Introduction

In this blog post, we will explore how to solve the LeetCode problem "354" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You are given a 2D array of integers envelopes where envelopes[i] = [wi, hi] represents the width and the height of an envelope. One envelope can fit into another if and only if both the width and height of one envelope are greater than the other envelope's width and height. Return the maximum number of envelopes you can Russian doll (i.e., put one inside the other). Note: You cannot rotate an envelope. Example 1: Input: envelopes = [[5,4],[6,4],[6,7],[2,3]] Output: 3 Explanation: The maximum number of envelopes you can Russian doll is 3 ([2,3] => [5,4] => [6,7]). Example 2: Input: envelopes = [[1,1],[1,1],[1,1]] Output: 1 Constraints: 1 <= envelopes.length <= 105 envelopes[i].length == 2 1 <= wi, hi <= 105

Explanation

Here's a breakdown of the solution:

• Sorting: Sort the envelopes based on width in ascending order. If widths are the same, sort by height in descending order. This is crucial because it ensures that when iterating, if widths are the same, we can't simply pick the envelope with the larger height, it has to be smaller to not violate the Russian doll condition.

• Longest Increasing Subsequence (LIS): After sorting, extract the heights of the envelopes and find the longest increasing subsequence (LIS) of these heights. The length of the LIS represents the maximum number of envelopes that can be Russian dolled.

• Binary Search for LIS: Use binary search to efficiently find the position to insert/update the current height in the LIS tail array.

• Time & Space Complexity:

  • Time Complexity: O(N log N), dominated by sorting and the binary search within the LIS algorithm.
  • Space Complexity: O(N), for storing the sorted envelopes and the tail array for the LIS.

Code

    def maxEnvelopes(envelopes):
    """
    Calculates the maximum number of envelopes that can be Russian dolled.

    Args:
        envelopes: A 2D array of integers where envelopes[i] = [wi, hi] represents the width and height of an envelope.

    Returns:
        The maximum number of envelopes that can be Russian dolled.
    """

    # Sort the envelopes based on width (ascending) and height (descending if widths are equal).
    envelopes.sort(key=lambda x: (x[0], -x[1]))

    # Extract the heights of the envelopes
    heights = [env[1] for env in envelopes]

    # Find the longest increasing subsequence (LIS) of the heights.
    tails = []
    for height in heights:
        # Binary search to find the smallest tail element that is >= current height.
        l, r = 0, len(tails)
        while l < r:
            mid = (l + r) // 2
            if tails[mid] < height:
                l = mid + 1
            else:
                r = mid

        # If no tail element is >= current height, append the current height.
        # Otherwise, update the smallest tail element that is >= current height.
        if l == len(tails):
            tails.append(height)
        else:
            tails[l] = height

    # The length of the LIS is the maximum number of envelopes that can be Russian dolled.
    return len(tails)