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Asked: 2024-09-24T18:35:54+05:30

A robot moves in a 2D grid starting from the origin (0, 0). It can only move up, down, left, or right, but cannot move diagonally. You are given a list of movements where ‘U’ denotes a move up, ‘D’ denotes a move down, ‘L’ denotes a move left, and ‘R’ denotes a move right. Your task is to determine the final coordinates of the robot after executing all the movements in the list. What are the final x and y coordinates?

Imagine this: you have a little robot that’s super eager to explore a 2D grid, starting its adventure right at the origin—coordinates (0, 0). The way this robot moves is pretty simple but kind of entertaining! It can scoot around with four different commands: ‘U’ for up, which means it goes up one unit in the y-direction; ‘D’ for down, moving it down one unit; ‘L’ for left, which takes it one unit to the left in the x-direction; and ‘R’ for right, sending it one unit to the right.

Now, picture that you’ve just given this robot a list of movements to follow. Let’s say you hand it a series of commands like this: “UULDRRUD”. What do you think will happen? This little guy starts with its tiny wheels spinning at (0, 0) and follows your commands step by step. First, it moves up twice to (0, 2), then it takes a little detour down to (0, 1), veers left to (-1, 1), and zooms over to the right for a couple of steps to end up at (1, 1). Seems easy, right?

But here’s where it gets a little tricky! What if you were to mix up the sequence? Let’s say you change it to “LRUDUUDR”. Now the robot has to process the new order carefully. It really needs to concentrate on whether it’s moving left, right, up, or down. After following this fresh set of commands, where would it end up?

The fun part is figuring out the final coordinates after all these movements. So, put your thinking cap on: if you were to run this sequence through our friendly robot’s little processing brain, what would those final x and y coordinates be? Share your reasoning, and let’s see how well you can calculate its new home on this grid!

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    2 Answers






    1. Robot Movement

      Robot Movement on a 2D Grid

      Okay, so we got this little robot starting at (0,0).

      It moves according to the commands: “LRUDUUDR”. Let’s break it down together!

      • Starting position: (0, 0)
      • Command ‘L’: Moves left to (-1, 0)
      • Command ‘R’: Moves right back to (0, 0)
      • Command ‘U’: Moves up to (0, 1)
      • Command ‘D’: Moves down back to (0, 0)
      • Command ‘U’: Again moves up to (0, 1)
      • Command ‘U’: Moves up again to (0, 2)
      • Command ‘D’: Moves down to (0, 1)
      • Command ‘R’: Moves right to (1, 1)

      So, after all those moves, the robot ends up at (1, 1). That’s the new home on the grid!


    2. The robot begins its journey at the starting coordinates of (0, 0). Following the original command sequence “UULDRRUD”, we can break down the movement step-by-step. Starting at (0, 0), the robot moves up twice (‘U’) to (0, 2). Then, it moves down (‘D’) to (0, 1), proceeds left (‘L’) to (-1, 1), and finally moves right twice (‘R’) ending up at (1, 1) after the final upward (‘U’) movement to (1, 2). Therefore, for the command string “UULDRRUD”, the final coordinates are (1, 2).

      Now, analyzing the mixed command sequence “LRUDUUDR”, we can calculate the new position starting again from (0, 0). The robot moves left (‘L’) to (-1, 0), then right (‘R’) back to (0, 0). Next, it moves up (‘U’) to (0, 1), then down (‘D’) to (0, 0) again. Continuing the movements, it goes up (‘U’) to (0, 1), then up again (‘U’) to (0, 2), and finally moves right (‘R’) to (1, 2). Thus, after executing the commands in this order, the robot finishes its journey at the coordinates (1, 2).