Find kth missing integer and redundant operations

You are given two independent coding tasks.

Task 1: K-th missing number

You are given an integer array nums (not necessarily sorted) containing distinct positive integers, and an integer k.

Define the missing numbers as the positive integers that do not appear in nums.

Return the k-th smallest missing positive integer.

Constraints (representative of an “optimal required” setting):

• 1 <= n <= 2e5
• 1 <= nums[i] <= 1e9 (distinct)
• 1 <= k <= 1e9

Example:

• nums = [2, 3, 7, 11], k = 5
• Missing positives are 1, 4, 5, 6, 8, 9, 10, 12, ...
• Answer: 8

Task 2: Count redundant operations within a time window

You are given two arrays of equal length ops[] and times[] describing a log of events, where:

• ops[i] is a string operation name (e.g., "login" , "refresh" )
• times[i] is the event time as an integer timestamp (seconds)

You are also given an integer window size W (seconds).

An event at index i is considered redundant if there exist two earlier events j < k < i such that:

• ops[j] == ops[k] == ops[i]
• times[i] - times[j] <= W (i.e., 3 occurrences of the same operation happen within a W -second window ending at times[i] )

Return the total number of redundant events in the log.

Assumptions/notes:

• The input may not be sorted; you may sort by time if needed.
• If multiple events share the same timestamp, treat earlier indices as earlier events.

Example:

• ops = ["A","B","A","A","A"], times = [1,2,3,4,10], W = 5
• The event at time 4 is redundant because A occurred at times 1,3,4 within 5 seconds.
• The event at time 10 is not redundant for window W=5 .
• Answer: 1