poj 2513 Colored Sticks(欧拉通路+并查集+字典树)

题目链接：poj 2513 Colored Sticks

题目大意：有N个木棍，每根木棍两端被涂上颜色，现在给定每个木棍两端的颜色，不同木棍之间拼接需要颜色相同的

端才可以，问最后能否将N个木棍拼接在一起。

解题思路：欧拉通路+并查集+字典树。欧拉通路，每个节点的统计度，度为奇数的点不能超过2个。并查集，判断节点

是否完全联通。字典树，映射颜色。

#include <cstdio>
#include <cstring>
#include <string>
#include <vector>
#include <iostream>
#include <algorithm>

using namespace std;
const int maxn = 5000005;
const int sigma_size = 26;
typedef pair<int,int> pii;

int N, E, far[maxn], cnt[maxn];
pii ed[maxn];

struct Tire {
    int sz, g[maxn][sigma_size];
    int val[maxn];

    void init();
    int idx(char ch);
    int insert(char* s);
}T;

inline int getfar(int x) {
    return x == far[x] ? x : far[x] = getfar(far[x]);
}

bool judge() {
    int ret = 0;
    for (int i = 1; i <= N; i++) {
        if (cnt[i]&1)
            ret++;
    }

    if (ret > 2)
        return false;

    for (int i = 0; i < E; i++) {
        int p = getfar(ed[i].first);
        int q = getfar(ed[i].second);
        if (p != q) {
            N--;
            far[p] = q;
        }
    }
    return N <= 1;
}

int main () {
    T.init();
    N = E = 0;
    char a[11], b[11];

    while (scanf("%s%s", a, b) == 2) {
        int p = T.insert(a);
        int q = T.insert(b);
        cnt[p]++, cnt[q]++;
        ed[E].first = p;
        ed[E].second = q;
        E++;
    }
    printf("%s\n", judge() ? "Possible" : "Impossible");
    return 0;
}

void Tire::init() {
    sz = 1;
    val[0] = 0;
    memset(g[0], 0, sizeof(g[0]));
}

int Tire::idx(char ch) {
    return ch - ‘a‘;
}

int Tire::insert(char* s) {
    int u = 0, n = strlen(s);

    for (int i = 0; i < n; i++) {
        int v = idx(s[i]);
        if (g[u][v] == 0) {
            g[u][v] = sz;
            memset(g[sz], 0, sizeof(g[sz]));
            val[sz++] = 0;
        }

        u = g[u][v];
    }

    if (val[u] == 0) {
        val[u] = ++N;
        far[N] = N;
        cnt[N] = 0;
    }
    return val[u];
}