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

class Solution {
    func lengthOfLIS(_ nums: [Int]) -> Int {
        if nums.isEmpty {
            return 0
        }

        var dp = [Int](repeating: Int.max, count: nums.count + 1)
        dp[0] = Int.min
        var length = 0

        for num in nums {
            var left = 0
            var right = length
            while left <= right {
                let mid = left + (right - left) / 2
                if dp[mid] < num {
                    left = mid + 1
                } else {
                    right = mid - 1
                }
            }
            dp[left] = num
            if left > length {
                length = left
            }
        }

        return length
    }
}