题目

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.

难度

Medium

方法

如果3个数之间等差，则为数列。对于a1,a2,a3,a4,a5，将3个数归为一组向后遍历，a1a2a3为一个序列，seriesNum=1; a2a3a4有2个序列，即a2a3a4和a1a2a3a4，因此a2a3a4的seriesNum=2，同理，a3a4a5对应的seriesNum=3。最后将各组的seriesNum相加则为总共的序列数。
注意[1,2,3,8,9,10]这种特殊情况

python代码

class Solution(object):
    def numberOfArithmeticSlices(self, A):
        """
        :type A: List[int]
        :rtype: int
        """
        i = 2
        result = 0
        seriesNum = 0
        while i < len(A):
            if A[i-1]-A[i-2] == A[i]-A[i-1]:
                seriesNum += 1
                result += seriesNum
            else:
                seriesNum = 0
            i += 1

        return result

assert Solution().numberOfArithmeticSlices([1,2,3,4]) == 3
assert Solution().numberOfArithmeticSlices([1,2,3,4,5]) == 6
assert Solution().numberOfArithmeticSlices([1,2,3,8,9,10]) == 2