joj1175

 1175: The Binomial Function

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Result	TIME Limit	MEMORY Limit	Run Times	AC Times	JUDGE
	3s	8192K	2837	844	Standard

1st Jilin University ACM International Collegiate Programming Contest

In this problem, you are to write a program to make the value of the binomial function:

where n and m are integers.

Input Specification

The input consists of several pairs of n and m(0<=n, m<=30). The end of input is marked by n=m=0, which should not be processed.

Output Specification

For each pair of n and m, you should print a line like this: "Binom(n, m) = v", where n, m and v have to be replaced by the values of n, m and v.

Sample Input

5 5
7 0
5 9
0 0

Sample Output

Binom(5, 5) = 1
Binom(7, 0) = 1
Binom(5, 9) = 32

 

 

主要是递归效率的问题，直接写递归会超时。用备忘优化一下AC。改成递推写，AC。

 

#include <stdio.h>

int array[31][31];

int binomA(int a, int b); //纯递归，会超时
int binomB(int a, int b); //带有备忘录
int binomC(int a, int b); //递推写法

int main(void)
{
    freopen("in.txt", "r", stdin);

    int a, b;

    while ((scanf("%d%d", &a, &b))==2)
    {
        if (0==a && 0==b)
        {
            break;
        }
        printf("Binom(%d, %d) = %d\n", a, b, binomB(a, b));
    }


    return 0;
}

int binomA(int a, int b)
{
    if (0==a || 0==b || a==b)
    {
        return 1;
    }
    else
    {
        return binomA(a-1, b)+binomA(a-1, b-1);
    }
}

int binomB(int a, int b)
{
    if (0==a || 0==b || a==b)
    {
        return 1;
    }
    else if (array[a][b])
    {
        return array[a][b];
    }
    else
    {
        return array[a][b] = binomB(a-1,b)+binomB(a-1,b-1);
    }
}


int binomC(int a, int b)
{
    int i, j;
    for (i=0; i<31; i++)
    {
        array[0][i] = 1;
        array[i][0] = 1;
        array[i][i] = 1;
    }
    for (i=1; i<31; i++)
    {
        for (int j=1; j<31; j++)
        {
            if (i != j)
            {
                array[i][j] = array[i-1][j]+array[i-1][j-1];
            }
        }
    }
    return array[a][b];
}