Find a Maximum-Sum Window in a Sparse Array

Question

The question asks the candidate to find a contiguous subarray (window) within a sparse array that has the maximum sum. The candidate should consider the challenges posed by the sparsity of the array.

Codemia · Accepted Answer

To solve the problem of finding a maximum-sum window in a sparse array, we can utilize a sliding window technique. This method allows us to maintain a dynamic sum of the current window while iterating through the array. Given the sparsity, we will need to skip over zero or null entries effectively.

1. Initialize variables for the maximum sum and current window sum.
2. Use a loop to iterate through the array. For each element:
   - If it is non-zero, add it to the current window sum.
   - If it is zero, compare the current window sum with the maximum sum and reset the current window sum.
3. After the loop, ensure to check the last window sum against the maximum sum.
4. Return the maximum sum found.

Here is a Python code implementation:
```python
def max_sum_window(sparse_array):
    max_sum = float('-inf')
    current_sum = 0

for num in sparse_array:
        if num != 0:
            current_sum += num
        else:
            max_sum = max(max_sum, current_sum)
            current_sum = 0

max_sum = max(max_sum, current_sum)  # Check last window
    return max_sum
```

The time complexity of this algorithm is O(n), where n is the number of elements in the sparse array. This is because we make a single pass through the array. The space complexity is O(1) since we are using a fixed amount of extra space for our variables.

Consider edge cases such as:
- An array filled entirely with zeros, where the maximum sum would be zero.
- An empty array, which should also return zero.
- A sparse array with only one non-zero element, where the maximum sum would equal that element.

Interviewers will pay attention to the clarity of your explanation and your ability to handle edge cases. They will also evaluate your coding style, efficiency of the algorithm, and whether you can articulate the thought process behind your decisions. Demonstrating knowledge of time and space complexity will also be a key focus.

Find a Maximum-Sum Window in a Sparse Array

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