LeetCode-in-All

300. Longest Increasing Subsequence

Medium

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:

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

Solution

object Solution {
    def lengthOfLIS(nums: Array[Int]): Int = {
        if (nums == null || nums.isEmpty) {
            return 0
        }

        val dp = Array.fill(nums.length + 1)(Int.MaxValue)
        val left = 1
        var right = 1

        for (curr <- nums) {
            var start = left
            var end = right

            while (start + 1 < end) {
                val mid = start + (end - start) / 2
                if (dp(mid) > curr) {
                    end = mid
                } else {
                    start = mid
                }
            }

            if (dp(start) > curr) {
                dp(start) = curr
            } else if (curr > dp(start) && curr < dp(end)) {
                dp(end) = curr
            } else if (curr > dp(end)) {
                dp(end + 1) = curr
                right += 1
            }
        }

        right
    }
}