Arithmetic Slices

Arithmetic Slices

What is this problem about?

The Arithmetic Slices interview question asks you to find the number of "arithmetic slices" in an array. An arithmetic slice is a contiguous subarray of at least three elements where the difference between consecutive elements is constant. For example, [1, 2, 3, 4] is an arithmetic slice because the difference is always 1. This Arithmetic Slices coding problem focuses on identifying patterns in sequences.

Why is this asked in interviews?

Companies like Microsoft and Amazon ask this to test a candidate's ability to optimize a sequence-counting problem. While a brute-force approach exists, the most efficient solution uses Dynamic Programming or a simple counter to track the current "streak" of arithmetic progression, which demonstrates an ability to avoid O(N^2) solutions in favor of O(N).

Algorithmic pattern used

This problem is solved using the Array, Sliding Window, Dynamic Programming interview pattern. You iterate through the array, comparing the difference between the current two elements with the difference between the previous two. If they match, you've extended an arithmetic sequence.

Example explanation

Consider the array [1, 3, 5, 7, 10, 13].

1. Differences: (3-1)=2, (5-3)=2, (7-5)=2, (10-7)=3, (13-10)=3.
2. The first four elements [1, 3, 5, 7] have a constant difference of 2. This creates slices: [1, 3, 5], [3, 5, 7], and [1, 3, 5, 7]. (Total 3).
3. The last three elements [7, 10, 13] have a constant difference of 3. This creates slice: [7, 10, 13]. (Total 1). The final answer is 3 + 1 = 4.

Common mistakes candidates make

• Ignoring Length Constraint: Forgetting that a slice must have at least three elements.
• Overcounting: Miscalculating how many new slices are formed when an arithmetic sequence is extended by one element.
• Subarrays vs Subsequences: Confusing "contiguous slices" with "subsequences" (which don't have to be contiguous).

Interview preparation tip

When you need to count contiguous subarrays that satisfy a property, try to find a formula for how the count increases when the property is maintained for an extra element. For arithmetic slices, if you have a streak of k differences, adding one more matching difference adds k new slices.