How do you solve Robot Bounded In Circle on LeetCode?

Robot Bounded In Circle (LeetCode #1041) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: The robot stays bounded if it returns to the origin or changes direction after one complete set of instructions.

What is the brute force solution for Robot Bounded In Circle?

The brute force approach for Robot Bounded In Circle is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we simulate the robot's movement step by step for a large number of iterations to see if it returns to the starting position or stays within a bounded area. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Robot Bounded In Circle?

Robot Bounded In Circle uses the following concepts: Math, String, Simulation. The recommended patterns to study are: Simulation, Coordinate Geometry.

What are the interview tips for Robot Bounded In Circle?

Always clarify the problem constraints and edge cases before jumping into coding. Think about the implications of the robot's movement and how it relates to the coordinate system. Practice simulating the robot's movement on paper to visualize the problem better.

What are common mistakes when solving Robot Bounded In Circle?

Not considering the direction change after executing the instructions. Assuming the robot will always return to the origin without checking its final direction.

#1041

Robot Bounded In Circle

Medium

MathStringSimulationSimulationCoordinate Geometry

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(1)

The optimal solution leverages the observation that if the robot returns to the origin or changes its direction after one complete set of instructions, it will remain bounded in a circle. This avoids unnecessary iterations.

⚙️

Algorithm

3 steps

1Step 1: Initialize the robot's position at (0, 0) and direction facing north.
2Step 2: Execute the instructions once to find the final position and direction.
3Step 3: If the robot is back at the origin or not facing north, return true; otherwise, return false.

solution.py14 lines

1def isRobotBounded(instructions):
2    x, y = 0, 0
3    direction = 0  # 0: North, 1: East, 2: South, 3: West
4    for instruction in instructions:
5        if instruction == 'G':
6            if direction == 0: y += 1
7            elif direction == 1: x += 1
8            elif direction == 2: y -= 1
9            else: x -= 1
10        elif instruction == 'L':
11            direction = (direction + 3) % 4
12        elif instruction == 'R':
13            direction = (direction + 1) % 4
14    return (x == 0 and y == 0) or direction != 0

ℹ

Complexity note: The time complexity is O(n) because we process each instruction exactly once, and the space complexity is O(1) since we only use a fixed amount of space for variables.

1The robot stays bounded if it returns to the origin or changes direction after one complete set of instructions.
2The movement and turning can be effectively modeled using simple coordinate changes.

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