Longest Increasing Subsequence LeetCode Solution

Problem – Longest Increasing Subsequence

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

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

Longest Increasing Subsequence LeetCode Solution in Java

public int lengthOfLIS(int[] nums) {
    int[] tails = new int[nums.length];
    int size = 0;
    for (int x : nums) {
        int i = 0, j = size;
        while (i != j) {
            int m = (i + j) / 2;
            if (tails[m] < x)
                i = m + 1;
            else
                j = m;
        }
        tails[i] = x;
        if (i == size) ++size;
    }
    return size;
}
// Runtime: 2 ms

Longest Increasing Subsequence LeetCode Solution in Python

def lengthOfLIS(self, nums):
    tails = [0] * len(nums)
    size = 0
    for x in nums:
        i, j = 0, size
        while i != j:
            m = (i + j) / 2
            if tails[m] < x:
                i = m + 1
            else:
                j = m
        tails[i] = x
        size = max(i + 1, size)
    return size

# Runtime: 48 ms

Longest Increasing Subsequence LeetCode Solution in C++

int lengthOfLIS(vector<int>& nums) {
    vector<int> res;
    for(int i=0; i<nums.size(); i++) {
        auto it = std::lower_bound(res.begin(), res.end(), nums[i]);
        if(it==res.end()) res.push_back(nums[i]);
        else *it = nums[i];
    }
    return res.size();
}
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