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Solution: Kth Smallest Prime Fraction

Explore the method to identify the kth smallest prime fraction from a sorted list of unique integers including 1 and primes. This lesson teaches how to use a min-heap to merge sorted sequences of fractions efficiently and explains the time and space complexity involved, helping you understand this coding pattern for interview preparation.

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 ...