300. Longest Increasing Subsequence

Question

Given an unsorted array of integers, find the length of longest increasing subsequence.

For example,
Given [10, 9, 2, 5, 3, 7, 101, 18],
The longest increasing subsequence is [2, 3, 7, 101], therefore the length is 4. Note that there may be more than one LIS combination, it is only necessary for you to return the length.

Your algorithm should run in O(n2) complexity.

Follow up: Could you improve it to O(n log n) time complexity?

Solution

dp[i] means the length of an increase sequence that includes nums[i], and it must equals a previous dp value add one which reaches the max.

class Solution(object):
    def lengthOfLIS(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        dp = [1]*len(nums)
        for i in xrange(len(nums)):
            for y in xrange(i):
                if nums[i] >nums[j]:
                    dp[i] = max(dp[i],dp[j]+1)
        return max(dp) if dp else 0