354. Russian Doll Envelopes

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354. Russian Doll Envelopes

Description

Difficulty: Hard

Related Topics: Array, Binary Search, Dynamic Programming, Sorting

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:

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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:

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Input: envelopes = [[1,1],[1,1],[1,1]]
Output: 1

Constraints:

  • 1 <= envelopes.length <= 105
  • envelopes[i].length == 2
  • 1 <= wi, hi <= 105

Hints/Notes

  • dp
  • sort the w in order but h reversely

Solution

Language: C++

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class Solution {
public:
    int maxEnvelopes(vector<vector<int>>& envelopes) {
        auto cmp = [](vector<int> lhs, vector<int> rhs) {
            if (lhs[0] != rhs[0]) {
                return lhs[0] < rhs[0];
            }
            return lhs[1] > rhs[1];
        };
        sort(envelopes.begin(), envelopes.end(), cmp);
        int res = 0;
        vector<int> dp(envelopes.size(), 1);
        for (int i = 0; i < envelopes.size(); i++) {
            for (int j = 0; j < i; j++) {
                if (envelopes[i][1] > envelopes[j][1]) {
                    dp[i] = max(dp[i], dp[j] + 1);
                }
            }
            res = max(res, dp[i]);
        }
        return res;
    }
};