413. Arithmetic Slices(数组中等差递增子区间的个数)

Posted 2021-02-13 shaer

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.

分析：用动态规划解决问题的关键是找到每个问题的核心公式，并且知道如何存表。例如本题，我们需要一个存储总数的变量，和一个存储差量的变量。
什么是等差数列？ A[i]-A[i-1]=A[i-1]-A[i-2]

 

时间复杂度：o（n）                       空间复杂度：o(1)