Asked in: UBER
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Solution
def findMaxTeamSize(skills):
ans = 1
skills.sort()
i = 0
// ... rest of solution available after purchaseExplanation
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To approach this problem, start by understanding the core requirement: forming the largest possible team where, after sorting the skill levels, the difference between any two consecutive members is either 0 or 1. This means the skill levels in the team form a sequence of integers where each next skill is at most one greater than the previous. Duplicates are allowed because a difference of 0 between consecutive elements is acceptable.
Step 1: Sort the Skills
The first logical step is to sort the array of skill levels in non-decreasing order. Sorting arranges the students in ascending order of skill, making it easier to identify consecutive runs where the difference between neighbors is 0 or 1.
Step 2: Identify Consecutive Runs
Once sorted, examine the skill levels from left to right, trying to find the longest contiguous subsequence where the difference between any adjacent elements is either 0 or 1.
For example, if you see a sequence like [2, 3, 3, 4], the differences are 1, 0, and 1, all valid, so this entire segment could form a valid team.
Step 3: Track Team Sizes While Scanning
Use two pointers or variables to keep track of the current team being evaluated. One pointer marks the start of the current run, and the other moves forward as you scan through the array.
If the difference between the current element and the previous one is more than 1, that means the run is broken. You finalize the current team size (distance between pointers) and start a new run from the current element.
Keep updating the maximum team size found so far with the size of the current valid run.
Step 4: Consider Edge Cases with Duplicates and Large Gaps
Since differences of 0 are allowed, duplicates extend the run. For example, [9, 9, 10] is valid with consecutive differences 0 and 1.
If a difference greater than 1 appears, you must end the current team and begin a new one.
Step 5: Handle Large Input Size Efficiently
Given constraints up to 10^5 elements, an O(n log n) solution is acceptable because sorting dominates. The scanning step is O(n), which is efficient enough.
Step 6: Alternative Approaches to Consider
- Frequency Map Approach:
You can also think of using a frequency map to count occurrences of each skill level, then iterate over sorted keys of this map and check the sum of counts for adjacent skill levels (skill and skill+1) to find the largest combined count. This is based on the observation that the team can be formed from skills that differ by 0 or 1, so combining frequencies of skill i and i+1 might yield the largest team.
- Sliding Window Approach:
Treat the problem as finding the longest subarray where max(skill) - min(skill) ≤ 1. Since the array is sorted, the difference between the first and last element in a window is easy to compute, and you can slide the window to find the largest valid segment.
Step 7: Summarize the Approach
- Sort the skills array.
- Iterate through the sorted list and find consecutive segments where differences between consecutive elements are at most 1.
- Track and update the maximum length of such segments.
- Return the maximum length as the size of the largest valid team.
By following these steps, you ensure that you consider all possible teams meeting the criteria and efficiently find the maximum possible size.
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