## Algorithm

Problem Name: 354. Russian Doll Envelopes

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`

## Code Examples

### #1 Code Example with C++ Programming

```Code - C++ Programming```

``````
class Solution {
public:
int maxEnvelopes(vector<pair<int, int>>& envelopes) {
sort(envelopes.begin(), envelopes.end(), [](pair < int, int>& p1, pair<int, int>& p2){
return p1.first == p2.first ? p1.second > p2.second : p1.first < p2.first;
});
vector<int>dp;
for(auto x: envelopes){
int pos = lower_bound(dp.begin(), dp.end(), x.second) - dp.begin();
if(pos == dp.size()) dp.push_back(x.second);
else dp[pos] = x.second;
}
return dp.size();
}
};
``````
Copy The Code &

Input

cmd
envelopes = [[5,4],[6,4],[6,7],[2,3]]

Output

cmd
3

### #2 Code Example with Javascript Programming

```Code - Javascript Programming```

``````
const maxEnvelopes = function(envelopes) {
const env = envelopes
env.sort((a, b) => a[0] - b[0] || b[1] - a[1])
const stk = []
for(const e of env) {
if(stk.length === 0 || e[1] > stk[stk.length - 1][1]) {
stk.push(e)
continue
}
let l = 0, r = stk.length - 1
while(l < r) {
const mid = l + Math.floor((r - l) / 2)
if(stk[mid][1]  <  e[1]> l = mid + 1
else r = mid
}

stk[l] = e
}

return stk.length
};
``````
Copy The Code &

Input

cmd
envelopes = [[5,4],[6,4],[6,7],[2,3]]

Output

cmd
3

### #3 Code Example with Python Programming

```Code - Python Programming```

``````
class Solution:
def maxEnvelopes(self, envelopes):
tails = []
for w, h in sorted(envelopes, key = lambda x: (x[0], -x[1])):
i = bisect.bisect_left(tails, h)
if i == len(tails): tails.append(h)
else: tails[i] = h
return len(tails)
``````
Copy The Code &

Input

cmd
envelopes = [[1,1],[1,1],[1,1]]

Output

cmd
1