Leetcode #1889: Minimum Space Wasted From Packaging
In this guide, we solve Leetcode #1889 Minimum Space Wasted From Packaging in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You have n packages that you are trying to place in boxes, one package in each box. There are m suppliers that each produce boxes of different sizes (with infinite supply).
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Array, Binary Search, Prefix Sum, Sorting
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
Input: packages = [2,3,5], boxes = [[4,8],[2,8]]
Output: 6
Explanation: It is optimal to choose the first supplier, using two size-4 boxes and one size-8 box.
The total waste is (4-2) + (4-3) + (8-5) = 6.
Python Solution
class Solution:
def minWastedSpace(self, packages: List[int], boxes: List[List[int]]) -> int:
mod = 10**9 + 7
ans = inf
packages.sort()
for box in boxes:
box.sort()
if packages[-1] > box[-1]:
continue
s = i = 0
for b in box:
j = bisect_right(packages, b, lo=i)
s += (j - i) * b
i = j
ans = min(ans, s)
if ans == inf:
return -1
return (ans - sum(packages)) % mod
Complexity
The time complexity is O(log n) or O(n log n). The space complexity is O(1).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.