<p>You are given a 2D array of integers <code>envelopes</code> where <code>envelopes[i] = [w<sub>i</sub>, h<sub>i</sub>]</code> represents the width and the height of an envelope.</p>

<p>One envelope can fit into another if and only if both the width and height of one envelope are greater than the other envelope&#39;s width and height.</p>

<p>Return <em>the maximum number of envelopes you can Russian doll (i.e., put one inside the other)</em>.</p>

<p><strong>Note:</strong> You cannot rotate an envelope.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> envelopes = [[5,4],[6,4],[6,7],[2,3]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The maximum number of envelopes you can Russian doll is <code>3</code> ([2,3] =&gt; [5,4] =&gt; [6,7]).
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> envelopes = [[1,1],[1,1],[1,1]]
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= envelopes.length &lt;= 10<sup>5</sup></code></li>
	<li><code>envelopes[i].length == 2</code></li>
	<li><code>1 &lt;= w<sub>i</sub>, h<sub>i</sub> &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution {
static bool comp(vector<int> &a, vector<int> &b){
        if(a[0]==b[0]){
            return a[1]>b[1];
        }
        return a[0]<b[0];
    }

public:
    int maxEnvelopes(vector<vector<int>>& envelopes) {
        sort(envelopes.begin(), envelopes.end(), comp);
        int n = envelopes.size();
        vector<int> lis;

        for (int i = 0; i < n; i++) {
            if (i == 0 || envelopes[i][1] > lis.back()) lis.push_back(envelopes[i][1]);
            else {
                int idx = findIdx(lis, envelopes[i][1]);
                lis[idx] = envelopes[i][1];
            }
        }
        return lis.size();
    }

    int findIdx(vector<int> lis, int num) {
        int s = 0, e = lis.size() - 1, res = -1;

        while (s <= e) {
            int mid = s + (e-s) / 2;

            if (lis[mid] >= num) {
                res = mid;
                e = mid - 1;
            } else {
                s = mid + 1;
            }
        }

        return res;
    }
};
210628