Arithmetic Slices

An integer array 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.

Given an integer array nums, return the number of arithmetic subarrays of nums.

A subarray is a contiguous subsequence of the array.

Example 1:

Input: nums = [1,2,3,4]
Output: 3
Explanation: We have 3 arithmetic slices in nums: [1, 2, 3], [2, 3, 4] and [1,2,3,4] itself.

Example 2:

Input: nums = [1]
Output: 0

Constraints:

• 1 <= nums.length <= 5000
• -1000 <= nums[i] <= 1000

SOLUTION:

class Solution:
    def numSlicesEndingHere(self, nums, i, n):
        if i in self.cache:
            return self.cache[i]
        if i < 2:
            return 0
        if i == 2:
            if nums[2] - nums[1] == nums[1] - nums[0]:
                self.cache[i] = 1
                return 1
            self.cache[i] = 0
            return 0
        if nums[i] - nums[i - 1] == nums[i - 1] - nums[i - 2]:
            val = 1 + self.numSlicesEndingHere(nums, i - 1, n)
            self.cache[i] = val
            return val
        self.cache[i] = 0
        return 0

    def numberOfArithmeticSlices(self, nums: List[int]) -> int:
        n = len(nums)
        self.cache = {}
        ctr = 0
        for i in range(n):
            ctr += self.numSlicesEndingHere(nums, i, n)
        return ctr