To solve this problem, we need to find the maximum sum of a subarray with a fixed length ( k ). The sliding window technique is ideal here as it allows us to compute the result efficiently in linear time.

Approach

The sliding window approach works by maintaining a window of size ( k ) and sliding it across the array. Here are the key steps:

1. Initial Window Sum: Calculate the sum of the first ( k ) elements (initial window).
2. Slide the Window: For each subsequent element:
   • Subtract the element that is sliding out of the window (leftmost element of the previous window).
   • Add the new element that is sliding into the window (next element to the right).
3. Track Maximum Sum: Keep updating the maximum sum whenever the current window sum is greater than the previous maximum.

Solution Code

def max_subarray_sum(arr, k):
    n = len(arr)
    if n < k or k <= 0:
        return 0  # Handle invalid inputs

    # Calculate initial sum of first k elements
    current_sum = sum(arr[:k])
    max_sum = current_sum

    # Slide the window across the array
    for i in range(k, n):
        current_sum += arr[i] - arr[i - k]
        if current_sum > max_sum:
            max_sum = current_sum

    return max_sum

Explanation

• Initial Window: The sum of the first ( k ) elements is computed once, which takes ( O(k) ) time.
• Sliding: For each element from index ( k ) to the end of the array, we adjust the current sum by adding the new element and subtracting the element that is no longer in the window. This step takes ( O(n - k) ) time.
• Efficiency: The overall time complexity is ( O(n) ) (since ( k \leq n )), and the space complexity is ( O(1) ) as we only use a few variables to track sums.

Example Usage

Let's test the function with an example:

arr = [1, 4, 2, 10, 23, 3, 1, 0, 20]
k = 4
print(max_subarray_sum(arr, k))  # Output: 39 (sum of [4,2,10,23])

This function efficiently computes the desired result and handles edge cases like invalid inputs (e.g., ( k ) larger than the array length or non-positive ( k )).

Answer: The Python script to calculate the maximum sum of a subarray with length ( k ) is as provided above. The final answer is the function itself, which returns the maximum sum for any valid input. For the given problem context, the code is the solution.

def max_subarray_sum(arr, k):
    n = len(arr)
    if n < k or k <= 0:
        return 0
    current_sum = sum(arr[:k])
    max_sum = current_sum
    for i in range(k, n):
        current_sum += arr[i] - arr[i - k]
        if current_sum > max_sum:
            max_sum = current_sum
    return max_sum

作者声明:本文包含人工智能生成内容。