洛谷 P1641 [SCOI2010]生成字符串

题意简述

将n个1和m个0组成字符串，使1的个数始终大于0的个数
求方案数

题解思路

预处理阶乘和阶乘逆元
最后答案为C(n + m, m) - C(n + m, m - 1)

代码

#include <cstdio>
using namespace std;
typedef long long ll;
const int mod = 20100403;
int n, m, x, ans;
int fac[2000010], inv[2000010];
int ksm(int x, int y, int s = 1)
{
    for (; y; y >>= 1, x = (ll)x * x % mod)
        if (y & 1)
            s = (ll)s * x % mod;
    return s;
}
int C(int x, int y)
{
	return ((ll)fac[x] * inv[y] % mod) * inv[x - y] % mod;
}
int main()
{
	scanf("%d%d", &n, &m);
	x = n + m;
	fac[0] = 1;
	for (register int i = 1; i <= x; ++i)
		fac[i] = (ll)fac[i - 1] * i % mod;
	inv[x] = ksm(fac[x], mod - 2);
	for (register int i = x - 1; i; --i)
		inv[i] = (ll)inv[i + 1] * (i + 1) % mod;
	ans = (((ll)C(n + m, m) - C(n + m, m - 1)) % mod + mod) % mod;
	printf("%d
", ans);
}