Arithmetic Sequence

Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 1846 Accepted Submission(s): 808

Problem Description

A sequence b1,b2,⋯,bn are called (d1,d2)-arithmetic sequence if and only if there exist i(1≤i≤n) such that for every j(1≤j<i),bj+1=bj+d1 and for every j(i≤j<n),bj+1=bj+d2.

Teacher Mai has a sequence a1,a2,⋯,an. He wants to know how many intervals [l,r](1≤l≤r≤n) there are that al,al+1,⋯,ar are (d1,d2)-arithmetic sequence.

Input

There are multiple test cases.

For each test case, the first line contains three numbers n,d1,d2(1≤n≤105,|d1|,|d2|≤1000), the next line contains n integers a1,a2,⋯,an(|ai|≤109).

Output

For each test case, print the answer.

Sample Input

5 2 -2

0 2 0 -2 0

5 2 3

2 3 3 3 3

Sample Output

Author

xudyh

Source

2015 Multi-University Training Contest 9

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题意：

定义N个数组成的序列b1、b2、b3、...、bn为(d1, d2)序列

满足：存在一个i 使得 b[j+1] = b[j] + d1(1<=j<i) && b[j] = b[j-1] + d2(i<=j<=N).

思路：构造两个等差数列

定义数组l[i]——为从左到右且以a[i]元素为末尾的等差数列的长度

定义数组r[i]——为从右到左且以a[i]元素为末尾的等差数列的长度

注：以后遇到两端分别连续的情况，还要结合的这一种，就要想到这种方法，标记一下以***为端点，同时以***为开始的特点。

代码：

#include<bits/stdc++.h>
using namespace std;
const int maxn=100100;
int main()
{
    int a[maxn];
    long long l[maxn],r[maxn];
    int n,d1,d2;
    while(scanf("%d%d%d",&n,&d1,&d2)!=EOF){
        for(int i=1;i<=n;i++){
            scanf("%d",&a[i]);
        }
        l[1]=1;
        for(int i=2;i<=n;i++){
            if(a[i]-a[i-1]==d1){
                l[i]=l[i-1]+1;
            }
            else
                l[i]=1;
        }
        r[n]=1;
        for(int i=n-1;i>=1;i--){
            if(a[i+1]-a[i]==d2){
                r[i]=r[i+1]+1;
            }
            else r[i]=1;
        }
        long long ans=0;
        if(d1!=d2){
            for(int i=1;i<=n;i++){
                ans+=l[i]*r[i];
            }
        }
        else{
            for(int i=1;i<=n;i++){
                ans+=r[i];
            }
        }
        cout<<ans<<endl;
    }
}

参考：https://blog.csdn.net/chenzhenyu123456/article/details/48661127

Arithmetic Sequence（构造等差数列）

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