Longest Increasing Subsequence.cpp

/*
Longest Increasing Subsequence
==============================

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


Follow up:
Could you come up with the O(n2) solution?
Could you improve it to O(n log(n)) time complexity?
*/

class Solution
{
public:
  int lengthOfLIS(vector<int> &nums)
  {
    int n = nums.size();
    vector<int> dp(n, 1);

    if (n <= 1)
      return n;

    dp[0] = 1;
    int ans = INT_MIN;

    for (int i = 1; i < n; ++i)
    {
      int maxPrev = 0;
      for (int j = 0; j < i; ++j)
      {
        if (nums[j] < nums[i])
          maxPrev = max(maxPrev, dp[j]);
      }
      dp[i] = maxPrev + 1;
      ans = max(ans, dp[i]);
    }

    return ans;
  }
};