Arithmetic Slices Count

Count the number of contiguous subarrays that form an arithmetic sequence.

arrays arithmetic counting subarrays

An arithmetic slice is a contiguous subarray of length at least 3 such that the difference between consecutive elements is constant. For example, [1, 3, 5] and [1, 3, 5, 7] are arithmetic slices, but [1, 3, 6] is not.

Write a function `count_arithmetic_slices(nums)` that takes a list of integers and returns the total number of arithmetic slices that exist in the list.

Note: A subarray is a contiguous part of the original list. The order of the elements must be preserved.

Constraints

0 <= len(nums) <= 10^4; -10^9 <= nums[i] <= 10^9. The answer fits in a 64-bit integer.

Example

>>> count_arithmetic_slices([1, 2, 3, 4])
3
>>> count_arithmetic_slices([1])
0
>>> count_arithmetic_slices([1, 2, 3, 8, 9, 10])
2

15 points ~20 min

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Hints

Scan the array and track the length of the current arithmetic sequence ending at each index.

If the difference between nums[i] and nums[i-1] equals the previous difference, extend the current sequence; otherwise reset.

For a sequence of length n, the number of arithmetic slices ending at the last element is n-2.

Sum the counts as you extend sequences to get the total.

Alternative: for each maximal run of equal differences of length L, add (L-1)*(L-2)//2.

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