longestIncreasingSubsequence.js

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

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
    -10^4 <= nums[i] <= 10^4

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

/**
 * @param {number[]} nums
 * @return {number}
 */
function lengthOfLIS(nums) {
    // O(n log n) using patience sorting (binary search)
    const tails = [];

    for (const num of nums) {
        let left = 0, right = tails.length;
        while (left < right) {
            const mid = Math.floor((left + right) / 2);
            if (tails[mid] < num) left = mid + 1;
            else right = mid;
        }
        tails[left] = num;
    }
    return tails.length;
}

// Example usage:
console.log(lengthOfLIS([10, 9, 2, 5, 3, 7, 101, 18])); // Output: 4
console.log(lengthOfLIS([0, 1, 0, 3, 2, 3]));           // Output: 4