Problem Brief

Encircular

NEW GRADINTERNOA

Build a computer simulation of a mobile robot. The robot moves on an infinite plane, starting from position (0, 0). Its movements are described by a command string consisting of one or more of the following three letters:

G instructs the robot to move forward one step.

L instructs the robot to turn left in place.

R instructs the robot to turn right in place.

The robot performs the instructions in a command sequence in an infinite loop. Determine whether there exists some circle such that the robot always moves within the circle.

Consider the commands R and G executed infinitely. A diagram of the robot's movement looks like:

The robot will never leave the circle.

Function Description

Complete the function doesCircleExist in the editor below. The function must return an array of n strings either YES or NO based on whether the robot is bound within a circle or not, in order of test results.

doesCircleExist has the following parameter(s):

commands[commands[0],...commands[n-1]]: An array of n commands[i] where each represents a list of commands to test.

1Example 1

Input

commands = ["G", "L", "RGRG"]

Output

["NO", "YES", "YES"]

Explanation

There are n = 2 commands: 1. For commands[0] = "G", the robot will move forward forever (G -> G-> G -> ...) without ever turning or being restricted to a circle. Set index 0 of the return array to NO. 2. For commands[1] = "L", the robot will just turn 90 degree left forever without ever moving forward (because there is no "G" instruction). The robot is effectively trapped at one spot, thus bound within a circle. Set index 1 of the return array to YES. 3. For commands[2] = "GRGR" , concatenate the string to "GRGRGRGR" and it will follow the circular path in the statement example. Set index 2 of the return array to YES.

Constraints

Limits and guarantees your solution can rely on.

1 <= |commands[i]| <= 2500

1 <= n <= 10

Each command consists of G, L, and R only.