python coding test course, sliding window

In computer science, algorithm problems are important elements that provide us with efficient methods to solve problems.
Among them, the sliding window technique is used to find continuous subarrays that satisfy certain conditions in linear data structures like arrays or strings.
In this lecture, we will solve a problem using the sliding window technique and examine how this technique is useful for problem-solving.

Problem Description

Given an integer array nums and an integer k, calculate the sum of the subarray with the maximum sum among subarrays of size k.
In other words, this is a problem of maximizing the sum of k consecutive elements.
For example, if the array is nums = [1, 3, 2, 5, 4, 8] and k = 3,
the sum of the subarray [5, 4, 8] is the largest, so the answer is 17.

Problem Requirements

  • Function input: integer array nums and integer k
  • Function output: maximum sum of the subarray

Approach to the Problem

By using the sliding window technique to solve this problem, we can reduce the time complexity to O(n) by traversing the input array only once.
The idea of this technique is to use two pointers to adjust the start and end of the current window to calculate the sum of the subarray.

Explanation of the Sliding Window Technique

  1. Define the initial window. Use pointers to select the first k elements and calculate their sum.
  2. Then, move to the second window by removing one element from the start of the window and adding one element to the end.
    Repeat this process until the end of the array.
  3. Record the sum obtained at each step and update the maximum sum by comparing it with the previously recorded maximum sum.

Code Implementation


def max_sum_subarray(nums, k):
    # Calculate initial window
    max_sum = sum(nums[:k])
    window_sum = max_sum
    
    # Apply sliding window
    for i in range(k, len(nums)):
        # Remove the leftmost number from the current window and add the newly added number.
        window_sum += nums[i] - nums[i - k]
        max_sum = max(max_sum, window_sum)
    
    return max_sum

# Example execution
nums = [1, 3, 2, 5, 4, 8]
k = 3
result = max_sum_subarray(nums, k)
print(f"Maximum sum of the subarray: {result}")

Code Explanation

The above function max_sum_subarray takes an array nums and an integer k as arguments and returns the maximum sum.
First, it calculates the sum of the initial window and then traverses the array using the sliding window method.
The sum of each window is obtained by removing the leftmost element from the previous sum and adding a new element,
recording each window’s sum to update the maximum sum.

Results and Testing

When you run the above example, the result Maximum sum of the subarray: 17 is produced.
By utilizing the sliding window technique, we can solve the problem quickly with just one traversal.

Conclusion

In this lecture, we solved the problem of finding the maximum subarray sum using the sliding window technique.
This technique is very useful as it reduces time complexity by traversing the entire array only once without the need to repeatedly compare the same elements.
It can also be applied to various other problems, making it a great help in areas where coding tests and algorithm problems are frequently presented.