寻找两个升序数组的中位数算法解析-优快云博客

本文链接：https://blog.youkuaiyun.com/cxxmaker/article/details/8900801

本文详细探讨了如何在给定的两个已排序数组中找到中位数的方法，阐述了通用解决方案的步骤和思路，适用于各种情况。

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一般情形的解法:

#include <cstdio>

double median(int arr[], int size)
{
    if (1 == size % 2)
    {
        return(arr[size / 2]);
    }
    else
    {
        return((arr[size / 2 - 1] + arr[size / 2]) / 2.0);
    }
}

double median(int arr_a[], int a_size, int arr_b[], int b_size)
{
    int a_low = 0;
    int a_hig = a_size - 1;
    int b_low = 0;
    int b_hig = b_size - 1;

    while (a_low <= a_hig && b_low <= b_hig)
    {
        int low = 0;
        if (arr_a[a_low] <= arr_b[b_low])
        {
            low = arr_a[a_low];
            ++a_low;
        }
        else
        {
            low = arr_b[b_low];
            ++b_low;
        }

        int hig = 0;
        if (arr_b[b_hig] >= arr_a[a_hig])
        {
            hig = arr_b[b_hig];
            --b_hig;
        }
        else
        {
            hig = arr_a[a_hig];
            --a_hig;
        }

        if (low == hig)
        {
            return(static_cast<double>(low));
        }

        if (a_low > a_hig && b_low > b_hig)
        {
            return((low + hig) / 2.0);
        }

        if (a_low > a_hig)
        {
            return(median(arr_b + b_low, b_hig - b_low + 1));
        }

        if (b_low > b_hig)
        {
            return(median(arr_a + a_low, a_hig - a_low + 1));
        }
    }

    return(0.0);
}

int main(int argc, char * argv[])
{
    {
        int arr_a[] = { 2, 4, 6, 8 };
        int a_size = sizeof(arr_a) / sizeof(arr_a[0]);
        int arr_b[] = { 1, 3, 5, 7 };
        int b_size = sizeof(arr_b) / sizeof(arr_b[0]);

        double d_median = median(arr_a, a_size, arr_b, b_size);

        printf("median is %g\n", d_median);
    }

    {
        int arr_a[] = { 2, 4, 6, 8, 9 };
        int a_size = sizeof(arr_a) / sizeof(arr_a[0]);
        int arr_b[] = { 1, 3, 5, 7 };
        int b_size = sizeof(arr_b) / sizeof(arr_b[0]);

        double d_median = median(arr_a, a_size, arr_b, b_size);

        printf("median is %g\n", d_median);
    }

    {
        int arr_a[] = { 2, 4, 6, 8 };
        int a_size = sizeof(arr_a) / sizeof(arr_a[0]);
        int arr_b[] = { 1, 3, 5, 7, 9 };
        int b_size = sizeof(arr_b) / sizeof(arr_b[0]);

        double d_median = median(arr_a, a_size, arr_b, b_size);

        printf("median is %g\n", d_median);
    }

    {
        int arr_a[] = { 2 };
        int a_size = sizeof(arr_a) / sizeof(arr_a[0]);
        int arr_b[] = { 1, 3, 5, 7 };
        int b_size = sizeof(arr_b) / sizeof(arr_b[0]);

        double d_median = median(arr_a, a_size, arr_b, b_size);

        printf("median is %g\n", d_median);
    }

    {
        int arr_a[] = { 2, 4, 6, 8 };
        int a_size = sizeof(arr_a) / sizeof(arr_a[0]);
        int arr_b[] = { 7 };
        int b_size = sizeof(arr_b) / sizeof(arr_b[0]);

        double d_median = median(arr_a, a_size, arr_b, b_size);

        printf("median is %g\n", d_median);
    }

    {
        int arr_a[] = { 4, 4, 4, 4 };
        int a_size = sizeof(arr_a) / sizeof(arr_a[0]);
        int arr_b[] = { 1, 3, 5, 7 };
        int b_size = sizeof(arr_b) / sizeof(arr_b[0]);

        double d_median = median(arr_a, a_size, arr_b, b_size);

        printf("median is %g\n", d_median);
    }

    {
        int arr_a[] = { 4, 4, 4, 4 };
        int a_size = sizeof(arr_a) / sizeof(arr_a[0]);
        int arr_b[] = { 4 };
        int b_size = sizeof(arr_b) / sizeof(arr_b[0]);

        double d_median = median(arr_a, a_size, arr_b, b_size);

