高精度乘法

/*

高精度乘法
输入：两行，每行表示一个非负整数（不超过10000位）
输出：两数的乘积。
*/

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <memory.h>

#define MAX 10001

int high_precision(int *sum,int *a,int *b,int a_len,int b_len)
{
    int i,j;
    memset(sum,0,sizeof(sum));
    int sum_len = 0 ;
    for(i=1;i<=a_len;i++) /*用数组模拟运算*/
        for(j=1,sum_len=i-1;j<=b_len;j++)
            sum[++sum_len] += b[j]*a[i];
    for(i=1;i<=sum_len;i++)/*进位处理*/
        if(sum[i] >= 10)
        {
            if(sum[sum_len] >= 10)
                sum_len++;
            sum[i+1] += sum[i]/10;
            sum[i] %= 10;
        }

    return sum_len;
}

void multiply(char* a, char* b, char* c)
{
    int i, j, ca, cb, * s;
    ca = strlen(a);
    cb = strlen(b);
    s = (int*)malloc(sizeof(int) * (ca + cb));
    for (i = 0; i < ca + cb; i++)
        s[i] = 0;
    for (i = 0; i < ca; i++)
        for (j = 0; j < cb; j++)
            s[i+j+1] += (a[i] - '0') * (b[j] - '0');
    for (i = ca + cb - 1; i >= 0; i--)
        if (s[i] >= 10)
        {
            s[i-1] += s[i] / 10;
            s[i] %= 10;
        }
    i = 0;
    while (s[i] == 0)
        i++;
    for (j = 0; i < ca + cb; i++, j++)
        c[j] = s[i] + '0';
    c[j] = '\0';
    free(s);
}

int main(int argc,char *argv[])
{
    int a[MAX]= {0},b[MAX]= {0},sum[MAX*2]= {0};
    int a_len=0,b_len=0,sum_len=0;
    int i,j;
    char c_a[MAX],c_b[MAX],c_sum[MAX*2];

    scanf("%s%s",c_a,c_b);

    a_len = strlen(c_a);
    b_len = strlen(c_b);

    for(i=1,j=a_len-1;i<= a_len;i++,j--)
        a[i] = c_a[j] - '0';
    for(i=1,j=b_len-1;i<= b_len;i++,j--)
        b[i] = c_b[j] - '0';

    sum_len = high_precision(sum,a,b,a_len,b_len) ;

    for(i=sum_len;i>=1;i--)
        printf("%d",sum[i]);
    putchar('\n');
    multiply(c_a,c_b,c_sum);
    printf("%s\n",c_sum);

    return 0 ;
}