Arithmetic Slices II - Subsequence

arraydynamic programming

Problem Statement

Given an integer array nums , return the number of all the arithmetic subsequences of nums .

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, [1, 3, 5, 7, 9] , [7, 7, 7, 7] , and [3, -1, -5, -9] are arithmetic sequences.

For example, [1, 1, 2, 5, 7] is not an arithmetic sequence.

A subsequence of an array is a sequence that can be formed by removing some elements (possibly none) of the array.

For example, [2,5,10] is a subsequence of [1,2,1, 2 ,4,1, 5 , 10 ] .

The test cases are generated so that the answer fits in 32-bit integer.

Examples

Example 1

Input: nums = [2,4,6,8,10]
Output: 7
All arithmetic subsequence slices are:
[2,4,6]
[4,6,8]
[6,8,10]
[2,4,6,8]
[4,6,8,10]
[2,4,6,8,10]
[2,6,10]

Example 2

Input: nums = [7,7,7,7,7]
Output: 16
Any subsequence of this array is arithmetic.

Constraints

1 <= nums.length <= 1000

-2 ^31 <= nums[i] <= 2 ^31 - 1

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming