poj 2823 Sliding Window 题解

Posted 2020-08-03 SBSOI

单调队列模板题

Sliding Window

Time Limit: 12000MS		Memory Limit: 65536K
Total Submissions: 53037		Accepted: 15207
Case Time Limit: 5000MS

Description

An array of size n ≤ 10⁶ is given to you. There is a sliding window of size k which is moving from the very left of the array to the very right. You can only see the k numbers in the window. Each time the sliding window moves rightwards by one position. Following is an example:
The array is [1 3 -1 -3 5 3 6 7], and k is 3.

Window position	Minimum value	Maximum value
[1  3  -1] -3  5  3  6  7	-1	3
1 [3  -1  -3] 5  3  6  7	-3	3
1  3 [-1  -3  5] 3  6  7	-3	5
1  3  -1 [-3  5  3] 6  7	-3	5
1  3  -1  -3 [5  3  6] 7	3	6
1  3  -1  -3  5 [3  6  7]	3	7

Your task is to determine the maximum and minimum values in the sliding window at each position.

Input

The input consists of two lines. The first line contains two integers n and k which are the lengths of the array and the sliding window. There are n integers in the second line.

Output

There are two lines in the output. The first line gives the minimum values in the window at each position, from left to right, respectively. The second line gives the maximum values.

Sample Input

8 3
1 3 -1 -3 5 3 6 7

Sample Output

-1 -3 -3 -3 3 3
3 3 5 5 6 7

Source

POJ Monthly--2006.04.28, Ikki

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单调队列模板题。

维护两个单调队列，一个单调增，一个单调减。

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<cstring>
 4 #include<cmath>
 5 #include<algorithm>
 6 #include<queue>
 7 #include<cstdlib>
 8 #include<iomanip>
 9 #include<cassert>
10 #include<climits>
11 #define maxn 1000001
12 #define F(i,j,k) for(int i=j;i<=k;i++)
13 #define M(a,b) memset(a,b,sizeof(a))
14 #define FF(i,j,k) for(int i=j;i>=k;i--)
15 #define inf 0x7fffffff
16 using namespace std;
17 int read(){
18     int x=0,f=1;char ch=getchar();
19     while(ch<\'0\'||ch>\'9\'){if(ch==\'-\')f=-1;ch=getchar();}
20     while(ch>=\'0\'&&ch<=\'9\'){x=x*10+ch-\'0\';ch=getchar();}
21     return x*f;
22 }
23 int a[maxn],q1[maxn],q2[maxn];
24 int main()
25 {
26     std::ios::sync_with_stdio(false);//cout<<setiosflags(ios::fixed)<<setprecision(1)<<y;
27     #ifdef LOCAL
28     freopen("data.in","r",stdin);
29     freopen("data.out","w",stdout);
30     #endif
31     int n,m,k;
32     cin>>n>>k;
33     F(i,1,n)
34     {
35         cin>>a[i];
36     }
37     int head=1,tail=0;
38     F(i,1,n)
39     {
40         while(head<=tail&&a[i]<=a[q1[tail]]) tail--;
41         q1[++tail]=i;
42         while(head<=tail&&q1[tail]-q1[head]>=k) head++;
43         if(i>=k) cout<<a[q1[head]]<<" ";
44     }
45     cout<<endl;
46     head=1,tail=0;
47     F(i,1,n)
48     {
49         while(head<=tail&&a[i]>=a[q2[tail]]) tail--;
50         q2[++tail]=i;
51         while(head<=tail&&q2[tail]-q2[head]>=k) head++;
52         if(i>=k) cout<<a[q2[head]]<<" ";
53     }
54     return 0;
55 }

poj 2823