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:
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?
Solution
import bisect
class Solution:
def lengthOfLIS(self, nums: List[int]) -> int:
if not nums:
return 0
dp = [float('inf')] * (len(nums) + 1)
dp[0] = float('-inf') # This makes sure we have a valid comparison at dp[1] = min(dp[1], num)
for num in nums:
index = bisect.bisect_left(dp, num, 1) # start searching from index 1
dp[index] = num
# Find the length of the longest increasing subsequence
for i in range(len(dp) - 1, 0, -1):
if dp[i] < float('inf'):
return i
return 0