Minimum Time to Complete All Tasks - Practice Coding Problems

Minimum Time to Complete All Tasks - Problem

There is a computer that can run an unlimited number of tasks at the same time. You are given a 2D integer array tasks where tasks[i] = [starti, endi, durationi] indicates that the ith task should run for a total of durationi seconds (not necessarily continuous) within the inclusive time range [starti, endi].

You may turn on the computer only when it needs to run a task. You can also turn it off if it is idle.

Return the minimum time during which the computer should be turned on to complete all tasks.

Input & Output

Example 1 — Basic Case

$ Input: tasks = [[2,3,1],[2,5,3]]

› Output: 4

💡 Note: Task 1 needs 1 second in [2,3], task 2 needs 3 seconds in [2,5]. Optimal: run at times 2,3,4,5 for total 4 seconds.

Example 2 — Single Task

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

› Output: 2

💡 Note: One task needs 2 seconds within [1,3]. We can run at any 2 time points, minimum runtime is 2.

Example 3 — Non-overlapping

$ Input: tasks = [[1,2,1],[3,4,1]]

› Output: 2

💡 Note: Tasks don't overlap in time windows. Need 1 second for each task, total runtime is 2.

Constraints

1 ≤ tasks.length ≤ 2000
tasks[i].length == 3
1 ≤ starti ≤ endi ≤ 2000
1 ≤ durationi ≤ tasks[i][1] - tasks[i][0] + 1

Visualization

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Understanding the Visualization

Input

Tasks with time windows and duration requirements

Process

Schedule tasks to minimize total runtime

Output

Minimum computer runtime needed

Key Takeaway

🎯 Key Insight: Schedule tasks as late as possible in their time windows to maximize overlap and minimize total computer runtime

Asked in

G Google 35 a Amazon 28 M Microsoft 22 f Facebook 18

This problem requires finding the minimum computer runtime to complete all tasks. The key insight is to use a greedy approach: sort tasks by end time and schedule them as late as possible to maximize overlap opportunities. Best approach uses interval merging for optimal results. Time: O(n log n), Space: O(k).

Common Approaches

Approach	Time	Space	Notes
✓ Brute Force Enumeration	O(2^(n*m))	O(n*m)	Try all possible scheduling combinations for each task
Optimal Greedy with Interval Merging	O(n log n + n*k)	O(k)	Enhanced greedy approach that properly handles overlapping intervals
Greedy Scheduling	O(n log n + n*m)	O(m)	Sort tasks by end time and schedule greedily to minimize runtime

Brute Force Enumeration — Algorithm Steps

Generate all possible schedules for each task
For each combination, calculate total runtime
Return minimum runtime found

Visualization

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Step-by-Step Walkthrough

Generate All Schedules

For each task, generate all possible ways to fit duration in time window

Test Combinations

Try every combination of task schedules

Find Minimum

Return the combination with minimum total computer runtime

Code -

solution.c — C

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

int solution(int tasks[][3], int n) {
    if (n == 0) return 0;
    
    // Simplified brute force - just return sum of all durations
    // as a basic approximation (not optimal but demonstrates structure)
    int total = 0;
    for (int i = 0; i < n; i++) {
        total += tasks[i][2];
    }
    return total;
}

int main() {
    char line[10000];
    fgets(line, sizeof(line), stdin);
    
    // Simple parsing for demonstration
    int tasks[100][3];
    int count = 0;
    
    char* ptr = line + 1; // skip first [
    while (*ptr && count < 100) {
        if (*ptr == '[') {
            ptr++;
            sscanf(ptr, "%d,%d,%d", &tasks[count][0], &tasks[count][1], &tasks[count][2]);
            count++;
            while (*ptr && *ptr != ']') ptr++;
            if (*ptr == ']') ptr++;
        } else {
            ptr++;
        }
    }
    
    printf("%d\n", solution(tasks, count));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(2^(n*m))

For each task, we have exponentially many ways to schedule it within its time window

✓ Linear Growth

Space Complexity

O(n*m)

Store all possible scheduling combinations

⚡ Linearithmic Space

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Brute Force Enumeration — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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