分治法求大整数乘法，给出c语言代码

以下是使用分治法求大整数乘法的C语言代码：

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

void multiply(char *a, char *b, char *result) {
    int n1 = strlen(a);
    int n2 = strlen(b);
 
    if (n1 == 0 || n2 == 0) {
        result[0] = '0';
        result[1] = '\0';
        return;
    }
 
    int n = n1 + n2;
    int *buffer = calloc(n, sizeof(int));
 
    int i, j;
    for (i = n1 - 1; i >= 0; i--) {
        for (j = n2 - 1; j >= 0; j--) {
            buffer[i + j + 1] += (a[i] - '0') * (b[j] - '0');
        }
    }
 
    for (i = n - 1; i > 0; i--) {
        buffer[i - 1] += buffer[i] / 10;
        buffer[i] %= 10;
    }
 
    int k = 0;
    while (buffer[k] == 0 && k < n - 1) k++;
 
    for (i = k, j = 0; i < n; i++, j++) {
        result[j] = buffer[i] + '0';
    }
    result[j] = '\0';
 
    free(buffer);
}

void karatsuba(char *x, char *y, char *result) {
    int n = strlen(x);

    if (n == 1) {
        int xy = (x[0] - '0') * (y[0] - '0');
        sprintf(result, "%d", xy);
        return;
    }

    int m = n / 2;

    char *xl = calloc(m + 1, sizeof(char));
    char *xr = calloc(n - m + 1, sizeof(char));
    char *yl = calloc(m + 1, sizeof(char));
    char *yr = calloc(n - m + 1, sizeof(char));
    char *p1 = calloc(2 * n + 1, sizeof(char));
    char *p2 = calloc(2 * n + 1, sizeof(char));
    char *p3 = calloc(2 * n + 1, sizeof(char));

    strncpy(xl, x, m);
    strncpy(xr, x + m, n - m);
    strncpy(yl, y, m);
    strncpy(yr, y + m, n - m);

    karatsuba(xl, yl, p1);
    karatsuba(xr, yr, p2);

    char *xl_plus_xr = calloc(n - m + 1, sizeof(char));
    char *yl_plus_yr = calloc(n - m + 1, sizeof(char));
    char *p4 = calloc(2 * n + 1, sizeof(char));

    multiply(xl, "1", xl_plus_xr);
    multiply(xr, "1", xl_plus_xr + m);
    multiply(yl, "1", yl_plus_yr);
    multiply(yr, "1", yl_plus_yr + m);

    karatsuba(xl_plus_xr, yl_plus_yr, p4);

    for (int i = 0; i < n; i++) {
        p4[i] = p4[i] - p1[i] - p2[i];
    }

    for (int i = 0; i < 2 * m; i++) {
        p3[i] = p1[i];
    }

    for (int i = 0; i < n; i++) {
        p3[i + m] += p4[i];
    }

    for (int i = 0; i < n - m; i++) {
        p3[i + n] += p2[i];
    }

    int i = 0;
    while (p3[i] == '0' && i < 2 * n - 1) i++;

    strncpy(result, p3 + i, 2 * n - i);
    result[2 * n - i] = '\0';

    free(xl);
    free(xr);
    free(yl);
    free(yr);
    free(p1);
    free(p2);
    free(p3);
    free(xl_plus_xr);
    free(yl_plus_yr);
    free(p4);
}

int main() {
    char a[1000], b[1000], result[2000];
    printf("Enter the first number: ");
    scanf("%s", a);
    printf("Enter the second number: ");
    scanf("%s", b);
    karatsuba(a, b, result);
    printf("Result: %s\n", result);
    return 0;
}

该代码使用了Karatsuba算法，一种分治法的变种，可以在O(n^log3)的时间内完成大整数乘法。