Given an input array of integers and a positive integer k, find out the maximum sum of a contiguous subarray of length exactly k
Example
Input: nums = [5, 6, 1, 2, 6, 6, 4, 3], k = 3
Output: 16
Explanation: The subarray nums[4...6] has the maximum sum of 16
The core challenge of this problem is to find the maximum sum of any contiguous subarray of length k within the given array. This problem is significant in various applications such as financial analysis, where one might want to find the maximum profit over a fixed number of days.
Potential pitfalls include misunderstanding the requirement for the subarray to be contiguous and not considering edge cases such as when the array length is less than k.
To solve this problem, we can use a sliding window approach which is more efficient than a naive solution. The naive solution would involve calculating the sum of every possible subarray of length k and then finding the maximum, which would have a time complexity of O(n*k). This is not optimal for large arrays.
The sliding window approach, on the other hand, allows us to calculate the sum in O(n) time. The idea is to maintain a window of size k and slide it across the array while keeping track of the maximum sum.
1. Calculate the sum of the first k elements.
2. Initialize the maximum sum as the sum of the first k elements.
3. Slide the window one element at a time to the right, updating the sum by subtracting the element that is left behind and adding the new element.
4. Update the maximum sum if the current window sum is greater.
def max_sum_subarray(nums, k):
# Step 1: Calculate the sum of the first k elements
window_sum = sum(nums[:k])
max_sum = window_sum
# Step 2: Slide the window across the array
for i in range(len(nums) - k):
# Update the window sum by subtracting the element that is left behind
# and adding the new element
window_sum = window_sum - nums[i] + nums[i + k]
# Update the maximum sum if the current window sum is greater
max_sum = max(max_sum, window_sum)
return max_sum
# Example usage
nums = [5, 6, 1, 2, 6, 6, 4, 3]
k = 3
print(max_sum_subarray(nums, k)) # Output: 16
The time complexity of the sliding window approach is O(n) because we only pass through the array once. The space complexity is O(1) as we are using a constant amount of extra space.
1. If the array length is less than k, the problem is invalid as we cannot form a subarray of length k.
2. If all elements are negative, the algorithm still works as it finds the maximum (least negative) sum.
3. If k is 1, the maximum sum subarray is simply the maximum element in the array.
To test the solution comprehensively, consider the following test cases:
When approaching such problems, it is crucial to understand the constraints and requirements clearly. Breaking down the problem and thinking about efficient ways to solve it, such as using sliding windows, can significantly improve performance. Practice similar problems to develop a strong intuition for these techniques.
In this blog post, we discussed how to find the maximum sum of a contiguous subarray of length k using a sliding window approach. This method is efficient with a time complexity of O(n) and is suitable for large arrays. Understanding and applying such techniques is essential for solving array-related problems effectively.