一道dp[不太好写]

http://acm.csu.edu.cn:20080/csuoj/problemset/problem?pid=2281

Description

An arithmetic progression is a sequence of numbers a1, a2, ..., ak where the difference of consecutive members ai + 1 − ai is a constant 1 ≤ i ≤ k − 1 . For example, the sequence 5, 8, 11, 14, 17 is an arithmetic progression of length 5 with the common difference 3.

In this problem, you are requested to find the longest arithmetic progression which can be formed selecting some numbers from a given set of numbers. For example, if the given set of numbers is {0, 1, 3, 5, 6, 9}, you can form arithmetic progressions such as 0, 3, 6, 9 with the common difference 3, or 9, 5, 1 with the common difference -4. In this case, the progressions 0, 3, 6, 9 and 9, 6, 3, 0 are the longest.

Input

The input consists of a single test case of the following format.

n
v1 v2 ... vn

n is the number of elements of the set, which is an integer satisfying 2 ≤ n ≤ 5000 . Each vi(1 ≤ i ≤ n) is an element of the set,which is an integer satisfying 0 ≤ vi ≤ 109.vi's are all different, i.e.,vi ≠ vj if i ≠ j

Output

Output the length of the longest arithmetic progressions which can be formed selecting some numbers from the given set of numbers.

Sample Input

6
0 1 3 5 6 9

Sample Output

4
题意：求出序列从小到大排序之后能形成的最长等差数列的长度。
题解：dp,dp[i][j]表示i和j作为前两项时的数列长度，如果先枚举第一项(O(N)),然后第二项如果和第三项在第一项的同一侧的话就是(O(N^2))，整体复杂度是(O(N^3))，难以接受，而如果先枚举第二项，然后第一项和第三项在第二项两侧，根据a[j]+a[k]=2*a[i]可以将复杂度降为O(N^2)

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int a[5005],dp[5005][5005];
int main(){
    int n;
    scanf("%d",&n);
    for(int i=1;i<=n;i++)scanf("%d",&a[i]);
    for(int i=1;i<=n;i++){
        for(int j=i;j<=n;j++){
            if(i!=j)dp[i][j]=2;
            else dp[i][j]=1;
        }
    }
    sort(a+1,a+1+n);
    int ans=2;
    for(int i=n-1;i>=2;i--){
        int j=i-1;
        int k=i+1;
        while(j>=1&&k<=n){
            if(a[j]+a[k]==2*a[i]){dp[j][i]=dp[i][k]+1;ans=max(ans,dp[j][i]);k++;j--;}
            else if(a[j]+a[k]<2*a[i]){k++;}
            else {j--;}
        }
    }
    cout<<ans<<endl;
    return 0;
}