http://acm.hdu.edu.cn/showproblem.php?pid=3037 Lucas定理

/*<br />Lucas theorem<br />m = mk * p^k + mk-1 * p^k-1 +... +m1 * p + m0;<br />n = nk * p^k + nk-1 * p^k-1 +... + n1 * p + n0;<br />C(m,n)=C(mk,nk)*C(mk-1,nk-1)*...*C(m1,n1)*C(m0,n0);<br />【題目大意】<br />求C(n+m,n) % p的值。<br />保證p是素數。<br />*/<br />#include <iostream><br />#include <cstdio><br />#define N 100009<br />#define LL long long<br />using namespace std;<br />LL ff[N+5];<br />LL M;<br />LL gcd(LL a,LL b)<br />{<br />if(b==0)<br />return a;<br />else<br />return gcd(b, a % b);<br />}<br />LL x,y;<br />void Extended_gcd(LL a, LL b)<br />{<br />if(b==0)<br />{<br />x = 1;<br />y = 0;<br />}<br />else<br />{<br />Extended_gcd(b, a % b);<br />LL t = x;<br />x = y;<br />y = t - ( a / b ) * y;<br />}<br />}<br />LL C(LL a,LL b)<br />{<br />if(b > a)<br />return 0;<br />b=( ff[a-b] * ff[b] ) % M;<br />a= ff[a];<br />LL c=gcd(a,b);<br />a /= c;<br />b /= c;<br />Extended_gcd(b, M);<br />x = ( x + M ) % M;<br />x = ( x * a ) % M;<br />return x;<br />}<br />LL func(LL n, LL m) //Lucas定理<br />{<br />LL ans = 1;<br />LL a, b;<br />while(m || n)<br />{<br />a = n % M;<br />b = m % M;<br />n /= M;<br />m /= M;<br />ans=(ans * C (a , b) ) % M;<br />}<br />return ans;<br />}<br />int main()<br />{<br />LL n, m, k;<br />int t;<br />scanf("%d", &t);<br />while(t--){<br />scanf("%I64d %I64d %I64d", &n, &m, &M);<br />ff[0]=1;<br />for(int i=1;i<=M;i++)<br />ff[i] = ( ff[i-1] * i ) % M;<br />printf("%I64d/n", func(n + m, m));<br />}<br />return 0;<br />}