arithmetic_slices_ii_subsequence.py

'''
Given an integer array nums, return the number of all the arithmetic subsequences of nums.

A sequence of numbers is called arithmetic if it consists of at least three elements and if the difference between any two consecutive elements is the same.

For example, [1, 3, 5, 7, 9], [7, 7, 7, 7], and [3, -1, -5, -9] are arithmetic sequences.
For example, [1, 1, 2, 5, 7] is not an arithmetic sequence.
A subsequence of an array is a sequence that can be formed by removing some elements (possibly none) of the array.

For example, [2,5,10] is a subsequence of [1,2,1,2,4,1,5,10].
The test cases are generated so that the answer fits in 32-bit integer.
'''


"""https://leetcode.com/problems/arithmetic-slices-ii-subsequence/"""
from collections import defaultdict


class Solution:
    def numberOfArithmeticSlices(self, nums: List[int]) -> int:
        if len(nums) <= 2:
            return 0
        dp = [defaultdict(int) for _ in range(len(nums))]
        ans = 0
        for i in range(len(nums)):
            for j in range(i):
                diff = nums[i] - nums[j]
                ans += dp[j][diff]
                dp[i][diff] += (dp[j][diff] + 1)

        return ans