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  • Unknown Treasure(hdu5446)

    Unknown Treasure

    Time Limit: 1500/1000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)
    Total Submission(s): 2112    Accepted Submission(s): 771


    Problem Description
    On the way to the next secret treasure hiding place, the mathematician discovered a cave unknown to the map. The mathematician entered the cave because it is there. Somewhere deep in the cave, she found a treasure chest with a combination lock and some numbers on it. After quite a research, the mathematician found out that the correct combination to the lock would be obtained by calculating how many ways are there to pick m different apples among n of them and modulo it with M. M is the product of several different primes.
     
    Input
    On the first line there is an integer T(T20) representing the number of test cases.

    Each test case starts with three integers n,m,k(1mn1018,1k10) on a line where k is the number of primes. Following on the next line are k different primes p1,...,pk. It is guaranteed that M=p1p2pk1018 and pi105 for every i{1,...,k}.
     
    Output
    For each test case output the correct combination on a line.
     
    Sample Input
    1
    9 5 2
    3 5
    Sample Output
    6
    题意:就是让你求组合数C(n,m)的值模M=p1*p2*...pk的值这写p;
    思路:中国剩余定理+lucas定理;
    因为组合数比较大,模数乘起来也很大,所以我们先用lucas定理求出对每个模数所求得的模,然后再通过中国剩余定理求对那个大模数的模;
    在使用中国剩余定理的时候,最后那个M可能会很大,所以乘法的时候可能会爆LL,要用快速乘去处理
      1 #include<stdio.h>
      2 #include<algorithm>
      3 #include<iostream>
      4 #include<string.h>
      5 #include<stdlib.h>
      6 #include<queue>
      7 #include<map>
      8 #include<math.h>
      9 using namespace std;
     10 typedef long long LL;
     11 int mod[20];
     12 LL a[100005];
     13 LL yu[30];
     14 LL quick(LL n,LL m,LL p)
     15 {
     16         LL ans=1;
     17         while(m)
     18         {
     19                 if(m&1)
     20                 {
     21                         ans=ans*n%p;
     22                 }
     23                 n=n*n%p;
     24                 m/=2;
     25         }
     26         return ans;
     27 }
     28 LL lucas(LL n,LL m,LL p)
     29 {
     30         if(n==0)
     31         {
     32                 return 1;
     33         }
     34         else
     35         {
     36                 LL nn=n%p;
     37                 LL mm=m%p;
     38                 if(mm<nn)
     39                         return 0;
     40                 else
     41                 {
     42                         LL ni=a[mm-nn]*a[nn]%p;
     43                         ni=a[mm]*quick(ni,p-2,p)%p;
     44                         return ni*lucas(n/p,m/p,p);
     45                 }
     46         }
     47 }
     48 LL mul(LL n, LL m,LL p)
     49 {
     50         n%=p;
     51         m%=p;
     52         LL ret=0;
     53         while(m)
     54         {
     55                 if(m&1)
     56                 {
     57                         ret=ret+n;
     58                         ret%=p;
     59                 }
     60                 m>>=1;
     61                 n<<=1;
     62                 n%=p;
     63         }
     64         return ret;
     65 }
     66 int main(void)
     67 {
     68         LL n,m;
     69         int k;
     70         int t;
     71         scanf("%d",&k);
     72         int i,j;
     73         while(k--)
     74         {
     75                 scanf("%lld %lld %d",&n,&m,&t);
     76                 for(i=0; i<t; i++)
     77                 {
     78                         scanf("%d",&mod[i]);
     79                         a[0]=1;
     80                         a[1]=1;
     81                         for(j=2; j<mod[i]; j++)
     82                         {
     83                                 a[j]=a[j-1]*j%mod[i];
     84                         }
     85                         yu[i]=lucas(m,n,mod[i]);
     86                 }
     87                 LL sum=1;
     88                 for(i=0; i<t; i++)
     89                 {
     90                         sum*=(LL)mod[i];
     91                 }
     92                 LL acc=0;
     93                 for(i=0; i<t; i++)
     94                 {
     95                         LL kk=sum/mod[i];
     96                         LL ni=quick(kk%mod[i],mod[i]-2,mod[i]);
     97                         acc=(acc+mul(yu[i],mul(kk,ni,sum),sum)%sum)%sum;
     98 
     99                 }
    100                 acc=acc%sum+sum;
    101                 acc%=sum;
    102                 printf("%lld
    ",acc);
    103         }
    104         return 0;
    105 }
    油!油!you@
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  • 原文地址:https://www.cnblogs.com/zzuli2sjy/p/5709791.html
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