2823 Sliding Window 求区间最值线段树好慢，能用单调队列

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本文介绍了一种基于滑动窗口的算法实现，该算法能够高效地处理数组中滑动窗口的最大值与最小值问题。通过使用线段树数据结构进行区间查询，可以有效地更新和维护滑动窗口内的最大值与最小值。

Sliding Window

Time Limit: 12000MS		Memory Limit: 65536K
Total Submissions: 14533		Accepted: 4096
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

#include<iostream>
#include<cstdio>
#include<algorithm>
using namespace std;
const int maxn=1100000;
const int inf=(1<<30);
int a[maxn];
struct node
{
    int left,right;
    int _min,_max;
};
node tree[maxn*3];
int lmin[maxn],lmax[maxn];
void buildtree(int id,int l,int r)
{
    tree[id].left=l,tree[id].right=r;
    if(tree[id].left==tree[id].right)
    {
        tree[id]._min=tree[id]._max=a[tree[id].left];
        return ;
    }
    int mid=(tree[id].left+tree[id].right)>>1;
    buildtree(2*id,l,mid);
    buildtree(2*id+1,mid+1,r);
    tree[id]._min=min(tree[2*id]._min,tree[2*id+1]._min);
    tree[id]._max=max(tree[2*id]._max,tree[2*id+1]._max);
}
int tmin,tmax;
void query(int id,int l,int r)
{
    if(tree[id].left==l&&tree[id].right==r)
    {
        tmin=min(tmin,tree[id]._min);
        tmax=max(tmax,tree[id]._max);
        return ;
    }
    int mid=(tree[id].left+tree[id].right)>>1;
    if(r<=mid) query(2*id,l,r);
    else if(l>mid) query(2*id+1,l,r);
    else
    {
        query(2*id,l,mid);
        query(2*id+1,mid+1,r);
    }
}
int main()
{
    int n,k;
    while(scanf("%d%d",&n,&k)==2)
    {
        k--;
        for(int i=1;i<=n;i++) scanf("%d",&a[i]);
        buildtree(1,1,n);
        for(int i=1;i+k<=n;i++)
        {
            tmin=inf;tmax=-inf;
            query(1,i,i+k);
            lmin[i]=tmin;
            lmax[i]=tmax;
        }
        printf("%d",lmin[1]);for(int i=2;i+k<=n;i++) printf(" %d",lmin[i]);printf("\n");
        printf("%d",lmax[1]);for(int i=2;i+k<=n;i++) printf(" %d",lmax[i]);printf("\n");
    }
    return 0;
}