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[11/27] 446. Arithmetic Slices II - Subsequence

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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.

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.

 

Example 1:

Input: nums = [2,4,6,8,10]
Output: 7
Explanation: All arithmetic subsequence slices are:
[2,4,6]
[4,6,8]
[6,8,10]
[2,4,6,8]
[4,6,8,10]
[2,4,6,8,10]
[2,6,10]

Example 2:

Input: nums = [7,7,7,7,7]
Output: 16
Explanation: Any subsequence of this array is arithmetic.

 

Constraints:

  • 1  <= nums.length <= 1000
  • -231 <= nums[i] <= 231 - 1
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Runtime: 3267 ms, faster than 24.85% of Python3 online submissions for Arithmetic Slices II - Subsequence.
Memory Usage: 185.7 MB, less than 14.20% of Python3 online submissions for Arithmetic Slices II - Subsequence.
from collections import defaultdict
class Solution:
    def numberOfArithmeticSlices(self, nums: List[int]) -> int:
        dp = defaultdict(int)
        res = 0
        
        for e in range(1, len(nums)):
            for s in range(e):
                diff = nums[e] - nums[s]
                res += dp[(s, diff)]
                dp[(e, diff)] += dp[(s,diff)] + 1
        
        return res
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