Class

KthSmallestSquareFinder

Method

Find Kth Smallest Square

long kthSmallestSquare(List<Integer> nums, int k)

• Returns the kth smallest square value formed from the elements of nums.
• The list nums is sorted in non-decreasing order.
• Each index contributes one square value, so duplicate values are counted multiple times.

Input

• nums: A sorted list of integers.
• k: The 1-based position of the square value to return after sorting all square values.

Output

• Return a long representing the kth smallest square value.

Constraints

• 1 ≤ nums.size() ≤ 100,000
• -1,000,000,000 ≤ nums[i] ≤ 1,000,000,000
• nums[i] ≤ nums[i + 1] for every valid index i
• 1 ≤ k ≤ nums.size()

Deterministic Rules

• Square values are compared by numeric value.
• If the same square value appears multiple times, every occurrence is counted separately.
• The answer is the value present at position k after sorting all square values in non-decreasing order.

Examples

Example 1

kthSmallestSquare(nums = List.of(-6, -4, -1, 3, 5), k = 2)

• Square values are 36, 16, 1, 9, 25.
• After sorting them, we get 1, 9, 16, 25, 36.
• The 2nd smallest square is 9.

Output: 9

Example 2

kthSmallestSquare(nums = List.of(-5, -2, -2, 0, 4), k = 4)

• Square values are 25, 4, 4, 0, 16.
• After sorting them, we get 0, 4, 4, 16, 25.
• The 4th smallest square is 16.

Output: 16

Example 3

kthSmallestSquare(nums = List.of(-3, -3, 3, 3), k = 3)

• Every element has square value 9.
• Duplicate square values are counted separately.
• The 3rd smallest square is 9.

Output: 9