413. Arithmetic Slices

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.

class Solution {
public:
    int numberOfArithmeticSlices(vector<int>& A) {
        int len = A.size();
        int result=0;
        if(len < 3) return 0;
        vector<int> dp(len, 0);
      
        for(int i=2; i<len; i++)
        {
            if(A[i]-A[i-1] == A[i-1]-A[i-2])
            {
               dp[i]=dp[i-1]+1;   //如果是连续等差序列，则子等差序列数+1，否则子等差序列数从0开始。
            }

               result+=dp[i];    //子等差序列求和（注：如果前一个不是等差序列，则dp[i]从0开始）
     
        }
        return result;
    }
};