LeetCode #413: Arithmetic Slices

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本文介绍了一道关于寻找数组中算术切片数量的算法题。文章详细解释了算术序列的概念，并提供了一个高效的Python解决方案。通过该算法，可以找出给定数组中所有的算术切片。

Problem Statement

(Source) 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.

Solution

Tags: Math.
Self-explained by following code.

class Solution(object):
    def numberOfArithmeticSlices(self, A):
        """
        :type A: List[int]
        :rtype: int
        """
        if not A or len(A) < 3:
            return 0
        res = 0
        cnt = 1
        diff = A[0] - A[1]
        for i in xrange(2, len(A)):
            if A[i - 1] - A[i] == diff:
                res += cnt
                cnt += 1
            else:
                diff = A[i - 1] - A[i]
                cnt = 1
        return res