Search⌘ K
AI Features

Solution: Kth Smallest Prime Fraction

Explore how to identify the kth smallest fraction formed by elements in a sorted array of unique integers, including prime numbers. Learn to apply a heap-based k-way merge algorithm to sequentially generate fractions, efficiently maintaining the next smallest fraction candidates. Understand the time and space complexity involved, and gain practical skills for solving related coding interview problems with optimized approaches.

Statement

You are given a sorted array of unique integers, arr, which includes the number 11 and other prime numbers. You are also given an integer kk.

For every index ii and jj where 0i<j<0 \leq i < j < arr.length, you can form a fraction by taking the number at index ii as the numerator and the number at index jj as the denominator, resulting in the fraction arr[i] / arr[j].

Your task is to return the kthk^{th} smallest fraction among these fractions. The answer should be returned as an array of two integers, where the first element, answer[0], is the numerator (arr[i]), and the second element, answer[1], is the denominator (arr[j]) corresponding to the kthk^{th} smallest fraction.

Constraints:

  • 22 \leq arr.length 103\leq 10^3

  • ...