Problem Description
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. Given an integer array nums, return the number of arithmetic subarrays of nums. A subarray is a contiguous subsequence of the array.
Key Insights
- An arithmetic subarray must have at least three elements.
- The difference between consecutive elements in an arithmetic subarray remains constant.
- We can utilize a dynamic programming approach to count the number of valid subarrays efficiently.
- By iterating through the array, we can track the length of the current arithmetic sequence and calculate the number of subarrays that can be formed from it.
Space and Time Complexity
Time Complexity: O(n), where n is the length of the array nums.
Space Complexity: O(1), as we are using a constant amount of space for variables.
Solution
To solve the problem, we can use a dynamic programming approach where we maintain a count of the current length of an arithmetic subarray. We iterate through the array, and whenever we find that the difference between two consecutive elements is the same as the previous difference, we increase the length of the current arithmetic subarray. For every valid length greater than or equal to 3, we can calculate the number of subarrays that can be formed from that length.