【CF】556D A Lot of Games

构建trie树，可以得到4类结点：必胜点，必负点，完全主宰点（可胜可负），完全无法主宰点（无法控制最终胜负）。递归到叶子结点，即为必胜点，回溯分情况讨论。注意叶子结点使用属性n来控制，n表示当前结点的儿子结点的数目，叶子结点没有儿子。

/* 456D */
#include <iostream>
#include <string>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <vector>
#include <deque>
#include <algorithm>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <cstring>
#include <climits>
#include <cctype>
#include <cassert>
using namespace std;

typedef struct trie_t {
    int n;
    int next[26];
    trie_t() {
        n = 0;
        memset(next, 0, sizeof(next));
    }
} trie_t;

const int maxn = 1e5+5;

trie_t T[maxn];
int L = 0;
char s[maxn];
int n, m;

int newTrie() {
    return ++L;
}

void create(char *s, int rt) {
    int p = rt;
    int i = 0, id;

    while (s[i]) {
        id = s[i] - 'a';
        if (T[p].next[id] == 0) {
            T[p].next[id] = ++L;
            ++T[p].n;
        }
        p = T[p].next[id];
        ++i;
    }
}

int dfs(int rt) {
    int i;
    int st = 0;
    
    if (T[rt].n == 0)
        return 2;

    for (i=0; i<26; ++i) {
        if (T[rt].next[i])
            st |= dfs(T[rt].next[i]);
    }
    switch(st) {
    case 0:
        return 3;
    case 1:
        return 2;
    case 2:
        return 1;
    case 3:
        return 0;
    default:
        return 0;
    }
}


int main() {
    int i, j, k;

    #ifndef ONLINE_JUDGE
        freopen("data.in", "r", stdin);
        freopen("data.out", "w", stdout);
    #endif

    scanf("%d %d", &n, &m);
    // build trie
    for (i=0; i<n; ++i) {
        scanf("%s", s);
        create(s, 0);
    }
    // get the key point
    int st = 0;
    for (i=0; i<26; ++i) {
        if (T[0].next[i])
            st |= dfs(T[0].next[i]);
    }
    
    if (st == 3) {
        puts("First");
        return 0;
    } else if (st == 0) {
        puts("Second");
        return 0;
    }
    if (st == 1) {
        puts("Second");
        return 0;
    }
    if (m & 1) {
        puts("First");
    } else {
        puts("Second");
    }

    #ifndef ONLINE_JUDGE
        printf("time = %d.
", (int)clock());
    #endif

    return 0;
}