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This is a homework problem. Let A[] is an array of integers and integer K -- window size. Generate array M of minimums seen in a window as it slides over A. I found an article with a solution for this problem but did not understand why it has O(n) complexity. Can anybody explain it to me?
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The Sliding window is a problem-solving technique of data structure and algorithm for problems that apply arrays or lists. These problems are painless to solve using a brute force approach in O(n²) or O(n³). However, the Sliding window technique can reduce the time complexity to O(n).
The Sliding Window algorithm is one way programmers can move towards simplicity in their code. This algorithm is exactly as it sounds; a window is formed over some part of data, and this window can slide over the data to capture different portions of it.
In the sliding window method, a window of specified length, Len, moves over the data, sample by sample, and the statistic is computed over the data in the window. The output for each input sample is the statistic over the window of the current sample and the Len - 1 previous samples.
This tends to catch people out. You would think it would take O(N^2) time since you reason adding takes O(N) time and you have O(N) elements. However, realise each element can only be added once and removed once. So in total it takes O(N) to slide over the whole array A.
This yields an amortised efficiency of O(1) every time you move the sliding window on by one element. In other words, the average time it takes to move the sliding window by one element is O(1).
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