Maximum Number of Weeks for Which You Can Work

Problem Description

You are given an integer array milestones where each milestones[i] denotes the number of milestones the i-th project has. You can work on the projects following these two rules:

1. Every week, you will finish exactly one milestone of one project. You must work every week.
2. You cannot work on two milestones from the same project for two consecutive weeks.

Return the maximum number of weeks you would be able to work on the projects without violating the rules mentioned above.

Key Insights

• You can only work on one milestone per week from different projects to avoid consecutive violations.
• The total number of weeks is constrained by the project with the most milestones.
• If the largest project has more milestones than the sum of all other projects plus one, it limits the maximum weeks you can work.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve this problem, we can follow these steps:

1. Calculate the total number of milestones across all projects.
2. Identify the project with the maximum number of milestones.
3. Use the following logic to determine the maximum weeks:
   • If the maximum project has more milestones than the sum of the other projects plus one, the maximum weeks will be limited by that condition.
   • Otherwise, the maximum weeks will be equal to the total number of milestones.

We will utilize simple arithmetic operations and a linear pass through the milestones array to derive our answer.

Code Solutions