Find all Arithmetic series of length greater than two

Overview

An Arithmetic series is a series in which the difference between each element is equal. In this program, an array of integers is given. The objective is to find all arithmetic series greater than two.

The problem is best understood with an example

Examples

Input: [2,3,4,5]
Output: 3

We have three arithmetic slices of length greater than 2 in the above array

2,3,4

3,4,5

2,3,4,5

It is a dynamic programming question as it has an optimal substructure. Let’s say the name of the array is input

dp[0] = 0

dp[1] = 0

dp[2] = 1 if dp[2] – dp[1] == dp[1] – dp[0]

dp[i] = 1 if dp[i] – dp[i-1] == dp[i-1] – dp[i-2]

where dp[i] represents the number of arithmetic series of length greater than 2 till length i+1

Program

Here is the program for the same.

package main

import "fmt"

func numberOfArithmeticSlices(nums []int) int {
	lenNums := len(nums)

	if lenNums <= 2 {
		return 0
	}

	dp := make([]int, lenNums)

	dp[0] = 0

	if (nums[2] - nums[1]) == nums[1]-nums[0] {
		dp[2] = 1
	}

	for i := 3; i < lenNums; i++ {
		if nums[i]-nums[i-1] == nums[i-1]-nums[i-2] {
			dp[i] = dp[i-1] + 1

		}
	}

	output := 0
	for i := 2; i < lenNums; i++ {
		output = output + dp[i]
	}

	return output

}

func main() {
	output := numberOfArithmeticSlices([]int{2, 3, 4, 5})
	fmt.Println(output)
}

Output