Longest Increasing Subsequence Program (Leetcode)

Longest Increasing Subsequence Program (Leetcode):

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?

1) O(n^2)

if len(nums) == 0:
    return 0

length = [1 for i in range(len(nums))]        
for i in range(len(nums)):
    for j in range(i):
        if nums[j] < nums[i] and length[j] + 1 > length[i]:
            length[i] = length[j] + 1
                    
return (max(length))

2)O(n log(n))

def binarySearch(start, end, val, nums, index):
    if start > end:
        return start
    mid = (start + end) // 2
    if nums[index[mid]] < val:
        start = mid + 1
    else:
        end = mid - 1
        
    return binarySearch(start, end, val, nums, index)

size = 0
index = [None for i in range(len(nums) + 1)]
for i in range(len(nums)):
        val = nums[i]
        bin_val = binarySearch(1, size, val, nums, index)
        index[bin_val] = i
        size = max(size, bin_val)
        #print(index)

return size