LeetCode 2463: Minimum Total Distance Traveled Solution

Master LeetCode problem 2463 (Minimum Total Distance Traveled), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

2463. Minimum Total Distance Traveled

Hard

Array Dynamic Programming Sorting

Problem Explanation

Explanation

To minimize the total distance traveled by all the robots, we can follow the steps:

Sort the robots' positions in ascending order.
For each factory, calculate the distance between it and the robots before it and after it.
Repair the robots based on the distances from the factory.
Calculate the total minimum distance traveled by all robots.

Time complexity: O(nlogn) where n is the number of robots. Space complexity: O(n) for storing the sorted robots' positions.

Solution Code

class Solution {
    public int minTotalDistance(int[] robot, int[][] factory) {
        Arrays.sort(robot);
        int n = robot.length;
        int totalDistance = 0;

        for (int[] fac : factory) {
            int pos = fac[0];
            int limit = fac[1];
            List<Integer> left = new ArrayList<>();
            List<Integer> right = new ArrayList<>();

            for (int r : robot) {
                if (r < pos) {
                    left.add(pos - r);
                } else if (r > pos) {
                    right.add(r - pos);
                }
            }

            Collections.sort(left);
            Collections.sort(right);

            int repaired = 0;
            for (int l : left) {
                if (repaired == limit) break;
                totalDistance += l;
                repaired++;
            }

            for (int r : right) {
                if (repaired == limit) break;
                totalDistance += r;
                repaired++;
            }
        }

        return totalDistance;
    }
}

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