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.

题目需要连续的arithmetic slices的个数。
如果A[i] 这个能构成arithmetic slices（先看的三个数），那么以它为最后结点能构成的个数是dp[i-1]+1

 public int numberOfArithmeticSlices(int[] A) {  
     int n = A.length;  
     int[] dp = new int[n];  
     int ans = 0;  
     for(int i = 2; i < n; i++){  
       if(A[i]-A[i-1] == A[i-1]-A[i-2]){  
         dp[i] = dp[i-1]+1;  
         ans+=dp[i];  
       }  
     }  
     return ans;  
   }