Educational Codeforces Round 69 (Rated for Div. 2)
Let's denote a k-step ladder as the following structure: exactly k+2 wooden planks, of which
- two planks of length at least k+1 — the base of the ladder;
- k planks of length at least 1 — the steps of the ladder;
Note that neither the base planks, nor the steps planks are required to be equal.
For example, ladders 1 and 3 are correct 2-step ladders and ladder 2 is a correct 1-step ladder. On the first picture the lengths of planks are [3,3] for the base and [1] for the step. On the second picture lengths are [3,3] for the base and [2] for the step. On the third picture lengths are [3,4] for the base and [2,3] for the steps.
You have n planks. The length of the i-th planks is ai. You don't have a saw, so you can't cut the planks you have. Though you have a hammer and nails, so you can assemble the improvised "ladder" from the planks.
The question is: what is the maximum number k such that you can choose some subset of the given planks and assemble a k-step ladder using them?
Input
The first line contains a single integer T (1≤T≤100) — the number of queries. The queries are independent.
Each query consists of two lines. The first line contains a single integer n (2≤n≤105) — the number of planks you have.
The second line contains n integers a1,a2,…,an (1≤ai≤105) — the lengths of the corresponding planks.
It's guaranteed that the total number of planks from all queries doesn't exceed 105.
Output
Print T integers — one per query. The i-th integer is the maximum number k, such that you can choose some subset of the planks given in the i-th query and assemble a k-step ladder using them.
Print 0 if you can't make even 1-step ladder from the given set of planks.
Example
input
4
4
1 3 1 3
3
3 3 2
5
2 3 3 4 2
3
1 1 2
output
2
1
2
0
Note
Examples for the queries 1−3 are shown at the image in the legend section.
The Russian meme to express the quality of the ladders:
题意：题目意思就是 定义k阶梯子为两边各一块木板长度至少k+1，中间k块木板至少为1 。
问 给你n块木板，最多能搭成几阶的梯子。
思路：显然对n块木板排序之后，取最长的两块木板搭旁边的两块梯子为最优解，
然后就是比较 最长的这两块木板的小的这块长度-1 和 剩余木板数量 的极小值为答案。
1 #include<iostream>
2 #include<cstdio>
3 #include<cmath>
4 #include<cstring>
5 #include<algorithm>
6 #include<map>
7 #include<set>
8 #include<vector>
9 #include<queue>
10 using namespace std;
11 #define ll long long
12 const int mod=1e9+7;
13 const int inf=1e9+7;
14
15 const int maxn=1e5+5;
16 int num[maxn];
17
18 int main()
19 {
20 ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
21
22 int T;
23 cin>>T;
24 int n;
25 while(T--)
26 {
27 cin>>n;
28
29 for(int i=0;i<n;i++)
30 cin>>num[i];
31
32 sort(num,num+n);
33
34 cout<<min(n-2,num[n-2]-1)<<endl;
35 }
36
37 return 0;
38 }