        printf("median is %g\n", d_median);
    }

    {
        int arr_a[] = { 2, 4, 6, 8, 13, 15, 19, 21 };
        int a_size = sizeof(arr_a) / sizeof(arr_a[0]);
        int arr_b[] = { 1, 3, 5, 7, 9, 10, 11, 15, 21, 21 };
        int b_size = sizeof(arr_b) / sizeof(arr_b[0]);

        double d_median = median(arr_a, a_size, arr_b, b_size);

        printf("median is %g\n", d_median);
    }

    {
        int arr_a[] = { 2, 4, 6, 8, 10 };
        int a_size = sizeof(arr_a) / sizeof(arr_a[0]);
        int arr_b[] = { 200, 400, 600, 800, 1000, 1100, 1200 };
        int b_size = sizeof(arr_b) / sizeof(arr_b[0]);

        double d_median = median(arr_a, a_size, arr_b, b_size);

        printf("median is %g\n", d_median);
    }

    return(0);
}

对于数组长度相等的情形, 有特殊解法:

当数组长度为奇数时:
如:
A B C D E
a b c d e
如果C > c
则abDE必定不是中位数的组成部分
反之
则ABde必定不是中位数的组成部分

当数组长度为偶数时:
如:
A B C D
a b c d
不能得到上述结论
但我们可以把BC,bc看成一个整体
再利用奇数的情形来解答

#include <cstdio>

double median(int arr[], int size)
{
    if (1 == size % 2)
    {
        return(arr[size / 2]);
    }
    else
    {
        return((arr[size / 2 - 1] + arr[size / 2]) / 2.0);
    }
}

double median(int * arr_a, int * arr_b, int size)
{
    while (true)
    {
        if (1 == size)
        {
            return((arr_a[0] + arr_b[0]) / 2.0);
        }

        if (2 == size)
        {
            int low = 0;
            if (arr_a[0] > arr_b[0])
            {
                low = arr_a[0];
            }
            else
            {
                low = arr_b[0];
            }

            int hig = 0;
            if (arr_a[1] < arr_b[1])
            {
                hig = arr_a[1];
            }
            else
            {
                hig = arr_b[1];
            }

            return((low + hig) / 2.0);
        }

        double a_median = median(arr_a, size);
        double b_median = median(arr_b, size);

        // a_median == b_median
        if (a_median - b_median < 0.1 && a_median - b_median > -0.1)
        {
            return(a_median);
        }

        int jump_over = (size - 1) / 2;

        if (a_median > b_median)
        {
            arr_b += jump_over;
        }
        else
        {
            arr_a += jump_over;
        }

        size -= jump_over;
    }

    return(0.0);
}

int main(int argc, char * argv[])
{
    {
        int arr_a[] = { 2, 4, 6, 8 };
        int arr_b[] = { 1, 3, 5, 7 };
        int size = sizeof(arr_a) / sizeof(arr_a[0]);

        double d_median = median(arr_a, arr_b, size);

        printf("median is %g\n", d_median);
    }

    {
        int arr_a[] = { 0, 2, 4, 6, 8 };
        int arr_b[] = { 1, 3, 5, 7, 9 };
        int size = sizeof(arr_a) / sizeof(arr_a[0]);

        double d_median = median(arr_a, arr_b, size);

        printf("median is %g\n", d_median);
    }

    {
        int arr_a[] = { 1, 2, 3, 4 };
        int arr_b[] = { 5, 6, 7, 8 };
        int size = sizeof(arr_a) / sizeof(arr_a[0]);

        double d_median = median(arr_a, arr_b, size);

        printf("median is %g\n", d_median);
    }

    {
        int arr_a[] = { 0, 1, 2, 3, 4 };
        int arr_b[] = { 5, 6, 7, 8, 9 };
        int size = sizeof(arr_a) / sizeof(arr_a[0]);

        double d_median = median(arr_a, arr_b, size);

        printf("median is %g\n", d_median);
    }

    {
        int arr_a[] = { 2, 4, 6 };
        int arr_b[] = { 1, 2, 3 };
        int size = sizeof(arr_a) / sizeof(arr_a[0]);

        double d_median = median(arr_a, arr_b, size);

        printf("median is %g\n", d_median);
    }

    {
        int arr_a[] = { 4, 6 };
        int arr_b[] = { 1, 3 };
        int size = sizeof(arr_a) / sizeof(arr_a[0]);

        double d_median = median(arr_a, arr_b, size);

        printf("median is %g\n", d_median);
    }

    {
        int arr_a[] = { 5 };
        int arr_b[] = { 4 };
        int size = sizeof(arr_a) / sizeof(arr_a[0]);

        double d_median = median(arr_a, arr_b, size);

        printf("median is %g\n", d_median);
    }

    return(0);
}