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:

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1, 3, 5, 7, 9
7, 7, 7, 7
3, -1, -5, -9

The following sequence is not arithmetic.

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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: 

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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.

思路

我们首先需要判断这个数组里面有几个连续的arithmetic sequence。Arithmetic sequence的长度与arithmetic slice的数目有一个定量的关系，而且这个关系可利用等差数列的公式来表示【number函数】。由此可以得出结果。

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class Solution(object):
    def numberOfArithmeticSlices(self, A):
        """
        :type A: List[int]
        :rtype: int
        """
        length = len(A)
        if (length < 3):
            return 0
        else:
            diff = A[1] - A[0]
            count = 0
            ans = 0
            for i in range(2,length):
                if (A[i] - A[i-1] == diff):
                    count += 1
                else:
                    ans += self.number(count)
                    diff = A[i] - A[i-1]
                    count = 0
                    
            ans += self.number(count)
        return ans
        
    def number(self, num):
        res = (num + 1) * num / 2
        return res