# 300. Longest Increasing Subsequence

#### Medium

***

Given an integer array `nums`, return the length of the longest strictly increasing subsequence.

A **subsequence** is a sequence that can be derived from an array by deleting some or no elements without changing the order of the remaining elements. For example, `[3,6,2,7]` is a subsequence of the array `[0,3,1,6,2,2,7]`.

 

**Example 1:**

```
Input: nums = [10,9,2,5,3,7,101,18]
Output: 4
Explanation: The longest increasing subsequence is [2,3,7,101], therefore the length is 4.
```

**Example 2:**

```
Input: nums = [0,1,0,3,2,3]
Output: 4
```

**Example 3:**

```
Input: nums = [7,7,7,7,7,7,7]
Output: 1
```

 

**Constraints:**

* `1 <= nums.length <= 2500`
* `-104 <= nums[i] <= 104`

&#x20;

**Follow up:** Can you come up with an algorithm that runs in `O(n log(n))` time complexity?

This solution has been done using : <https://en.wikipedia.org/wiki/Patience_sorting>

PDF : <https://drive.google.com/file/d/173u84oR_iZEIpd4YNx2UeAf8ImbdJgxu/view?usp=sharing>

```python
class Solution:
    def lengthOfLIS(self, nums: List[int]) -> int:
        # Patience Algorithm
        # O(nlogn)
        piles = [0]*len(nums)
        size = 0
        for num in nums:
            left, right = 0, size
            while left < right:
                mid = (left+right) //2
                if piles[mid] < num:
                    left = mid+1
                else:
                    right = mid
            piles[left] = num
            size = max(left+1, size)
        return s
```