The sliding window algorithm is among the various other algorithms that are crucial for learning due to its use cases in the range of problems that arise. In this article, we will look at the fundamentals of the sliding window algorithm and solve problems optimized with the sliding window algorithm.
What is sliding window algorithm?
The sliding window algorithm is an optimization approach used to efficiently process paintings, ropes, or other data structures. The basic idea is to maintain a ‘window’ of items in the data, and as you move through it, you drag the window to cover the next set of items. This technique is particularly powerful in scenarios where you need to find a subset of data that meets certain criteria.
You can consider an array of integers and the task of finding the maximum sum of a subarray of a given size. Instead of recalculating the sum for each subarray from scratch, the sliding window keeps track of the sum as it moves through the array, effectively reducing the time complexity of the operation.
Sliding Window Algorithm Overview
Let’s take an example of a list of integers, i.e. (1,2,3,4,5,6)
Now we want to take a window size of 2, which means we will cover two adjacent integer blocks at a time, here is a visual representation of the sliding window algorithm.
Here we can see that by taking a window size of 2, we get the following pairs of integers at each step:
(1,2)
(2.3)
(3,4)
(4,5)
(5,6)
Key Components of a Sliding Window Algorithm
- Window initialization: The first step in implementing a sliding window algorithm is to initialize the window. This involves setting start and end points based on the problem requirements.
- Processing elements: When the window moves, it processes elements within its bounds. The nature of this treatment depends on the specific problem. This may involve calculations, comparisons or any other operation relevant to the task at hand.
- Window movement: Window movement is an important aspect of sliding window algorithms. It dictates how elements are included or excluded from the window as it moves through the table.
Optimize time and space complexity
One of the main strengths of the sliding window algorithm is its ability to optimize both time and space. complexity. As it maintains a constant window size as it traverses the dataset, the algorithm avoids redundant calculations, leading to a more efficient solution. This is particularly advantageous when dealing with large data sets or real-time data streams where performance is very important.
Additionally, the sliding window often eliminates the need for additional data structures, which helps us reduce the overall space complexity of the algorithm. This minimalist approach contributes to its elegance and effectiveness in solving a wide range of problems.
Common Sliding Window Variations
As with many algorithms, the sliding window algorithm comes in different variations suited to solving specific types of problems. One such variation is the fixed-size sliding window, in which the window size remains constant throughout. This is useful in situations such as the maximum subarray sum problem.
Another variation is the variable-size sliding window, in which the window size dynamically adjusts based on certain conditions. This flexibility is particularly beneficial when dealing with problems involving finding patterns or subsets of varying length in the data.
When to use the sliding window algorithm
The sliding window algorithm is best exploited in situations that meet a few key criteria:
- Sequential or chronological data: The data arrives in the form of a long continuous sequence or a history over time. For example, log streams, sensor readings and video images.
- Need for real-time incremental processing: The processing task should be performed continuously and in real time as new data arrives rather than batch post-processing.
- Repeated costly calculations: Naive algorithms end up needlessly doing the same complex, resource-intensive calculations over and over again as the sequence evolves.
- Reference locality: Calculation results tend to have high locality, meaning that only recent context is needed rather than all historical data.
- Benefits of memorization: Intermediate results of processing subsequences can be cached or temporarily stored to avoid recalculating from scratch.
Python Example of Sliding Window Algorithm
Here is one of the most common DSA questions: Find the maximum sum of a subarray of a given size. Let’s try to solve this problem with python.
def max_subarray_sum(nums, k):
max_sum = float('-inf')
current_sum = 0
for i in range(len(nums)):
current_sum += nums(i)
if i >= k - 1:
max_sum = max(max_sum, current_sum)
current_sum -= nums(i - (k - 1))
return max_sum
print(max_subarray_sum((4, 5, 6, 7, 1, 4, 9, 0, 3, 1, 7), 3)) # Output: 18
In the python code written above, we have written a function max_subarray_sum() which takes two parameters: nums and, k which are the list and the size of the maximum subarray. We initialized our max_sum variable with the minimum float value and current_sum to 0, which will calculate our sum in each window.
Then we run a for
iterate through the list and add the current value of the item, that is, nums(i)
At current_sum
variable. After that we check, if the value of our index (i) is greater than 1- the given size of our window (k), if it is true then it means that the current size of the window is equal to the size data of the window in question, we therefore assign to the max_sum variable the maximum of our max_sum and current_sum values.
We will also need to iterate over our window, so to do this we need to remove the first item from our window, which is why we do it current_sum -= nums(i-(k-1))
and we return our max_sum.
Link to Leetcode question: Maximum sum of subarray
Conclusion
To summarize, the sliding window algorithm improves the time and space complexity of solutions through its optimization technique. Its use cases vary from string manipulation, array manipulation and much more. I hope you have a good understanding of what the sliding window algorithm is with our comprehensive guide and examples.
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