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);
}