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, 97, 7, 7, 73, -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.\

思路：使用动态规划。子问题是更短的列有多少个arithmetic slices。注意到通式，对于一个具有arithmetic属性的列，若有n个slices，再加上一个元素后，若新列仍为arithmetic，那么新列有slices n + 新列长 - 2个。用result[j]记录以下标为j + 2的元素为结尾的子列的arithmetic slice数，result[A.size() - 3]为我们的结果。

class Solution {public:    int numberOfArithmeticSlices(vector<int>& A) {        if (A.size() < 3) {            return 0;        }         int result[A.size()], length = 2;        for (int i = 0; i < A.size(); i++) {            result[i] = 0;        }        for (int j = 0; j < A.size() - 2; j++) {            if (A[j] - A[j + 1] == A[j + 1] - A[j + 2]) {                length++;                if (j == 0) {                    result[j] = 1;                }                else {                    result[j] = result[j - 1] + length - 2;                }            }            else {                length = 2;                if (j == 0) {                    result[j] = 0;                }                else {                    result[j] = result[j - 1] + length - 2;                }            }        }        return result[A.size() - 3];    }};