scanf("%s%s",s,t)) {
        int d = Insert(s);
        int e = Insert(t);
        Union(d,e);
    }
    for(int i = 1;i <= pos1;i ++) {
        if(getf(i) == i) root ++;
        if(num[i] % 2) odd ++;
    }
    if(root <= 1 && odd <= 2)puts("Possible");
    else puts("Impossible");
}