413. Arithmetic Slices (Medium)

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 <= P < Q < N.

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.

题意：
若一组数至少包含三个元素，且相邻两个元素之差均相等，则为arithmetic sequence（等差数列）；

即求等差数列的子等差数列的个数；
思路：
1.若序列S为等差数列，长度为N，则arithmetic slices个数为：sum=(n-2)+(n-1)+...+2+1；
2.函数返回数组等差数列切片的个数sum；

class Solution():
    def numberOfArithmeticSlices(self, A):
        """
        :type A: List[int]
        :rtype: int
        """
        n = len(A)
        sum_s = cnt = 0
        if n < 3:
            return 0
        diff = A[1] - A[0]
        for i in range(2, n):
            if A[i] - A[i-1] == diff:
                cnt += 1
                sum_s += cnt
            else:
                diff = A[i] - A[i-1]
                cnt = 0
        return sum_s