Arithmetic Slices - Leetcode Solution

Problem Statement:

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, these are arithmetic sequences:

1, 3, 5, 7, 9 7, 7, 7, 7 3, -1, -5, -9 The following sequence is not arithmetic.

1, 1, 2, 5, 7

A zero-indexed array A consisting of N numbers is given. A slice of that array is any pair of integers (P, Q) such that 0 ≤ P < Q < N.

A slice (P, Q) of the array A is called arithmetic if the sequence: A[P], A[P+1], ..., A[Q-1], A[Q] is arithmetic. In particular, this means that P + 1 < Q.

The function should return the number of arithmetic slices in the array A.

Example:

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

Solution:

The solution to this problem requires counting all arithmetic slices in an array A. To achieve this, we start by using a variable count to keep track of the number of arithmetic series present. We then loop through the array A, checking every P-Q slice in the array to see if it forms an arithmetic series.

To check if a slice is an arithmetic series, we compare the differences between neighboring elements. For any 0 <= P <= Q < N, if A[P+2] - A[P+1] is equal to A[P+1] - A[P], then we increment count by 1. This is because there is a new arithmetic series present.

The solution has a time complexity of O(N) and a space complexity of O(1).

Pseudo code:

initialize the count to 0 initialize a variable P to 0 for Q in range(2, N): if A[Q] - A[Q-1] == A[Q-1] - A[Q-2]: increment the count by P increment P by 1 else: set P to 0 return the count

Explanation:

The solution first initializes the count variable to 0 to keep track of the number of arithmetic slices. We then proceed to initialize variable P to 0. We loop through the array A, checking every P-Q slice in the array to see if it forms an arithmetic series.

We do this by comparing the differences between neighboring elements. If the difference is the same, then we increment the count variable by P. This is because we have a new arithmetic series, and all previously checked slices will also form arithmetic series.

If they are not equal, then the slice does not form an arithmetic series, and we reset P to 0. After looping through all the slices, we return the count variable.

1