709952. Robots
Robots
Summary
The problem involves a group of robots that are moving in a specific pattern. The goal is to determine if all robots will eventually meet at the same location, given their initial positions and movements.
Detailed Explanation
To solve this problem, we can start by analyzing the movements of the robots. Each robot moves according to a predefined pattern, which can be represented as a series of left and right turns. We need to determine if these movements will eventually lead all robots to meet at the same location.
One approach is to simulate the movements of the robots step-by-step, keeping track of their positions and directions. This can help us identify if any robot reaches a dead end or if they continue moving in the same direction indefinitely.
Here's a step-by-step breakdown of the solution:
- Initialize an array to store the positions of the robots.
- Iterate through each robot's movement pattern, updating its position accordingly.
- Check if any two robots are moving towards each other (i.e., their directions are opposite). If they are, update their positions based on the direction of the closest one.
- Repeat steps 2-3 until no more movements can be made or all robots converge to a single location.
Time complexity: O(n), where n is the number of robots and their movement patterns. Space complexity: O(1), as we only need a constant amount of space to store the robot positions.
Optimized Solutions
Java
public class RobotMovement {
public static boolean allRobotsMeet(int[][] movements) {
int[] positions = new int[movements.length];
for (int i = 0; i < movements.length; i++) {
positions[i] = movements[i][0]; // initial position
}
for (int i = 0; i < movements.length; i++) {
int direction = movements[i][1];
while (direction > 0) {
positions[i]++;
if (positions[i] >= 5) {
return false; // robot reaches dead end
}
direction--;
}
}
for (int i = 0; i < movements.length - 1; i++) {
int dir1 = movements[i][1];
int dir2 = movements[i + 1][1];
if ((dir1 > 0 && dir2 > 0) || (dir1 < 0 && dir2 < 0)) { // robots moving towards each other
positions[i] += Math.abs(dir1);
positions[i + 1] -= Math.abs(dir2);
}
}
return true; // all robots meet at the same location
}
}