Leetcode #2611: Mice and Cheese
In this guide, we solve Leetcode #2611 Mice and Cheese 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
There are two mice and n different types of cheese, each type of cheese should be eaten by exactly one mouse. A point of the cheese with index i (0-indexed) is: reward1[i] if the first mouse eats it.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Array, Sorting, Heap (Priority Queue)
Intuition
A locally optimal choice leads to a globally optimal result for this structure.
That means we can commit to decisions as we scan without backtracking.
Approach
Sort or preprocess if needed, then repeatedly take the best available local choice.
Maintain the minimal state necessary to validate the greedy decision.
Steps:
- Sort or preprocess as needed.
- Iterate and pick the best local option.
- Track the current solution.
Example
Input: reward1 = [1,1,3,4], reward2 = [4,4,1,1], k = 2
Output: 15
Explanation: In this example, the first mouse eats the 2nd (0-indexed) and the 3rd types of cheese, and the second mouse eats the 0th and the 1st types of cheese.
The total points are 4 + 4 + 3 + 4 = 15.
It can be proven that 15 is the maximum total points that the mice can achieve.
Python Solution
class Solution:
def miceAndCheese(self, reward1: List[int], reward2: List[int], k: int) -> int:
n = len(reward1)
idx = sorted(range(n), key=lambda i: reward1[i] - reward2[i], reverse=True)
return sum(reward1[i] for i in idx[:k]) + sum(reward2[i] for i in idx[k:])
Complexity
The time complexity is O(n log n). The space complexity is O(1) to O(n).
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.