Codeforces_789C_(dp)

最新推荐文章于 2022-05-09 01:15:19 发布

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最新推荐文章于 2022-05-09 01:15:19 发布

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原文链接：http://www.cnblogs.com/jasonlixuetao/p/6652904.html

本文介绍了一种解决特定数学问题的方法——即求解Uzhlyandian函数的最大值。该函数涉及绝对值计算及区间最大值求解。文章提供了详细的算法思路与C++实现代码。

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Something happened in Uzhlyandia again... There are riots on the streets... Famous Uzhlyandian superheroes Shean the Sheep and Stas the Giraffe were called in order to save the situation. Upon the arriving, they found that citizens are worried about maximum values of the Main Uzhlyandian Function f, which is defined as follows:

$\text{[math]}$

In the above formula, 1 ≤ l < r ≤ n must hold, where n is the size of the Main Uzhlyandian Array a, and |x| means absolute value of x. But the heroes skipped their math lessons in school, so they asked you for help. Help them calculate the maximum value of f among all possible values of l and r for the given array a.

Input

The first line contains single integer n (2 ≤ n ≤ 10^5) — the size of the array a.

The second line contains n integers a1, a2, ..., an (-10^9 ≤ ai ≤ 10^9) — the array elements.

Output

Print the only integer — the maximum value of f.

Examples

input

5
1 4 2 3 1

output

input

4
1 5 4 7

output

题意：求公式的最大值。
思路：
　　b[i]:abs(num[i]-num[i+1]),c[N]:-abs(num[i]-num[i+1])　　(i%2==1)
　　b[i]:-abs(num[i]+num[i+1]),c[N]:abs(num[i]-num[i+1])　　(i%2==0)
　　然后分别求b,c的区间连续最大值，二者中较大着就是答案。

#include<bits/stdc++.h>
using namespace std;
#define N 100005
#define LL long long
#define INF 10000000005
int num[N],b[N],c[N];

int main()
{
    int n;
    scanf("%d",&n);
    for(int i=0;i<n;i++)
        scanf("%d",&num[i]);
    for(int i=0;i<n-1;i++)
    {
        if(i%2)
        {
            b[i]=abs(num[i]-num[i+1]);
            c[i]=-abs(num[i]-num[i+1]);
        }
        else 
        {
            b[i]=-abs(num[i]-num[i+1]);
            c[i]=abs(num[i]-num[i+1]);
        }
    }
    LL res1=-INF,res2=-INF,tmp=0,l=0;
    for(int i=0;i<n-1;i++)
    {
        tmp+=b[i];
        if(tmp>res1)
            res1=tmp;
        if(tmp<0)
            tmp=0;
    }
    tmp=0;
    for(int i=0;i<n-1;i++)
    {
        tmp+=c[i];
        if(tmp>res2)
            res2=tmp;
        if(tmp<0)
            tmp=0;
    }
    printf("%I64d\n",max(res1,res2));
    return 0;
}