Maximize the Eligible Carpool Group

Question

The question asks the candidate to determine the maximum number of passengers that can carpool together based on their individual limits for the number of additional passengers they can tolerate.

Codemia · Accepted Answer

The problem involves maximizing the number of passengers that can share a carpool while adhering to individual limits on how many additional passengers they can accept. Each passenger has a lower and upper limit on the number of fellow passengers they are comfortable with, represented by two arrays, L and H. The goal is to find the largest group size k such that each selected passenger meets the condition L[i] <= k - 1 <= H[i].

To solve this problem efficiently, we can use a greedy approach combined with sorting. First, we will create a list of pairs containing the lower and upper limits for each passenger. Then, we will sort this list based on the upper limits. This way, we can iterate through the sorted list and determine the maximum size of the carpool group that can be formed.

1. Create a list of tuples from the L and H arrays.
2. Sort the list of tuples based on the upper limit H[i].
3. Initialize a variable to keep track of the maximum group size k.
4. Iterate through the sorted list and for each passenger, check if they can be included in the current group based on the conditions. If they can, increment k.
5. Return the maximum k found during the iteration.

Here is a Python implementation of the described approach:

```python
def max_carpool_group(L, H):
    N = len(L)
    limits = sorted(zip(L, H), key=lambda x: x[1])
    max_group_size = 0
    current_group_size = 0

for i in range(N):
        current_group_size += 1
        # Check if current group size is valid for the current passenger
        if limits[i][0] <= current_group_size - 1 <= limits[i][1]:
            max_group_size = max(max_group_size, current_group_size)
        else:
            current_group_size -= 1  # Remove the passenger if not valid

return max_group_size
```
This code sorts the passengers based on their upper limits and iterates through them to find the largest valid group.

The time complexity of this solution is O(N log N) due to the sorting step. However, the iteration through the list is O(N). To achieve O(N) complexity, we could consider using a bucket sort approach if the range of L and H is limited. This would involve counting occurrences and finding valid group sizes without explicit sorting.

Maximize the Eligible Carpool Group

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