Robot Return to Origin

Problem Statement

In this problem, a robot initiates its movement from the origin, coordinate (0,0), on a two-dimensional plane. Throughout its journey, it follows a sequence of steps predefined in the string moves, where each character indicates a specific direction ('L' for left, 'R' for right, 'U' for up, and 'D' for down). The challenge is to determine if, after executing all the moves in the sequence, the robot returns exactly to its starting point at the origin. The function should return true if the robot does return to (0, 0), and false otherwise. Each move is of uniform magnitude, and the orientation or 'facing direction' of the robot is not necessary for the computation of its final position.

Examples

Example 1

Input:

moves = "UD"

Output:

true

Explanation:

The robot moves up once, and then down once. All moves have the same magnitude, so it ended up at the origin where it started. Therefore, we return true.

Example 2

Input:

moves = "LL"

Output:

false

Explanation:

The robot moves left twice. It ends up two "moves" to the left of the origin. We return false because it is not at the origin at the end of its moves.

Constraints

• 1 <= moves.length <= 2 * 104
• moves only contains the characters 'U', 'D', 'L' and 'R'.

Approach and Intuition

When considering how to determine if the robot returns to the origin, it becomes apparent that each move can either cancel out another move or contribute to a net displacement from the origin:

1. Each 'R' (right) and 'L' (left) move impacts the robot's x-coordinate.

   • 'R' moves the robot one unit to the right, and 'L' one unit to the left.
   • If the robot makes equal numbers of 'R' and 'L' moves, their effects cancel out, resulting in a net x-coordinate of 0.

2. Each 'U' (up) and 'D' (down) move impacts the robot's y-coordinate.

   • 'U' moves the robot one unit upward, and 'D' one unit downward.
   • Similarly, if the robot makes equal numbers of 'U' and 'D' moves, their effects cancel out, resulting in a net y-coordinate of 0.

3. To determine if the robot returns to the origin:

   • Count the occurrences of each move type.
   • Check if the counts of 'L' matches 'R' and if the counts of 'U' matches 'D'.
   • If both conditions hold true, the robot returns to the origin, and the function should return true. If either condition fails, the function should return false.

This logic effectively checks for a balance in horizontal and vertical movements, ensuring that any movement away from the origin in any direction is matched by an equivalent movement back towards the origin.

Solutions

class Solution {
    public boolean checkRobotReturnToOrigin(String path) {
        int horizontal = 0, vertical = 0;
        for (char direction : path.toCharArray()) {
            switch (direction) {
                case 'U': vertical--; break;
                case 'D': vertical++; break;
                case 'L': horizontal--; break;
                case 'R': horizontal++; break;
            }
        }
        return horizontal == 0 && vertical == 0;
    }
}