How do you solve Minimum Total Distance Traveled on LeetCode?

Minimum Total Distance Traveled (LeetCode #2463) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(1) space complexity. Key insight: Sorting both robots and factories allows for efficient pairing based on proximity.

What is the time complexity of Minimum Total Distance Traveled?

The optimal solution for Minimum Total Distance Traveled runs in O(n log n) time and uses O(1) space. The sorting step dominates the complexity, making it O(n log n), while the traversal of robots and factories is linear.

What is the brute force solution for Minimum Total Distance Traveled?

The brute force approach for Minimum Total Distance Traveled is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible combination of robots and factories to find the minimum distance. This is simple but inefficient, as it doesn't leverage any structure in the problem. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Minimum Total Distance Traveled?

Minimum Total Distance Traveled uses the following concepts: Array, Dynamic Programming, Sorting. The recommended patterns to study are: Greedy Algorithms, Sorting, Two Pointers.

What are the interview tips for Minimum Total Distance Traveled?

Always consider sorting as a first step when dealing with positions or distances. Think about how to use two pointers or greedy algorithms to optimize your solution. Practice explaining your thought process clearly, as it helps in interviews.

What are common mistakes when solving Minimum Total Distance Traveled?

Failing to sort the robots and factories before processing. Not keeping track of factory limits correctly, leading to incorrect distance calculations.

#2463

Minimum Total Distance Traveled

Hard

ArrayDynamic ProgrammingSortingGreedy AlgorithmsSortingTwo Pointers

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(1)

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Intuition

Time O(n log n)Space O(1)

The optimal solution sorts both robots and factories, then uses a greedy approach to assign robots to the nearest available factory. This minimizes the distance efficiently by ensuring that each factory repairs as many robots as possible within its limit.

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Algorithm

3 steps

1Step 1: Sort the robot and factory arrays based on their positions.
2Step 2: Use two pointers to traverse the robots and factories.
3Step 3: For each robot, assign it to the nearest factory that has not reached its limit, updating the total distance accordingly.

solution.py12 lines

1def minDistance(robot, factory):
2    robot.sort()
3    factory.sort()
4    total_distance = 0
5    j = 0
6    for r in robot:
7        while j < len(factory) and factory[j][1] == 0:
8            j += 1
9        if j < len(factory):
10            total_distance += abs(r - factory[j][0])
11            factory[j][1] -= 1
12    return total_distance

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Complexity note: The sorting step dominates the complexity, making it O(n log n), while the traversal of robots and factories is linear.

1Sorting both robots and factories allows for efficient pairing based on proximity.
2Using a greedy approach ensures that we minimize the distance for each robot by always choosing the nearest available factory.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.