LC300.cpp

/*
300. Longest Increasing Subsequence

Given an unsorted array of integers, find the length of longest increasing subsequence.

Example:

Input: [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. 
Note:

There may be more than one LIS combination, it is only necessary for you to return the length.
Your algorithm should run in O(n2) complexity.
Follow up: Could you improve it to O(n log n) time complexity?
*/

class Solution 
{
public:
    int lengthOfLIS(vector<int> &nums) 
    {
        vector<int> dp;
        
        for (auto num:nums) 
        {
            auto maxOfNum = lower_bound(dp.begin(), dp.end(), num);
            
            if (maxOfNum != dp.end())
            {
                *maxOfNum = num;
            } 
            else 
            {
                dp.push_back(num);
            }
        }
        
        return dp.size();
    }
};