POJ-2513 Colored Sticks 【欧拉通路+Trie】

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

---

题解：

把每种颜色看成顶点，棍子看成边，即转化为求是否存在欧拉通路问题，这题数据量大，Map超时，用hash恰当的mod值取不来（discuss里神tm1000过了一脸懵逼），用Trie可以过。

代码：

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
#include<queue>
#include<map>
using namespace std;
const int N = 250000 * 2 + 5;
int deg[N], p[N];
struct Edge {
    int u, v;
}edge[N];

int ch[N][26], val[N], num = 0, tot = 0;
int insert(char *s) {
    int now = 0, len = strlen(s);
    for (int i = 0; i < len; ++i) {
        int id = s[i] - 'a';
        if (!ch[now][id]) ch[now][id] = ++num;
        now = ch[now][id];
    }
    val[now] = ++tot;
    return val[now];
}

int find(char *s) {
    int now = 0, len = strlen(s);
    for (int i = 0; i < len; ++i) {
        int id = s[i] - 'a';
        if (!ch[now][id]) return 0;
        now = ch[now][id];
    }
    return val[now];
}

int Find(int x) {return x == p[x] ? x : p[x] = Find(p[x]);}

void Union(int x, int y) {
    x = Find(x); y = Find(y);
    if (x != y) p[x] = y;
}

bool bconnect(int n, int m) {
    for (int i = 1; i <= m; ++i) p[i] = i;
    for (int i = 0; i < n; ++i) {
        int u = edge[i].u, v = edge[i].v;
        if (u != v) Union(u, v);
    }
    for (int i = 2; i <= m; ++i)
        if (Find(i) != Find(1)) return false;
    return true;
}

int main() {
    char s1[15], s2[15];
    int edgenum = 0, u, v;
    while (~scanf("%s%s", s1, s2)) {
        u = find(s1); v = find(s2);
        if (!u) u = insert(s1);
        if (!v) v = insert(s2);
        edge[edgenum].u = u;
        edge[edgenum].v = v;
        ++edgenum;
        deg[u]++; deg[v]++;
    }
    bool eular = true;
    int odd = 0;
    for (int i = 1; i <= tot; ++i) {
        if (deg[i] % 2 == 1) ++odd;
        if (odd > 2) {eular = false; break;}
    }
    if (!bconnect(edgenum, tot)) eular = false;
    if (eular) printf("Possible\n");
    else printf("Impossible\n");

    return 0;
}