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Apple Redistribution into Boxes

Difficulty: Easy

Problem Description

You are given an array apple of size n and an array capacity of size m. There are n packs where the ith pack contains apple[i] apples. There are m boxes as well, and the ith box has a capacity of capacity[i] apples. Return the minimum number of boxes you need to select to redistribute these n packs of apples into boxes. Note that apples from the same pack can be distributed into different boxes.

Key Insights

  • The total number of apples must fit into the selected boxes.
  • Each box can hold a certain number of apples, and we want to minimize the number of boxes used.
  • A greedy algorithm approach can be applied by selecting boxes with the highest capacity first.
  • Sorting the box capacities in descending order allows for efficient filling of apples.

Space and Time Complexity

Time Complexity: O(m log m) + O(n) (where m is the number of boxes and n is the number of apple packs)
Space Complexity: O(1) (additional space used for calculations)

Solution

To solve this problem, we can use a greedy algorithm approach. The steps are as follows:

  1. Calculate the total number of apples by summing up the elements in the apple array.
  2. Sort the capacity array in descending order to prioritize larger boxes first.
  3. Initialize a counter for the number of boxes used and a variable to keep track of the remaining apples.
  4. Iterate through the sorted capacity array, adding the capacity of each box to the total used until all apples are accommodated.
  5. Count the number of boxes used until the total capacity reaches or exceeds the total number of apples.

Code Solutions

def min_boxes(apple, capacity):
    total_apples = sum(apple)  # Calculate total apples
    capacity.sort(reverse=True)  # Sort capacities in descending order
    used_boxes = 0
    current_capacity = 0
    
    for cap in capacity:
        current_capacity += cap  # Add the capacity of the current box
        used_boxes += 1  # Increment the box count
        if current_capacity >= total_apples:  # Check if we have enough capacity
            return used_boxes  # Return the number of boxes used

# Example usage
print(min_boxes([1, 3, 2], [4, 3, 1, 5, 2]))  # Output: 2
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