两个个数相同的数组，通过交换数组内容，实现数组之和之间的差值最小

Posted 2020-11-10 zccblogs

这个思路比较简单：

• 对两个数组排序，计算数组和
• 计算当前差值
• 和较大的数组从前到后，较小的数组从后到前，比较数值的差值，如果差值的2倍小于数组和的差值就进行交换，直到数组和差值不再减小

//简单的插入排序
void sort_arr(int *arr, int size)
{
    int tmp, i, j, k;
    for (i = 1; i < size; i++)
    {
        for (j = 0; j < i; j++)
        {
            if (arr[i] < arr[j])
            {
                tmp = arr[i];
                for (k = i; k > j; k--)
                {
                    arr[k] = arr[k-1];
                }
                arr[j] = tmp;
            }
        }
    }
}
//计算数组和
int sum_arr(int *arr, int size)
{
    int sum = 0;
    int i;
    for (i = 0; i < size; i++)
        sum += arr[i];
    return sum;
}
void min_devation(int *arr1, int *arr2, int size)
{
    int sumA = sum_arr(arr1, size);
    int sumB = sum_arr(arr2, size);
    int sumMa = (sumA>sumB)?sumA:sumB;
    int sumMi = (sumA>sumB)?sumB:sumA;
    int *arrMx = (sumA>sumB)?arr1:arr2;
    int *arrMi = (sumA>sumB)?arr2:arr1;
    int mi, mx, i, j, tmp;
    int de = sumMa - sumMi;
    int de_tmp, ex;
    printf("0.sumMi = %d, sumMx = %d\n", sum_arr(arrMi, size), sum_arr(arrMx, size));
    if (0 == de)
        return ;
    sort_arr(arrMx, size);
    sort_arr(arrMi, size);
    while (de)
    {
        de_tmp = de;
        mi = arrMi[0];
        mx = arrMx[size-1];
        ex = 2*(mx-mi);
        //交换后使得差值为0，直接交换并退出
        if (ex == de)
        {
            tmp = mi;
            arrMi[0] = arrMx[size-1];
            arrMx[size-1] = tmp;
            printf("1.sumMi = %d, sumMx = %d\n", sum_arr(arrMi, size), sum_arr(arrMx, size));
            return;
        }
        //差值比数组和大，查找是否存在更小的差值
        if (ex > de)
        {
            for (i = 0; i < size; i++)
            {
                for (j = size-1; j >= 0; j--)
                {
                    tmp = 2*(arrMx[j] - arrMi[i]);
                    //差值等于数组和差，直接交换返回
                    if (tmp == de)
                    {
                        tmp = arrMi[i];
                        arrMi[i] = arrMx[j];
                        arrMx[j] = tmp;
                        printf("2.sumMi = %d, sumMx = %d\n", sum_arr(arrMi, size), sum_arr(arrMx, size));
                        return;
                    }
                    //负的差值不需要交换，只会增大数组和的差
                    if (tmp <= 0)
                    {
                        break;
                    }
                    if (tmp < de)
                    {
                        ex = arrMi[i];
                        arrMi[i] = arrMx[j];
                        arrMx[j] = ex;
                        sort_arr(arrMi, size);
                        sort_arr(arrMx, size);
                        de -= tmp;
                    }
                }
            }
        }
        else
        {
            tmp = mi;
            arrMi[0] = arrMx[size-1];
            arrMx[size-1] = tmp;
            sort_arr(arrMi, size);
            sort_arr(arrMx, size);
        }
        de = sum_arr(arrMx, size) - sum_arr(arrMi, size);
        printf("de = %d, de_tmp = %d\n", de, de_tmp);
        if (de_tmp <= de)
        {
            break;
        }
    }
    printf("4.sumMi = %d, sumMx = %d\n", sum_arr(arrMi, size), sum_arr(arrMx, size));
    return;
}