Maximum Number of Weeks for Which You Can Work - Problem

Array Greedy Medium

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.

You can work on the projects following these two rules:

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

Once all the milestones of all the projects are finished, or if the only milestones that you can work on will cause you to violate the above rules, you will stop working. Note that you may not be able to finish every project's milestones due to these constraints.

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

Input & Output

Example 1 — Basic Case

$ Input: milestones = [1,2,3]

› Output: 6

💡 Note: We can work on all milestones: Week 1-Project 2, Week 2-Project 1, Week 3-Project 2, Week 4-Project 0, Week 5-Project 2, Week 6-Project 1. Total: 6 weeks.

Example 2 — Constraint Limiting

$ Input: milestones = [5,2,1]

› Output: 7

💡 Note: Project 0 has 5 milestones, others have 3 total. We can work: P0-P1-P0-P2-P0-P1-P0, then stop (can't work on P0 again). Total: 7 weeks.

Example 3 — Equal Projects

$ Input: milestones = [5,5,5]

› Output: 15

💡 Note: All projects equal, can perfectly interleave: P0-P1-P2-P0-P1-P2... until all done. Total: 15 weeks.

Constraints

n == milestones.length
1 ≤ n ≤ 10⁵
1 ≤ milestones[i] ≤ 10⁹

Visualization

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Asked in

G Google 15 a Amazon 12 M Microsoft 8

The key insight is that we can work maximum weeks when the largest project can be perfectly interleaved with all other projects. If the largest project has more milestones than all others combined plus one, we're constrained by the interleaving rule. Best approach uses mathematical greedy analysis in O(n) time.

Common Approaches

✓ Mathematical Greedy Solution

⏱️ Time: O(n) Space: O(1)

The key insight is that we can work all weeks if and only if the project with the most milestones doesn't exceed the sum of all other projects plus one. This is because we need to interleave the largest project with others.

Simulation with Priority Queue

⏱️ Time: O(n log n) Space: O(n)

Use a max heap to always work on the project with the most remaining milestones. After working on a project, we cannot work on it next week, so we temporarily remove it and work on the next highest.

Mathematical Greedy Solution — Algorithm Steps

Find the maximum milestones in any project
Calculate total milestones
Check if max ≤ (total - max) + 1
Return total if true, otherwise return 2 * (total - max) + 1

Visualization

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Step-by-Step Walkthrough

Calculate Values

Find total milestones and maximum project size

Check Constraint

Can largest project be interleaved with others?

Apply Formula

Return total or constrained result

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

long long solution(int* milestones, int milestonesSize) {
    long long total = 0;
    int maxMilestone = 0;
    
    for (int i = 0; i < milestonesSize; i++) {
        total += milestones[i];
        if (milestones[i] > maxMilestone) {
            maxMilestone = milestones[i];
        }
    }
    
    if (maxMilestone <= total - maxMilestone + 1) {
        return total;
    } else {
        return 2 * (total - maxMilestone) + 1;
    }
}

int main() {
    char line[10000];
    fgets(line, sizeof(line), stdin);
    
    int milestones[1000];
    int size = 0;
    
    char *token = strtok(line, "[,]");
    while (token != NULL) {
        if (strlen(token) > 0 && token[0] != ' ' && token[0] != '\n') {
            milestones[size++] = atoi(token);
        }
        token = strtok(NULL, "[,]");
    }
    
    printf("%lld\n", solution(milestones, size));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single pass through array to find max and sum

✓ Linear Growth

Space Complexity

O(1)

Only using a few variables for calculations

✓ Linear Space

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Maximum Number of Weeks for Which You Can Work - Problem

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Mathematical Greedy Solution — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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