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Find the Kth Largest Integer in the Array

Number: 2113

Difficulty: Medium

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Companies: Meta

Problem Description

Given an array of strings nums where each string represents an integer without leading zeros, and an integer k, return the string that represents the kth largest integer in nums. Note that duplicate numbers are counted separately.

Key Insights

  • Since each number is represented as a string and can be very long (up to 100 digits), converting them to numeric types might be impractical in some languages; instead, compare using string properties.
  • The key observation is that one integer is greater than another if its string length (number of digits) is larger; if lengths are equal, lexicographical order gives the order.
  • Sorting the array in descending order using a custom comparator (first comparing lengths, then lexicographically) allows direct access to the kth largest element.
  • Alternatively, selection algorithms (e.g., Quickselect) or heaps can be used, but a sort is simple and effective given the input constraints.

Space and Time Complexity

Time Complexity: O(n log n * m) where m is the maximum string length (for comparing two numbers)
Space Complexity: O(n) (space used by sorting)

Solution

The solution involves sorting the array of strings in descending order based on their numeric value. We define a custom comparator that:

  1. Compares the lengths of the strings. A longer string indicates a larger integer.
  2. If the lengths are equal, compares them lexicographically.

After sorting, the kth largest integer is simply found at the k-1 index in the sorted array. This approach avoids pitfalls with very large numbers since it relies only on string properties.

Code Solutions

Below are line-by-line code solutions in Python, JavaScript, C++, and Java.

# Define a function to find the kth largest integer in the array
def kthLargestNumber(nums, k):
    # Sort the list 'nums' in descending order by using a custom key:
    # 1. Compare by the length of the string (more digits means larger number)
    # 2. If lengths are equal, compare lexicographically.
    nums.sort(key=lambda x: (len(x), x), reverse=True)
    # Return the kth largest element (0-indexed array so k-1)
    return nums[k - 1]

# Example usage:
if __name__ == "__main__":
    nums = ["3","6","7","10"]
    k = 4
    result = kthLargestNumber(nums, k)
    print(result)  # Expected output: "3"
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