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  • [解题报告]369 Combinations

     Combinations 

    Computing the exact number of ways that N things can be taken M at a time can be a great challenge when Nand/or M become very large. Challenges are the stuff of contests. Therefore, you are to make just such a computation given the following:

    GIVEN:

    displaymath41

    Compute the EXACT value of:

    displaymath43

    You may assume that the final value of C will fit in a 32-bit Pascal LongInt or a C long.

    For the record, the exact value of 100! is:

         93,326,215,443,944,152,681,699,238,856,266,700,490,715,968,264,381,621,
            468,592,963,895,217,599,993,229,915,608,941,463,976,156,518,286,253,
            697,920,827,223,758,251,185,210,916,864,000,000,000,000,000,000,000,000

    Input and Output

    The input to this program will be one or more lines each containing zero or more leading spaces, a value forN, one or more spaces, and a value for M. The last line of the input file will contain a dummy NM pair with both values equal to zero. Your program should terminate when this line is read.

    The output from this program should be in the form:

    N things taken M at a time is C exactly.

    Sample Input

         100  6
          20  5
          18  6
           0  0

    Sample Output

    100 things taken 6 at a time is 1192052400 exactly.
    20 things taken 5 at a time is 15504 exactly.
    18 things taken 6 at a time is 18564 exactly.

    略水,注意存储形式

    #include<stdio.h>
    long long int C(int n,int m)
    {
        int i;
        long long int temp = 1;
        m=(n-m<m)?n-m:m;
        for(i=1;i<=m;i++)
        {
        temp*=n;
        temp/=i;
        n--;
        }
        return temp;
    }
    int main()
    {
        int m,n;
        while(scanf("%d %d",&n,&m)&&n&&m)
        {
              printf("%d things taken %d at a time is %lld exactly.\n",n,m,C(n,m));
        }
      return 0;
    }
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  • 原文地址:https://www.cnblogs.com/TheLaughingMan/p/2923028.html
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