leetcode

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.

最简单的就是使用 动态规划
例如： 数组 1，2，3，4，5

dp[2] = 1 (因为1，2,3是等差
dp[3] = 2 = dp[1]+1 ( 可以理解为以A[3]为结尾但不包括以A[2]为结尾的等差123 也就是 234,1234,共2个
dp[4] = 3 = dp[3]+1 ( 依次类推 12345,2345,345 3个

以此构成动态规划的公式 dp[i]=dp[i-1]

c++实现的代码如下：

class Solution {
public:
    int numberOfArithmeticSlices(vector<int>& A) {
        int n = A.size();
        int res = 0;
        vector<int> dp(n,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;
            res+=dp[i];
        }
        return res;
    }
};