300. Longest Increasing Subsequence

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:

• 1 <= nums.length <= 2500
• -104 <= nums[i] <= 104

Follow up:

• Could you come up with the O(n2) solution?
• Could you improve it to O(n log(n)) time complexity?

# @lc code=start
using LeetCode

function length_of_LIS(nums::Vector{Int})
    f = [first(nums)]
    for num in @view(nums[2:end])
        if num > f[end]
            push!(f, num)
        else
            f[searchsortedfirst(f, num)] = num
        end
    end
    length(f)
end
# @lc code=end

length_of_LIS (generic function with 1 method)

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