K-th Smallest Prime Fraction

arraytwo pointersbinary search

Problem Statement

You are given a sorted integer array arr containing 1 and prime numbers, where all the integers of arr are unique. You are also given an integer k .

For every i and j where 0 <= i < j < arr.length , we consider the fraction arr[i] / arr[j] .

Return the k ^th smallest fraction considered . Return your answer as an array of integers of size 2 , where answer[0] == arr[i] and answer[1] == arr[j] .

Examples

Example 1

Input: arr = [1,2,3,5], k = 3
Output: [2,5]
The fractions to be considered in sorted order are:
1/5, 1/3, 2/5, 1/2, 3/5, and 2/3.
The third fraction is 2/5.

Example 2

Input: arr = [1,7], k = 1
Output: [1,7]

Constraints

2 <= arr.length <= 1000

1 <= arr[i] <= 3 * 10 ^4

arr[0] == 1

arr[i] is a prime number for i > 0 .

All the numbers of arr are unique and sorted in strictly increasing order.

1 <= k <= arr.length * (arr.length - 1) / 2

Follow up: Can you solve the problem with better than O(n ^2 ) complexity?

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicTwo Pointers