求C(n+m,m)%p ,n和m很大,p是小于10^5的素数。
LUCAS定理。
1 #include <string.h> 2 #include <stdio.h> 3 typedef long long LL; 4 int cas; 5 LL n, m, p; 6 LL fac[100005]; 7 LL powmod(LL a, LL b, LL p){ 8 LL ans = 1, tmp = a; 9 for (; b; b >>= 1, tmp = tmp * tmp % p) 10 if (b&1) ans = ans * tmp % p; 11 return ans; 12 } 13 LL lucas(LL n, LL m, LL p){ 14 LL ans = 1; 15 while (n&&m) { 16 LL a = n%p, b = m%p; 17 if (a < b) return 0; 18 ans = ans * fac[a] * powmod(fac[b]*fac[a-b]%p,p-2,p) % p; 19 n /= p, m /= p; 20 } 21 return ans; 22 } 23 void getfact(LL p){ 24 fac[0]=1; 25 for (int i = 1; i <= p; i++) 26 fac[i] = fac[i-1] * i % p; 27 28 } 29 int main(){ 30 scanf("%d", &cas); 31 while (cas--) { 32 scanf("%I64d%I64d%I64d", &n, &m, &p); 33 getfact(p); 34 printf("%I64d\n", lucas(n+m, m, p)); 35 } 36 return 0; 37 }