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Back to ChallengesLongest Increasing Subsequence (LIS)Medium 25 min

Longest Increasing Subsequence (LIS)

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

Examples

Input: nums = [10,9,2,5,3,7,101,18]
Output: 4
The longest increasing subsequence is [2,3,7,101], length 4.
Input: nums = [0,1,0,3,2,3]
Output: 4
The longest increasing subsequence is [0,1,2,3].

Constraints

  • • 1 <= nums.length <= 2500
  • • -10^4 <= nums[i] <= 10^4

Complexity Analysis

Time
O(n^2)
nested loop DP. Note that O(n log n) is possible using binary search.
Space
O(n)
DP array.

Test Cases

#1 Standard LIS
Input: [10,9,2,5,3,7,101,18]
Expected: 4
#2 Array with duplicate values
Input: [0,1,0,3,2,3]
Expected: 4
#3 All identical values
Input: [7,7,7,7,7]
Expected: 1
JavaScript
Output
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