Arithmetic Slices——Difficulty：Memium

Problem :

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.

Example:

For example, these are arithmetic sequence:1, 3, 5, 7, 97, 7, 7, 73, -1, -5, -9The following sequence is not arithmetic.1, 1, 2, 5, 7A 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.

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Algorithm:

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注意到：随着等差数列的增加，等差数列的子序列的个数也呈差值为1的等差数列递增

序列                个数        差值1 2 3               1         1 2 3 4             3           21 2 3 4 5           6           31 2 3 4 5 6         10          4

根据这个特征，可以用一个变量记录增加的个数，当不连续后，就重置这个变量。

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Code：

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