hdu 4828 Grids(拓展歐幾裡得+卡特蘭數)

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題目連結：hdu 4828 Grids

題目大意：略。

解題思路：將上一行看成是入棧，下一行看成是出棧，那麼執著的方案就是卡特蘭數，用遞推的方式求解。

#include <cstdio>#include <cstring>typedef long long ll;const int N = 1000005;const ll MOD = 1e9+7;ll dp[N];ll extendGcd(ll a, ll b, ll& x, ll& y) {    if (b == 0) {        x = 1;        y = 0;        return a;    }    ll d = extendGcd(b, a%b, y, x);    y -= a / b * x;    return d;}ll solve (ll n) {    ll x, y;    ll tmp = extendGcd(n + 1, MOD, x, y);    x = (x % MOD + MOD) % MOD;    return x;}void init () {    dp[1] = 1;    dp[2] = 2;    for (ll i = 3; i < N; i++)        dp[i] = (dp[i-1] * (4 * i - 2) % MOD * solve(i)) % MOD;}int main () {    int cas, n;    scanf("%d", &cas);    init();    for (int i = 1; i <= cas; i++) {        scanf("%d", &n);        printf("Case #%d:\n%lld\n", i, dp[n]);    }    return 0;}