What is the brute force solution for Minimum Space Wasted From Packaging?

The brute force approach for Minimum Space Wasted From Packaging is Brute Force, with O(n²) time complexity and O(1) space complexity. In this approach, we will try every supplier's boxes and calculate the total wasted space for each configuration. This is straightforward but inefficient as it checks all combinations. The optimal Optimal Solution approach improves this to O(n log n + m log m + m * k), where n is the number of packages, m is the number of suppliers, and k is the average number of boxes per supplier..

What algorithm or data structure is used to solve Minimum Space Wasted From Packaging?

Minimum Space Wasted From Packaging uses the following concepts: Array, Binary Search, Sorting, Prefix Sum. The recommended patterns to study are: Sorting, Prefix Sum.

What are the interview tips for Minimum Space Wasted From Packaging?

Always consider edge cases, such as boxes that can't fit the largest package. Explain your thought process clearly when discussing your approach. Practice writing clean and efficient code, as clarity is crucial in interviews.

What are common mistakes when solving Minimum Space Wasted From Packaging?

Forgetting to check if the largest box can fit the largest package. Not using prefix sums to optimize waste calculations.

#1889

Minimum Space Wasted From Packaging

Hard

ArrayBinary SearchSortingPrefix SumSortingPrefix Sum

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n + m log m + m * k), where n is the number of packages, m is the number of suppliers, and k is the average number of boxes per supplier.
Space	O(1)	O(n)

💡

Intuition

Time O(n log n + m log m + m * k), where n is the number of packages, m is the number of suppliers, and k is the average number of boxes per supplier.Space O(n)

This approach uses sorting and binary search to efficiently find the best fitting boxes for packages, minimizing wasted space. By leveraging prefix sums, we can quickly calculate total waste for each supplier.

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Algorithm

5 steps

1Step 1: Sort the packages array.
2Step 2: For each supplier's box sizes, sort the box sizes.
3Step 3: If the largest box size is less than the largest package, skip this supplier.
4Step 4: Use a prefix sum array to calculate the total size of packages up to each index.
5Step 5: For each box size, use binary search to find how many packages can fit and calculate the waste using the prefix sum.

solution.py20 lines

1def minWastedSpace(packages, boxes):
2    packages.sort()
3    prefix_sum = [0] * (len(packages) + 1)
4    for i in range(len(packages)):
5        prefix_sum[i + 1] = prefix_sum[i] + packages[i]
6    min_waste = float('inf')
7    for box_sizes in boxes:
8        box_sizes.sort()
9        if box_sizes[-1] < packages[-1]:
10            continue
11        waste = 0
12        j = 0
13        for box in box_sizes:
14            count = 0
15            while j < len(packages) and packages[j] <= box:
16                j += 1
17            waste += (j - count) * box - (prefix_sum[j] - prefix_sum[count])
18            count = j
19        min_waste = min(min_waste, waste)
20    return min_waste if min_waste != float('inf') else -1

ℹ

Complexity note: The complexity is dominated by the sorting of packages and boxes, and the prefix sum array takes linear space.

1Sorting the packages and box sizes allows for efficient fitting and waste calculation.
2Using prefix sums helps in quickly calculating the total size of packages that fit into boxes.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.