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# LeetCode 300. Longest Increasing Subsequence (javascript solution)

### 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;
};
``````

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