两个升序数组的中位数

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);}