300. Longest Increasing Subsequence

Medium (Trung bình) Python 🔗 Xem trên LeetCode

📋 Đề Bài

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

 

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?

🧠 Thuật Toán & Kỹ Thuật

Dynamic Programming (Quy hoạch động)
⏱️ Thời gian O(n²)
💾 Không gian O(n)

💻 Lời Giải

Python 0300-longest-increasing-subsequence.py
class Solution:
    def lengthOfLIS(self, nums: List[int]) -> int:
        n = len(nums)
        dp = [1 for _ in range(n)]
        ans = 1
        
        for i in range(1, n):
            for j in range(i):
                if nums[j] < nums[i]:
                    dp[i] = max(dp[i], dp[j] + 1)
            ans = max(ans, dp[i])
            
        return ans