#1985

Medium

LeetCode Problem Workspace

Find the Kth Largest Integer in the Array

This problem asks to find the kth largest integer in an array of string numbers, highlighting sorting and string-based comparisons.

array string divide and conquer sorting heap priority queue

Problem Statement

You are given an array of strings nums, each representing an integer without leading zeros. Your task is to find the kth largest integer in the array.

Note that duplicate numbers should be counted distinctly. For example, if nums is ["1","2","2"], the first "2" is considered the largest, the second "2" is the second-largest, and "1" is the third-largest.

Examples

Example 1

Input: nums = ["3","6","7","10"], k = 4

Output: "3"

The numbers in nums sorted in non-decreasing order are ["3","6","7","10"]. The 4th largest integer in nums is "3".

Example 2

Input: nums = ["2","21","12","1"], k = 3

Output: "2"

The numbers in nums sorted in non-decreasing order are ["1","2","12","21"]. The 3rd largest integer in nums is "2".

Example 3

Input: nums = ["0","0"], k = 2

Output: "0"

The numbers in nums sorted in non-decreasing order are ["0","0"]. The 2nd largest integer in nums is "0".

Constraints

1 <= k <= nums.length <= 104
1 <= nums[i].length <= 100
nums[i] consists of only digits.
nums[i] will not have any leading zeros.

Solution Approach

Sorting

Sorting the strings as integers is one straightforward approach. The strings are compared based on their numerical values, and the array is sorted in non-decreasing order. The kth largest integer is then picked directly from the sorted list.

Heap (Priority Queue)

Using a heap, we can maintain a min-heap of size k to efficiently keep track of the kth largest integer while iterating through the list. This reduces the need to fully sort the entire list.

Quickselect

Quickselect is a divide-and-conquer algorithm that can be used to find the kth largest element in the array in average linear time. It works by partitioning the array around a pivot and narrowing down the search range until the kth element is found.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity varies depending on the chosen approach. Sorting the array has a time complexity of O(n log n), where n is the length of the array. Using a heap yields a time complexity of O(n log k), and Quickselect can achieve an average time complexity of O(n). Space complexity will similarly depend on the approach: O(n) for sorting, O(k) for the heap, and O(n) for Quickselect due to recursion stack usage.

What Interviewers Usually Probe

Look for understanding of string comparison versus numerical comparison.
Test knowledge of heap data structures, especially in maintaining kth largest elements.
Evaluate efficiency considerations between sorting, heaps, and Quickselect.

Common Pitfalls or Variants

Common pitfalls

Misunderstanding how to compare strings numerically, particularly when strings have different lengths.
Overusing sorting when a more efficient heap or Quickselect approach could be applied.
Confusing the ordering of integers and failing to handle duplicates correctly.

Follow-up variants

Find the kth smallest integer in the array instead of the kth largest.
Handle an array of numbers with leading zeros.
Consider a scenario where k equals the length of the array.

FAQ

What is the most efficient way to solve the "Find the Kth Largest Integer in the Array" problem?

Using a heap (priority queue) is often the most efficient solution as it maintains the kth largest integer in O(n log k) time complexity.

How do I compare string numbers to find the largest integer?

String numbers should be compared numerically, which requires handling different string lengths correctly by considering their numeric values.

What is the time complexity of sorting the array for this problem?

The time complexity of sorting the array is O(n log n), where n is the length of the array.

How does Quickselect help with this problem?

Quickselect helps by reducing the time complexity to O(n) on average, allowing you to find the kth largest element without sorting the entire array.

What happens if the numbers in the array are not unique?

Even if numbers are duplicated, they are counted distinctly. For example, repeated numbers will still occupy their respective largest positions in the order.

terminal

Solution

Solution 1: Sorting or Quickselect

We can sort the strings in the $\textit{nums}$ array in descending order as integers, and then take the $k$-th element. Alternatively, we can use the quickselect algorithm to find the $k$-th largest integer.

1

2

3

class Solution:
    def kthLargestNumber(self, nums: List[str], k: int) -> str:
        return nlargest(k, nums, key=lambda x: int(x))[k - 1]

Continue Practicing

#2343 query kth smallest trimmed number #1738 find kth largest xor coordinate value #973 k closest points to origin