300. Longest Increasing Subsequence

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300. Longest Increasing Subsequence

Description

Difficulty: Medium

Related Topics: Array, Binary Search, Dynamic Programming

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

Example 1:

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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:

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Input: nums = [0,1,0,3,2,3]
Output: 4

Example 3:

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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?

Hints/Notes

Solution

Language: C++

nlogn solution:

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class Solution {
public:
    int lengthOfLIS(vector<int>& nums) {
        vector<int> res;
        for (int num : nums) {
            if (res.empty() || num > res.back()) {
                res.push_back(num);
            } else {
                auto it = ranges::lower_bound(res, num);
                *it = num;
            }
        }
        return res.size();
    }
};
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class Solution {
public:
    int lengthOfLIS(vector<int>& nums) {
        vector<int> res(nums.size(), 1);
        int longest = 0;
        for (int i = 0; i < nums.size(); i++) {
            for (int j = 0; j < i; j++) {
                if (nums[j] < nums[i]) {
                    res[i] = max(res[i], res[j] + 1);
                }
            }
            longest = max(longest, res[i]);
        }
        return longest;
    }
};