Question

Given two sorted arrays of size m and n respectively, you are tasked with finding the element that would be at the k-th position of the final sorted array. Note that a linear time algorithm is trivial (and therefore we are not interested in). Input:

Array 1 - 2 3 6 7 9

Array 2 - 1 4 8 10

K

a) 1

b) 2

c) 3

d) 4

Answer 1

The question involves finding the k-th smallest element from two sorted arrays without merging them. By using two pointers and iterating only until the k-th element, we can find the desired element at each k position from 1 to 4 without fully merging the arrays. For k values 1 to 4, the elements in the merged sorted array would be 1, 2, 3, and 4 respectively.

Step-by-step explanation:

The student's question concerns finding the element at the k-th position in the merged array of two sorted arrays without using a linear time algorithm. Since the arrays are already sorted, a linear merge like in the merge step of the merge sort algorithm could be used, but since we're looking for an element at a specific position and not trying to sort the entire array, a more optimal solution exists.

Here's a step-by-step explanation to find the k-th smallest element without merging the two arrays:

1. First, consider two pointers, starting at the beginning of each array.
2. Compare the elements where the pointers are pointing, increment the pointer which is pointing to the lesser value, and decrease k by one.
3. If one of the pointers reaches the end of the array, the k-th smallest element is just the k-th element from the other array.
4. Continue this process until k is 1, at which point the current element where the pointer is at is the desired k-th element.

For the input given (Array 1: 2 3 6 7 9, Array 2: 1 4 8 10, and k values 1 through 4), here are the answers:

• k = 1: The 1st smallest element is 1.
• k = 2: The 2nd smallest element is 2.
• k = 3: The 3rd smallest element is 3.
• k = 4: The 4th smallest element is 4.