poj 2823 Sliding Window (单调队列)

Sliding Window
 Time Limit: 12000MS Memory Limit: 65536K Total Submissions: 46705 Accepted: 13485 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

Sample Output

Source

a)从队头到队尾，元素在我们所关注的指标下是递减的（严格递减，而不是非递增），比如查询如果每次问的是窗口内的最小值，那么队列中元素从左至右就应该递增，如果每次问的是窗口内的最大值，则应该递减，依此类推。这是为了保证每次查询只需要取队头元素。

b)从队头到队尾，元素对应的时刻（此题中是该元素在数列a中的下标）是递增的，但不要求连续，这是为了保证最左面的元素总是最先过期，且每当有新元素来临的时候一定是插入队尾。

POJ2823就是上面描述的那道题。

http://www.cnblogs.com/Jason-Damon/archive/2012/04/19/2457889.html

作者： CrazyKK

ex-ACMer@hust，stackoverflow-engineer@sensetime