Binary search is used similarly. K'th element is found in more productive way.
Step-by-step explanation:
arr1 and arr2 are the middle elements which are compared, let us compute as mid1 and mid2. Let us predict arr1 [mid1] k, the elements are not needed after mid2 elements. arr2 are set as last element for arr2 [mid2]. New sub problems are defined. When one array is half the size.
C++ code for the algorithm.
#include <iostream>
using namespace std;
int kth(int *arr1, int *arr2, int *end1, int *end2, int k)
{
if (arr1 == end1)
return arr2[k];
if (arr2 == end2)
return arr1[k];
int mid1 = (end1 - arr1) / 2;
int mid2 = (end2 - arr2) / 2;
if (mid1 + mid2 < k)
{
if (arr1[mid1] > arr2[mid2])
return kth(arr1, arr2 + mid2 + 1, end1, end2,
k - mid2 - 1);
else
return kth(arr1 + mid1 + 1, arr2, end1, end2,
k - mid1 - 1);
}
else
{
if (arr1[mid1] > arr2[mid2])
return kth(arr1, arr2, arr1 + mid1, end2, k);
else
return kth(arr1, arr2, end1, arr2 + mid2, k);
}
int main()
{
int arr1[5] = {2, 3, 6, 7, 9};
int arr2[4] = {1, 4, 8, 10};
int k = 5;
cout << kth(arr1, arr2, arr1 + 5, arr2 + 4, k - 1);
return 0;
}