HDU 3037 Saving Beans (Lucas定理)
2014-06-17 18:53
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题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=3037
推出公式为C(n + m, m) % p, 用Lucas定理求大组合数取模的值
代码:
#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;
int t;
long long n, m, p;
long long pow(long long n, long long k) {
if (k == 0) return 1;
if (k == 1) return n;
long long ans = pow(n * n % p, k>>1);
if (k&1) ans = ans * n % p;
return ans;
}
long long C(long long n, long long m) {
if (m > n) return 0;
m = min(m, n - m);
long long zi = 1, mu = 1;
for (long long i = 0; i < m; i++) {
zi = zi * (n - i) % p;
mu = mu * (i + 1) % p;
}
return zi * pow(mu, p - 2) % p;
}
long long Lucas(long long n, long long m, long long p) {
if (m == 0) return 1;
return C(n % p, m % p) * Lucas(n / p, m / p, p) % p;
}
int main() {
scanf("%d", &t);
while (t--) {
scanf("%lld%lld%lld", &n, &m, &p);
printf("%lld\n", Lucas(n + m, m, p));
}
return 0;
}
推出公式为C(n + m, m) % p, 用Lucas定理求大组合数取模的值
代码:
#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;
int t;
long long n, m, p;
long long pow(long long n, long long k) {
if (k == 0) return 1;
if (k == 1) return n;
long long ans = pow(n * n % p, k>>1);
if (k&1) ans = ans * n % p;
return ans;
}
long long C(long long n, long long m) {
if (m > n) return 0;
m = min(m, n - m);
long long zi = 1, mu = 1;
for (long long i = 0; i < m; i++) {
zi = zi * (n - i) % p;
mu = mu * (i + 1) % p;
}
return zi * pow(mu, p - 2) % p;
}
long long Lucas(long long n, long long m, long long p) {
if (m == 0) return 1;
return C(n % p, m % p) * Lucas(n / p, m / p, p) % p;
}
int main() {
scanf("%d", &t);
while (t--) {
scanf("%lld%lld%lld", &n, &m, &p);
printf("%lld\n", Lucas(n + m, m, p));
}
return 0;
}
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