[leetcode-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.

思路：

动态规划，如果序列后三个数字满足等差数列的话，

dp[i] = dp[i - 1] + 1；

dp[i] means the number of arithmetic slices ending with A[i].

 

int numberOfArithmeticSlices(vector<int>& A)
     {
         int n = A.size();
         if (n < 3 ) return 0;
         vector<int>dp(n, 0);
         if (A[2] - A[1] == A[1] - A[0]) dp[2] = 1;
         int result = dp[2];
         for (int i = 3; i < n;i++)
         {
             if (A[i] - A[i-1] == A[i-1]-A[i-2]) dp[i] = dp[i - 1] + 1;
             result += dp[i];
         }
         return result;
     }

参考:

https://discuss.leetcode.com/topic/62992/3ms-c-standard-dp-solution-with-very-detailed-explanation