Arithmetic Slices II - Subsequence
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 a 32-bit integer.
Example 1
Input
nums = [2,4,6,8,10]Output
7There are 7 arithmetic subsequence slices: [2,4,6], [4,6,8], [6,8,10], [2,4,6,8], [4,6,8,10], [2,4,6,8,10], and [2,6,10].
Example 2
Input
nums = [7,7,7,7,7]Output
16Any subsequence of this array with at least three elements is arithmetic, giving 16 total arithmetic subsequences.
Constraints
- 1 <= nums.length <= 1000
- -2^31 <= nums[i] <= 2^31 - 1