LeetCode 300. Longest Increasing Subsequence (javascript solution)

#algorithms #javascript

Description:

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].

Solution:

Time Complexity : O(n^2)
Space Complexity: O(n)

// Dynamic programming
var lengthOfLIS = function (nums) {
    // Create dp array
    const dp = Array.from(nums, () => 1);
    // Max subsequence length
    let max = 1
    // Check all increasing subsequences up to the current ith number in nums
    for (let i = 1; i < nums.length; i++) {
        // Keep track of subsequence length in the dp array
        for (let j = 0; j < i; j++) {
            // Only change dp value if the numbers are increasing
            if (nums[i] > nums[j]) {
                // Set the value to be the larget subsequence length
                dp[i] = Math.max(dp[i], dp[j] + 1)
                // Check if this subsequence is the largest
                max = Math.max(dp[i], max)
            }
        }
    }
  return max;
};