Build the Largest Available Sequence

Problem Statement

You are given an array of integers nums and an integer k. You need to construct a sequence of length k by repeatedly picking the largest available integer from nums.

However, there is a constraint: you cannot pick the same integer more than limit times consecutively. Specifically, if you have already picked the same integer limit times in a row, the next element in your sequence must be a different integer from the remaining available numbers. If no other integers are available to break the sequence, the construction stops.

Write a function constructLargestSequence(nums, k, limit) that returns the lexicographically largest sequence of length k. If it is impossible to construct a sequence of length k, return an empty list.

Function Signature

def constructLargestSequence(nums: List[int], k: int, limit: int) -> List[int]:

Examples

Example 1: Input: nums = [4, 4, 3, 3, 3], k = 4, limit = 2 Output: [4, 4, 3, 3] Explanation: We pick two 4s, then we are forced to pick a 3. We pick two 3s, and we have reached length 4.

Example 2: Input: nums = [5, 5, 5, 2], k = 3, limit = 1 Output: [5, 2, 5] Explanation: We pick 5, then are forced to pick 2, then we can pick 5 again.

Constraints

• 1 <= k <= len(nums) <= 10^5
• 1 <= limit <= len(nums)
• nums elements are between 1 and 10^6.