A sequence of number 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 sequence:
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 

A slice (P, Q) of 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:

A = [1, 2, 3, 4]

return: 3, for 3 arithmetic slices in A: [1, 2, 3], [2, 3, 4] and [1, 2, 3, 4] itself.

Source: leetcode | Difficulty: MEDIUM_HARD
Tags: Dynamic programming

Data structures

Starter code: class Solution:
    def numberOfArithmeticSlices(self, A: List[int]) -> int:
        

Solutions:
class Solution:

	def numberOfArithmeticSlices(self, A):
		(curr, sum) = (0, 0)
		for i in range(2, len(A)):
			if A[i] - A[i - 1] == A[i - 1] - A[i - 2]:
				curr += 1
				sum += curr
			else:
				curr = 0
		return sum


class Solution:

	def sums(self, n):
		return int((n - 2) * (n - 1) / 2)

	def numberOfArithmeticSlices(self, A):
		if len(A) < 3:
			return 0
		res = []
		cnt = 2
		diff = 0
		i = 1
		while i < len(A) - 1:
			if i == 1:
				diff = A[i] - A[0]
			while i < len(A) - 1 and A[i + 1] - A[i] == diff:
				cnt += 1
				i += 1
			if cnt >= 3:
				res.append(cnt)
			if i < len(A) - 1:
				diff = A[i + 1] - A[i]
				cnt = 2
				i += 1
		return sum((self.sums(x) for x in res))


class Solution:

	def numberOfArithmeticSlices(self, A):
		(dp, counts) = ([0, 0], 1)
		for i in range(2, len(A)):
			if A[i] - A[i - 1] == A[i - 1] - A[i - 2]:
				dp.append(dp[i - 1] + counts)
				counts += 1
			else:
				dp.append(dp[i - 1])
				counts = 1
		return dp[-1]


class Solution:

	def numberOfArithmeticSlices(self, A):
		ans = [0] * len(A)
		for i in range(0, len(A)):
			if i < 2:
				ans[i] = 0
			else:
				ans[i] = ans[i - 1]
				temp = A[:i + 1][::-1]
				for j in range(0, i - 1):
					slice = temp[j:j + 3]
					if self.checkArithmetic(slice):
						ans[i] += 1
					else:
						break
		return 0 if len(A) == 0 else ans[-1]

	def checkArithmetic(self, slice):
		diff = slice[1] - slice[0]
		for i in range(len(slice) - 1):
			if slice[i + 1] - slice[i] != diff:
				return False
		return True


class Solution:

	def numberOfArithmeticSlices(self, A):
		count = 0
		addend = 0
		for i in range(2, len(A)):
			if A[i - 1] - A[i] == A[i - 2] - A[i - 1]:
				addend += 1
				count += addend
			else:
				addend = 0
		return count


class Solution:

	def numberOfArithmeticSlices(self, A):
		if len(A) < 3:
			return 0
		count = 0
		l = len(A)
		i = 0
		while i < l - 2:
			j = i + 2
			while j < l:
				if A[i] - A[i + 1] == A[j - 1] - A[j]:
					count += j - i - 1
					j += 1
				else:
					i = j - 1
					break
			if j == l:
				break
		return count


class Solution:

	def numberOfArithmeticSlices(self, A):
		res = 0
		dp = [0] * len(A)
		for i in range(2, len(A)):
			if A[i] - A[i - 1] == A[i - 1] - A[i - 2]:
				dp[i] = dp[i - 1] + 1
				res += dp[i]
		return res


class Solution:

	def numberOfArithmeticSlices(self, A):
		size = len(A)
		if size < 3:
			return 0
		ans = 0
		cnt = 0
		delta = A[1] - A[0]
		for x in range(2, size):
			if A[x] - A[x - 1] == delta:
				cnt += 1
				ans += cnt
			else:
				delta = A[x] - A[x - 1]
				cnt = 0
		return ans


class Solution:

	def __init__(self):
		self.total_sum = 0

	def numberOfArithmeticSlices(self, A):
		self.slices(A, len(A) - 1)
		return self.total_sum

	def slices(self, A, i):
		if i < 2:
			return 0
		temp = 0
		if A[i] - A[i - 1] == A[i - 1] - A[i - 2]:
			temp = 1 + self.slices(A, i - 1)
			self.total_sum += temp
		else:
			self.slices(A, i - 1)
		return temp