413. Arithmetic Slices

Medium

3710

245

Add to List

Share

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 1: Bottom up DP

• Let dp[i] denote the number of arithmetic subarray ends at nums[i].
• If if nums[i-1] - nums[i-2] == nums[i] - nums[i-1] then we can form the Arithmetic subarray ends at nums[i].
  • So dp[i] = dp[i-1] + 1.