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

public class Solution {
    public int LengthOfLIS(int[] nums) {
        if (nums == null || nums.Length == 0) {
            return 0;
        }
        int[] dp = new int[nums.Length + 1];
        // prefill the dp table
        for (int i = 1; i < dp.Length; i++) {
            dp[i] = int.MaxValue;
        }
        int left = 1;
        int right = 1;
        foreach (int curr in nums) {
            int start = left;
            int end = right;
            // binary search, find the one that is lower than curr
            while (start + 1 < end) {
                int mid = start + (end - start) / 2;
                if (dp[mid] > curr) {
                    end = mid;
                } else {
                    start = mid;
                }
            }
            // update our dp table
            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] = curr;
                right++;
            }
        }
        return right;
    }
}