How do you solve Russian Doll Envelopes on LeetCode?

Russian Doll Envelopes (LeetCode #354) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Sorting envelopes by width and height helps in reducing the complexity of finding the longest increasing subsequence.

What is the brute force solution for Russian Doll Envelopes?

The brute force approach for Russian Doll Envelopes is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible pair of envelopes to see if one can fit into another. This is simple but inefficient as it requires comparing each envelope with every other envelope. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Russian Doll Envelopes?

Russian Doll Envelopes uses the following concepts: Array, Binary Search, Dynamic Programming, Sorting. The recommended patterns to study are: Dynamic Programming, Binary Search, Sorting.

What are the interview tips for Russian Doll Envelopes?

Always clarify the problem constraints and edge cases before diving into coding. Think about how sorting can simplify the problem — it’s a common technique in many DSA problems. Practice explaining your thought process while coding; it helps in interviews.

What are common mistakes when solving Russian Doll Envelopes?

Students often forget to sort the envelopes correctly, especially handling the case when widths are equal. Confusing the conditions for fitting envelopes can lead to incorrect comparisons.

#354

Russian Doll Envelopes

Hard

ArrayBinary SearchDynamic ProgrammingSortingDynamic ProgrammingBinary SearchSorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(n)

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Intuition

Time O(n log n)Space O(n)

The optimal solution involves sorting the envelopes and then applying a dynamic programming approach to find the longest increasing subsequence based on height. This is efficient because it reduces the problem to a well-known algorithm.

⚙️

Algorithm

3 steps

1Step 1: Sort the envelopes by width in ascending order. If widths are the same, sort by height in descending order.
2Step 2: Extract the heights from the sorted envelopes.
3Step 3: Use a dynamic programming approach (or binary search) to find the length of the longest increasing subsequence of heights.

solution.py16 lines

1# Full working Python code
2import bisect
3
4def maxEnvelopes(envelopes):
5    envelopes.sort(key=lambda x: (x[0], -x[1]))
6    dp = []
7    for _, h in envelopes:
8        pos = bisect.bisect_left(dp, h)
9        if pos == len(dp):
10            dp.append(h)
11        else:
12            dp[pos] = h
13    return len(dp)
14
15# Example usage
16print(maxEnvelopes([[5,4],[6,4],[6,7],[2,3]]))

ℹ

Complexity note: The sorting step takes O(n log n) time, and finding the longest increasing subsequence using binary search takes O(n log n) as well, leading to an overall complexity of O(n log n).

1Sorting envelopes by width and height helps in reducing the complexity of finding the longest increasing subsequence.
2Using binary search to maintain the longest increasing subsequence allows us to efficiently find the position to replace or append heights.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.