Maximum Sum Subarray Of Length K in C++

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: 4 6
Explanation: The subarray nums[4...6] has the maximum sum of 16

Understanding the Problem

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 period with the highest revenue.

Potential pitfalls include misunderstanding the requirement for the subarray to be contiguous and not considering edge cases where the array length is less than k.

Approach

To solve this problem, we can use a sliding window approach, which is more efficient than a naive approach. The naive approach would involve calculating the sum of every possible subarray of length k, which would be computationally expensive with a time complexity of O(n*k).

The sliding window approach, on the other hand, allows us to calculate the sum in O(n) time by maintaining a running sum of the current window and adjusting it as we slide the window across the array.

Naive Approach

The naive approach involves iterating through the array and calculating the sum of every possible subarray of length k. This approach is not optimal due to its high time complexity.

Optimized Approach: Sliding Window

The sliding window approach involves the following steps:

Calculate the sum of the first k elements.
Slide the window one element at a time to the right, adjusting the sum by subtracting the element that is left behind and adding the new element that enters the window.
Keep track of the maximum sum encountered during this process.

Algorithm

Here is a step-by-step breakdown of the sliding window algorithm:

Initialize the sum of the first k elements.
Initialize the maximum sum as the sum of the first k elements.
Iterate through the array starting from the k-th element to the end.
For each new element, update the current sum by subtracting the element that is left behind and adding the new element.
Update the maximum sum if the current sum is greater.

Code Implementation


#include <iostream>
#include <vector>
#include <algorithm> // For std::max

// Function to find the maximum sum of a subarray of length k
int maxSumSubarrayOfLengthK(const std::vector<int>& nums, int k) {
    int n = nums.size();
    if (n < k) {
        std::cerr << "Array length is less than k" << std::endl;
        return -1; // or handle the error as appropriate
    }

    // Calculate the sum of the first k elements
    int max_sum = 0;
    for (int i = 0; i < k; ++i) {
        max_sum += nums[i];
    }

    int current_sum = max_sum;

    // Slide the window over the array
    for (int i = k; i < n; ++i) {
        current_sum += nums[i] - nums[i - k];
        max_sum = std::max(max_sum, current_sum);
    }

    return max_sum;
}

int main() {
    std::vector<int> nums = {5, 6, 1, 2, 6, 6, 4, 3};
    int k = 3;
    int result = maxSumSubarrayOfLengthK(nums, k);
    std::cout << "Maximum sum of subarray of length " << k << " is " << result << std::endl;
    return 0;
}

Complexity Analysis

The time complexity of the sliding window approach is O(n), where n is the length of the array. This is because we only pass through the array once. The space complexity is O(1) as we are using a constant amount of extra space.

Edge Cases

Potential edge cases include:

Array length less than k: The function should handle this gracefully, possibly by returning an error or a specific value.
All elements are negative: The algorithm should still correctly identify the subarray with the maximum (least negative) sum.
Array with all identical elements: The algorithm should return the sum of any subarray of length k.

Testing

To test the solution comprehensively, consider the following test cases:

Simple cases with small arrays and small k.
Cases where the array length is exactly k.
Cases with negative numbers.
Edge cases where the array length is less than k.

Thinking and Problem-Solving Tips

When approaching such problems, it is helpful to:

Understand the problem requirements and constraints thoroughly.
Consider both naive and optimized solutions.
Break down the problem into smaller, manageable parts.
Practice similar problems to improve problem-solving skills.

Conclusion

In this blog post, we discussed how to find the maximum sum of a contiguous subarray of length k using a sliding window approach. We covered the problem definition, approach, algorithm, code implementation, complexity analysis, edge cases, and testing. Understanding and solving such problems is crucial for improving algorithmic thinking and coding skills.

Additional Resources

For further reading and practice, consider the following resources:

Maximum Sum Subarray of length K in C++ (Time Complexity: O(n))