Dark is going to attend Motarack’s birthday. Dark decided that the gift he is going to give to Motarack is an array a of n non-negative integers.
Dark created that array 1000 years ago, so some elements in that array disappeared. Dark knows that Motarack hates to see an array that has two adjacent elements with a high absolute difference between them. He doesn’t have much time so he wants to choose an integer k (0≤k≤109) and replaces all missing elements in the array a with k.
Let m be the maximum absolute difference between all adjacent elements (i.e. the maximum value of |ai−ai+1| for all 1≤i≤n−1) in the array a after Dark replaces all missing elements with k.
Dark should choose an integer k so that m is minimized. Can you help him?
Input
The input consists of multiple test cases. The first line contains a single integer t (1≤t≤104) — the number of test cases. The description of the test cases follows.
The first line of each test case contains one integer n (2≤n≤105) — the size of the array a.
The second line of each test case contains n integers a1,a2,…,an (−1≤ai≤109). If ai=−1, then the i-th integer is missing. It is guaranteed that at least one integer is missing in every test case.
It is guaranteed, that the sum of n for all test cases does not exceed 4⋅105.
Output
Print the answers for each test case in the following format:
You should print two integers, the minimum possible value of m and an integer k (0≤k≤109) that makes the maximum absolute difference between adjacent elements in the array a equal to m.
Make sure that after replacing all the missing elements with k, the maximum absolute difference between adjacent elements becomes m.
If there is more than one possible k, you can print any of them.
Example
inputCopy
7
5
-1 10 -1 12 -1
5
-1 40 35 -1 35
6
-1 -1 9 -1 3 -1
2
-1 -1
2
0 -1
4
1 -1 3 -1
7
1 -1 7 5 2 -1 5
outputCopy
1 11
5 35
3 6
0 42
0 0
1 2
3 4
Note
In the first test case after replacing all missing elements with 11 the array becomes [11,10,11,12,11]. The absolute difference between any adjacent elements is 1. It is impossible to choose a value of k, such that the absolute difference between any adjacent element will be ≤0. So, the answer is 1.
In the third test case after replacing all missing elements with 6 the array becomes [6,6,9,6,3,6].
|a1−a2|=|6−6|=0;
|a2−a3|=|6−9|=3;
|a3−a4|=|9−6|=3;
|a4−a5|=|6−3|=3;
|a5−a6|=|3−6|=3.
So, the maximum difference between any adjacent elements is 3.
题意:
给你n个数，有些位置得数会丢少，那么该位置就为-1 .问你在丢少的位置上填什么数，可以使得相邻数差得绝对值最小。填完数之后再问你1~n差值最大是多少。
解析:
有三种情况
第一种 : 8,-1,-1,-1
第二种:-1,-1,-1,-1;
第三种 :8,-1,9
从第三种入手，我们可以找该种类型的数，-1在中间，然后记录左右两边的最大最小值。这样会一定使得差值最小。
对于第一种和第二种，我们只要初始化最大值为1e9，最小值为0.
#include<bits/stdc++.h>
using namespace std;
const int N=1e5+1000;
int a[N];
int t;
int n;
int main()
{
scanf("%d",&t);
while(t--)
{
scanf("%d",&n);
int maxn=0;
int minn=1e9;
a[0]=-1;a[n+1]=-1;
for(int i=1;i<=n;i++) scanf("%d",&a[i]);
for(int i=1;i<=n;i++)
{
if(a[i]==-1)
{
if(a[i-1]!=-1)
{
maxn=max(maxn,a[i-1]);
minn=min(minn,a[i-1]);
}
if(a[i+1]!=-1)
{
maxn=max(maxn,a[i+1]);
minn=min(minn,a[i+1]);
}
// cout<<maxn<<" "<<minn<<endl;
}
}
//cout<<maxn<<" "<<minn<<endl;
int p=(maxn+minn)/2;
int ans=0;
for(int i=1;i<=n-1;i++)
{
if(a[i]==-1) a[i]=p;
if(a[i+1]==-1) a[i+1]=p;
ans=max(ans,abs(a[i]-a[i+1]));
}
cout<<ans<<" "<<p<<endl;
}
}
