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Problem solution · C++

Russian Doll Envelopes

Russian Doll Envelopes: a C++ solution using binary search. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Binary search
Source
walkccc LeetCode Solutions
Length
35 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Binary search

For Russian Doll Envelopes, the implementation exploits a monotonic condition to discard half of the remaining search space after every check.

  1. Identify the ordered answer range or sorted search domain.
  2. Write a predicate whose truth changes only once.
  3. Move the appropriate boundary after each midpoint check and return the final feasible position.

Code notes

  • 35 lines of C++ from the credited upstream file 354.cpp.
  • The implementation visibly relies on sequence storage.
  • 1 loop block detected.

Complexity

Multiply the logarithmic number of midpoint checks by the cost of one predicate evaluation.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeRussian Doll Envelopes · C++C++
Use this to learn the idea, then write your own version.
class Solution { public:  int maxEnvelopes(vector<vector<int>>& envelopes) {    ranges::sort(envelopes, ranges::less{}, [](const vector<int>& envelope) {      const int w = envelope[0];      const int h = envelope[1];      return pair<int, int>{w, -h};    });    return lengthOfLIS(envelopes);  }  private:  // Same to 300. Longest Increasing Subsequence  int lengthOfLIS(vector<vector<int>>& envelopes) {    // tails[i] := the minimum tail of all the increasing subsequences having    // length i + 1    vector<int> tails;     for (const vector<int>& envelope : envelopes) {      const int h = envelope[1];      if (tails.empty() || h > tails.back())        tails.push_back(h);      else        tails[firstGreaterEqual(tails, h)] = h;    }     return tails.size();  }  private:  int firstGreaterEqual(const vector<int>& arr, int target) {    return ranges::lower_bound(arr, target) - arr.begin();  }};

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