0954MediumMathStringSimulation

Does the Rover Stay Near Home

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Trains the technique from

This is an original problem, written from a brief that listed the technique, the difficulty, the topics, the function shape and the input bounds — none of that problem's wording, examples, hints or editorials. The link is there so you can map your practice onto the standard set.

Same function shape, different story and different numbers.

A rover starts at the origin facing north and follows instructions, one character at a time: 'G' moves it one step forward in the direction it faces, 'L' turns it a quarter turn to the left, and 'R' a quarter turn to the right.

The rover repeats the whole list of instructions over and over, without end. Return true when there is some circle around the origin that the rover never leaves.

Examples

Example 1

Input: instructions = "GGLRGGRL"
Output: false

A left turn and a right turn cancel each other out, so the rover ends four steps north still facing north, and every repeat carries it four further.

Example 2

Input: instructions = "GLGLGLGL"
Output: true

The rover traces a unit square and comes back to where it started facing north, so it goes round that square forever.

Example 3

Input: instructions = "GGRGGR"
Output: true

The rover ends two steps north and two east facing south. Repeating turns the whole journey a half turn each time, so the two halves cancel and it stays near home.

Constraints

1 <= instructions.length <= 100
instructions[i] is 'G', 'L' or 'R'

The signature

The editor is preloaded with this. It matches the parent problem's shape, so a solution that works here transfers to a judge unchanged.

Python

def is_robot_bounded(instructions: str) -> bool:

Java

public boolean isRobotBounded(String instructions)

The intended approach

Time O(n) for n instructions, one pass.Space O(1).

Run the instructions through once and note two things: where the rover ends up, and which way it is then facing. If it ends facing north again, every repeat shifts it by the same step, so it stays near home exactly when that step is nothing at all. If it ends facing any other way, each repeat turns the whole journey by that quarter turn, and four repeats bring the facing back to north while the four shifts, each turned a quarter further than the last, cancel out. So it always stays near home. That makes the whole test one pass and two comparisons.

Pythonentry point: is_robot_bounded

def is_robot_bounded(instructions):
    # facing: 0 north, 1 east, 2 south, 3 west
    steps = ((0, 1), (1, 0), (0, -1), (-1, 0))
    facing = 0
    x = 0
    y = 0
    for ch in instructions:
        if ch == "G":
            x += steps[facing][0]
            y += steps[facing][1]
        elif ch == "L":
            facing = (facing + 3) % 4
        else:
            facing = (facing + 1) % 4
    if facing != 0:
        return True
    return x == 0 and y == 0

The obvious version

Follow the instructions four times over and see whether the rover is back at the origin, since four repeats always bring the facing back to north and any drift shows up by then. Walks the whole journey rather than reasoning about the facing.

This is not filler. It was written independently of the fast solution and the two were run against thousands of random inputs to confirm they agree — which is how the answer above is known to be right. Read it when the intended approach feels like a rabbit pulled out of a hat.

Python

def bf_is_robot_bounded(instructions):
    steps = ((0, 1), (1, 0), (0, -1), (-1, 0))
    facing = 0
    x = 0
    y = 0
    for _ in range(4):
        for ch in instructions:
            if ch == "G":
                x += steps[facing][0]
                y += steps[facing][1]
            elif ch == "L":
                facing = (facing + 3) % 4
            else:
                facing = (facing + 1) % 4
    return x == 0 and y == 0

How this problem was checked

Reference solution executed against 11 test cases — 11 passed
3 worked examples confirmed by running the code
0 eight-word sequences shared with the parent problem's text
Agrees with an independent brute-force implementation on random inputs
Test set proven to catch deliberately broken solutions
Reviewed by a separate quality pass
Function arity matches the parent problem's

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