Leetcode 673. Number of Longest Increasing Subsequence

Problem

Given an integer array nums, return the number of longest increasing subsequences.

Notice that the sequence has to be strictly increasing.

Algorithm

Dynamic Programming (DP). Use to lists dp_L[i] and dp_N[i] to save the length and size of longest increasing subsequences of the first i items. Then sum all the items with the longest length.

Code

class Solution:
    def findNumberOfLIS(self, nums: List[int]) -> int:
        nlen = len(nums)
        dp_L = [1] * nlen
        dp_N = [1] * nlen
        for i in range(1, nlen):
            dp_L[i] = 1
            dp_N[i] = 1
            for j in range(i):
                if nums[j] < nums[i]:
                    if dp_L[i] == dp_L[j] + 1:
                        dp_N[i] += dp_N[j]
                    if dp_L[i] <= dp_L[j]:
                        dp_L[i] = dp_L[j] + 1
                        dp_N[i] =  dp_N[j]
        
        ans = 0
        max_l = max(dp_L)
        for i in range(nlen):
            if max_l == dp_L[i]:
                ans += dp_N[i]
        return ans