Find Length of Longest Increasing Subsequence in Python

Suppose we have a list of numbers. We have to find the length of longest increasing subsequence. So if the input is like [6, 1, 7, 2, 8, 3, 4, 5], then the output will be 5, as the longest increasing subsequence is [2,3,4,5,6].

To solve this, we will follow these steps −

• Make an array called tails whose size is same as nums, and fill this with 0.

• size := 0

• for each element x in nums array −

  • i := 0, j := size

  • while i is not same as j, then

    • mid := i + (j – i)/2

    • if tails[mid] < x, then i := mid + 1 otherwise j := mid

  • tails[i] := x

  • size := max ofi + 1 and size

• return size.

Let us see the following implementation to get better understanding −

Example

class Solution(object):
   def solve(self, nums):
      tails =[0 for i in range(len(nums))]
      size = 0
      for x in nums:
         i=0
         j=size
         while i!=j:
            mid = i + (j-i)//2
            if tails[mid]> x:
               i= mid+1
            else:
               j = mid
         tails[i] = x
         size = max(i+1,size)
      return size

ob = Solution()
nums = [7, 2, 8, 3, 9, 4, 5, 6]
print(ob.solve(nums))

Input

[7, 2, 8, 3, 9, 4, 5, 6]

Output

5