Sliding Window
Time Limit: 12000MS
Memory Limit: 65536K
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
1: #include <iostream>
2: #include <cstdio>
3: #include <cstring>
4: #include <algorithm>
5: using namespace std;
6: #define lson l,m,rt<<1
7: #define rson m+1,r,rt<<1|1
8: typedef long long ll;
9: const int maxn=1111111;
10: int a[maxn<<2],b[maxn<<2];
11: int small[maxn],big[maxn],cnt=0;
12:
13: void PushUp(int rt)
14: {
15: a[rt]=max(a[rt<<1],a[rt<<1|1]);
16: b[rt]=min(b[rt<<1],b[rt<<1|1]);
17: }
18:
19: void build(int l,int r,int rt)
20: {
21: if(l==r){
22: scanf("%d",&a[rt]);
23: b[rt]=a[rt];
24: return;
25: }
26: int m=(l+r)>>1;
27: build(lson); build(rson);
28: PushUp(rt);
29: }
30:
31: void query(int L,int R,int l,int r,int rt,int &ma,int &mi)
32: {
33: if(L<=l&&R>=r)
34: {
35: ma=a[rt];
36: mi=b[rt];
37: return;
38: }
39: int m=(r+l)>>1;
40: if(L<=m&&R>m)
41: {
42: int x1,y1,x2,y2;
43: query(L,R,lson,x1,y1);
44: query(L,R,rson,x2,y2);
45: ma=max(x1,x2);
46: mi=min(y1,y2);
47: }
48: else if(L<=m)
49: query(L,R,lson,ma,mi);
50: else
51: query(L,R,rson,ma,mi);
52: }
53:
54: void show(int n,int e[])
55: {
56: for(int i=0; i<n ; i++){
57: if(i) printf(" ");
58: printf("%d",e[i]);
59: }
60: printf("\n");
61: }
62:
63: void run(int n,int k)
64: {
65: cnt=0;
66: build(1,n,1);
67: for(int i=k; i<=n; i++)
68: {
69: query(i-k+1,i,1,n,1,big[cnt],small[cnt]);
70: cnt++;
71: }
72: show(cnt,small);
73: show(cnt,big);
74: }
75:
76: int main()
77: {
78: int n,k;
79: while(scanf("%d%d",&n,&k)!=EOF)
80: run(n,k);
81: return 0;
82: }