Find the Kth Largest Integer in the Array

Find the Kth Largest Integer in the Array

What is this problem about?

The Find the Kth Largest Integer in the Array interview question asks you to find the $k^{th}$ largest value in a list of numeric strings. The numbers can be extremely large (up to 100 digits), so they cannot be converted into standard 64-bit integers. You must perform the selection or sorting based on the string values while respecting their numeric magnitude.

Why is this asked in interviews?

Companies like Meta and Google ask the Find the Kth Largest Integer in the Array coding problem to test a candidate's ability to handle custom sorting. Standard sorting logic for strings ("10" < "2") is different from numeric logic (10 > 2). It also evaluations your knowledge of selection algorithms like Quickselect or Heap (Priority Queue) interview patterns for finding the $k^{th}$ element efficiently.

Algorithmic pattern used

This problem is best solved using a Min-Heap or Custom Sorting.

1. Custom Comparator: Define a comparison rule for two strings $A$ and $B$:

• If $length(A) eq length(B)$, the longer string is numerically larger.
• If $length(A) == length(B)$, perform a lexicographical comparison.

1. Heap Approach: Maintain a Min-Heap of size $k$. For each string in the array, push it onto the heap. If the heap size exceeds $k$, pop the smallest element. The top of the heap at the end is the $k^{th}$ largest.
2. Quickselect: A more advanced $O(N)$ average-time approach that partitions the array around a pivot until the $k^{th}$ position is found.

Example explanation

Array: ["3", "6", "7", "10"], $k = 4$.

1. Convert comparison to numeric: 10 is largest (len 2), then 7, 6, 3.
2. $4^{th}$ largest is "3". If $k=2$:
3. Top 2 are "10" and "7".
4. $2^{nd}$ largest is "7".

Common mistakes candidates make

• Standard String Sort: Using default sort, which puts "10" before "2".
• Integer Conversion: Attempting to parse strings into int or long, which causes overflow for 100-digit numbers.
• Full Sort: Sorting the entire array ($O(N \log N)$) when a Heap ($O(N \log K)$) or Quickselect ($O(N)$) is more efficient for small $k$.

Interview preparation tip

Whenever you deal with numbers as strings, always consider the length first. In a numeric context, length is the primary indicator of magnitude. This is a core String interview pattern for large-number problems.