#3471

Easy

auto_awesomeArray scanning plus hash lookup

LeetCode Problem Workspace

Find the Largest Almost Missing Integer

Find the largest almost missing integer in an array where it appears in exactly one subarray of size k.

Problem Statement

You are given an integer array nums and an integer k. An integer x is almost missing from nums if it appears in exactly one subarray of size k within nums. Your task is to return the largest almost missing integer from nums. If no such integer exists, return -1.

The solution should involve scanning the array and using a hash table to track how many subarrays each integer appears in, while ensuring the algorithm works efficiently for different values of k, including edge cases like k = 1 or k = n.

Examples

Example 1

Input: nums = [3,9,2,1,7], k = 3

Output: 7

We return 7 since it is the largest integer that appears in exactly one subarray of size k .

Example 2

Input: nums = [3,9,7,2,1,7], k = 4

Output: 3

We return 3 since it is the largest and only integer that appears in exactly one subarray of size k .

Example 3

Input: nums = [0,0], k = 1

Output: -1

There is no integer that appears in only one subarray of size 1.

Constraints

1 <= nums.length <= 50
0 <= nums[i] <= 50
1 <= k <= nums.length

Solution Approach

Array Scanning and Hash Table

We scan the array and use a hash table to track the frequency of each integer across all possible subarrays of size k. This enables quick lookups and identification of integers that appear in exactly one subarray.

Handle Edge Cases for k = 1 and k = n

For edge cases where k = 1 or k = n, we adjust the solution to handle these scenarios effectively. For k = 1, we simply check for integers that appear only once in the entire array. For k = n, the entire array is one subarray, so we focus on integers that appear only once in that range.

Finding the Largest Integer

Once we've identified the integers that appear exactly once in a subarray of size k, we return the largest of them. If no such integer exists, we return -1. Sorting or scanning the filtered integers ensures we find the largest one.

Complexity Analysis

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

Time complexity depends on the approach for tracking subarrays and integers, but generally, it involves iterating through the array and checking subarrays, making it O(n * k) in most cases. Space complexity is determined by the hash table, which can store up to n unique elements, making it O(n).

What Interviewers Usually Probe

Candidate demonstrates a good understanding of array scanning and hash tables.
The candidate correctly handles edge cases, particularly when k = 1 or k = n.
The candidate suggests an efficient approach to find the largest integer, showcasing optimal use of data structures.

Common Pitfalls or Variants

Common pitfalls

Not correctly handling edge cases where k = 1 or k = n.
Overcomplicating the solution by using additional data structures or algorithms not needed for this problem.
Failing to efficiently identify the largest almost missing integer due to an incorrect filtering process.

Follow-up variants

Implement a version that returns the smallest almost missing integer.
Extend the problem to allow for larger values of k beyond the constraints.
Modify the problem to find the integer that appears in exactly two subarrays of size k.

FAQ

How do I handle edge cases in this problem?

Edge cases like k = 1 or k = n require special handling. For k = 1, check integers that appear only once in the entire array. For k = n, treat the entire array as a single subarray.

What is the time complexity of this solution?

The time complexity is typically O(n * k), where n is the length of the array and k is the size of the subarrays.

Can I use a different data structure for this problem?

While a hash table is optimal for tracking subarray frequencies, other data structures like arrays or sets could be used with more complexity.

What happens if no integer appears exactly once in a subarray of size k?

If no integer fits this criterion, the correct output is -1, indicating that no almost missing integer was found.

What pattern should I focus on for solving this problem?

The problem pattern involves array scanning combined with hash lookups to efficiently track integer frequencies within subarrays of size k.

terminal

Solution

Solution 1: Case Analysis

If $k = 1$, then each element in the array forms a subarray of size $1$. In this case, we only need to find the maximum value among the elements that appear exactly once in the array.

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class Solution:
    def largestInteger(self, nums: List[int], k: int) -> int:
        def f(k: int) -> int:
            for i, x in enumerate(nums):
                if i != k and x == nums[k]:
                    return -1
            return nums[k]

        if k == 1:
            cnt = Counter(nums)
            return max((x for x, v in cnt.items() if v == 1), default=-1)
        if k == len(nums):
            return max(nums)
        return max(f(0), f(len(nums) - 1))

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