Leetcode #2589: Minimum Time to Complete All Tasks
In this guide, we solve Leetcode #2589 Minimum Time to Complete All Tasks 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 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].
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Stack, Greedy, Array, Binary Search, Sorting
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
Input: tasks = [[2,3,1],[4,5,1],[1,5,2]]
Output: 2
Explanation:
- The first task can be run in the inclusive time range [2, 2].
- The second task can be run in the inclusive time range [5, 5].
- The third task can be run in the two inclusive time ranges [2, 2] and [5, 5].
The computer will be on for a total of 2 seconds.
Python Solution
class Solution:
def findMinimumTime(self, tasks: List[List[int]]) -> int:
tasks.sort(key=lambda x: x[1])
vis = [0] * 2010
ans = 0
for start, end, duration in tasks:
duration -= sum(vis[start : end + 1])
i = end
while i >= start and duration > 0:
if not vis[i]:
duration -= 1
vis[i] = 1
ans += 1
i -= 1
return ans
Complexity
The time complexity is , and the space complexity is . 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.