hdoj 5805 NanoApe Loves Sequence（模拟）_郑林楷nanoape微博-优快云博客

NanoApe在数学课上面对一个序列挑战：从n个数中随机删除一个数后，计算剩余相邻数差值绝对值的最大值F的期望。通过预处理得到前缀和f与后缀和g，实现O(n)的时间复杂度。

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官方题解：

求出前 $i$ 个数里相邻差值的最大值 $f_i$ ， $i$ 到 $n$ 里相邻差值的最大值 $g_i$ ，那么 $ans=\sum_{i=1}^n \max(|A_{i-1}-A_{i+1}|,f_{i-1},g_{i+1})$

$a n s = \sum i = 1 n max (∣ A i - 1 - A i + 1 ∣, f i - 1 , g i + 1 )$ 。

时间复杂度 $O (n)$ 。

代码:

#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
using namespace std;
typedef long long ll;
const int maxn = 1e5+5;
int a[maxn], f[maxn], g[maxn], n, t;
int main(void)
{
    cin >> t;
    while(t--)
    {
        scanf("%d", &n);
        memset(f, 0, sizeof(f));
        memset(g, 0, sizeof(g));
        for(int i = 1; i <= n; i++)
            scanf("%d", &a[i]);
        for(int i = 2; i <= n; i++)
            f[i] = max(f[i-1], abs(a[i]-a[i-1]));
        for(int i = n-1; i >= 1; i--)
            g[i] = max(g[i+1], abs(a[i]-a[i+1]));
        ll ans = g[2]+f[n-1];
        for(int i = 2; i <= n-1; i++)
            ans += max(max(abs(a[i-1]-a[i+1]), f[i-1]), g[i+1]);
        printf("%lld\n", ans);
    }
    return 0;
}

NanoApe Loves Sequence

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 262144/131072 K (Java/Others)
Total Submission(s): 1369 Accepted Submission(s): 533

Problem Description

NanoApe, the Retired Dog, has returned back to prepare for the National Higher Education Entrance Examination!

In math class, NanoApe picked up sequences once again. He wrote down a sequence with

n numbers on the paper and then randomly deleted a number in the sequence. After that, he calculated the maximum absolute value of the difference of each two adjacent remained numbers, denoted as

F .

Now he wants to know the expected value of

F , if he deleted each number with equal probability.

Input

The first line of the input contains an integer

T , denoting the number of test cases.

In each test case, the first line of the input contains an integer

n , denoting the length of the original sequence.

The second line of the input contains

n integers

A1,A2,...,An , denoting the elements of the sequence.

1≤T≤10, 3≤n≤100000, 1≤Ai≤109

Output

For each test case, print a line with one integer, denoting the answer.

In order to prevent using float number, you should print the answer multiplied by

n .

Sample Input