[leetcode]Math-413. Arithmetic Slices

Posted 2020-10-20 chenhan05

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.

#include <iostream>    
#include <vector>    
using namespace std;    
    
class Solution {    
public:    
    int numberOfArithmeticSlices(vector<int>& A) {        
        if(A.size()<3)//序列长小于3直接返回0     
        return 0;    
        int ans=0;int start=0;int diff=A[1]-A[0];    
        for(int i=1;i<A.size();i++)    
        {    
            int newdiff=A[i]-A[i-1];    
            if(newdiff!=diff||i==A.size()-1)    
            {    
                int len=0;    
                if(i==A.size()-1)//到达序列尾部时的长度计算与数列断层长度不一样     
                len=i-start+1;    
                if(newdiff!=diff)    
                len=i-start;    
                if(len==3)    
                ans+=1;    
                else if(len>3)    
                ans+=(len-1)*(len-2)/2;//数学方法求出的通项公式     
                cout<<ans<<endl;    
                start=i-1;    
                diff=newdiff;    
            }    
        }    
        return ans;    
    }    
};