Leetcode #1953: Maximum Number of Weeks for Which You Can Work
In this guide, we solve Leetcode #1953 Maximum Number of Weeks for Which You Can Work 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 n projects numbered from 0 to n - 1. You are given an integer array milestones where each milestones[i] denotes the number of milestones the ith project has.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Array
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: milestones = [1,2,3]
Output: 6
Explanation: One possible scenario is:
- During the 1st week, you will work on a milestone of project 0.
- During the 2nd week, you will work on a milestone of project 2.
- During the 3rd week, you will work on a milestone of project 1.
- During the 4th week, you will work on a milestone of project 2.
- During the 5th week, you will work on a milestone of project 1.
- During the 6th week, you will work on a milestone of project 2.
The total number of weeks is 6.
Python Solution
class Solution:
def numberOfWeeks(self, milestones: List[int]) -> int:
mx, s = max(milestones), sum(milestones)
rest = s - mx
return rest * 2 + 1 if mx > rest + 1 else s
Complexity
The time complexity is , where is the number of projects. The space complexity is .
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.