# [SDOI2019]移动金币 阶梯博弈 dp

[SDOI移动金币

链接

vijos

思路

阶梯博弈，dp统计.

参见wxyww

代码

#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 7, mod = 1e9 + 9;
int read() {
    int x = 0, f = 1; char s = getchar();
    for (;s > '9' || s < '0'; s = getchar()) if (s == '-') f = -1;
    for (;s >= '0' && s <= '9'; s = getchar()) x = x * 10 + s - '0';
    return x * f;
}
int n, m, f[20][N], jc[N], inv[N];
int q_pow(int a, int b) {
    int ans = 1;
    while (b) {
        if (b & 1) ans = 1LL * a * ans % mod;
        a = 1LL * a * a % mod;
        b >>= 1;
    }
    return ans;
}
int C(int n, int m) {return 1LL * jc[n] * inv[m] % mod * inv[n-m] % mod;}
int main() {
    n = read(), m = read();
    jc[0] = inv[0] = jc[1] = inv[1] = 1;
    for (int i = 2; i <= n; ++i) {
        jc[i] = 1LL * jc[i-1] * i % mod;
        inv[i] = q_pow(jc[i], mod - 2);
    }
    int ans = C(n, m);
    n -= m;
    int num = (m + 1) >> 1;
    f[0][0] = 1;
    for (int i = 1; i <= 19; ++i) {
        for (int j = 0; j <= n; ++j) {
            for (int k = 0; (k << i - 1) <= j && k <= num; k += 2) {
                f[i][j] += 1LL * f[i-1][j - (k << i - 1)] * C(num, k) % mod;
                f[i][j] %= mod;
            }
        }
    }
    for (int i = 0; i <= n; ++i) {
        ans -= 1LL * f[19][i] * C(n + m / 2 - i, m / 2) % mod;
        ans = (ans + mod) % mod;
    }
    printf("%lld", ans);
    return 0;
}