Step by Step solution about How to resolve the algorithm Stair-climbing puzzle step by step in the Haskell programming language

Overview:

This Haskell program simulates a robot that takes random steps in either direction, with a 50% chance of stepping up or down. It runs this simulation until the robot reaches a certain threshold of steps and then prints the final step count.

Code Structure:

1. stepUp Function:

• stepUp is the main function that performs the simulation.
• It uses the untilM helper function to repeatedly call the step function until a condition is met.

2. untilM Function:

• The untilM function is a generic function that repeatedly applies an action until a test condition becomes false.
• It takes two arguments:
  • test: A monadic action that returns True or False.
  • action: A monadic action to perform.
• It repeatedly calls test, and if test returns True, it stops. Otherwise, it calls action and then calls untilM again.

3. Robot Type:

• Robot is an alias for a state transformer with a state type of (Int, StdGen).
• This state type represents the robot's current position (as an integer) and the current state of a random number generator (as a StdGen).

4. step Function:

• The step function is the action that simulates the robot taking a step.
• It reads the current state, generates a random Bool value (succeeded), and updates the state based on whether the robot succeeded (stepped up) or failed (stepped down).
• It also returns succeeded to indicate whether the robot stepped up or down.

5. startingPos Variable:

• startingPos is the initial position of the robot. It is set to 20 in this program.

6. main Function:

• The main function initializes the random number generator and prints the initial position of the robot.
• It then uses the execState function to run the stepUp simulation, which returns the final position of the robot.
• It finally prints the final position.

How the Program Works:

1. The main function initializes the random number generator and sets the initial position of the robot.
2. The stepUp function is called to repeatedly simulate robot steps until the robot reaches a threshold (in this case, it runs indefinitely).
3. Inside the step function, a random Bool value is generated to determine whether the robot steps up or down.
4. The state is updated accordingly, and the step function returns True or False to indicate whether the robot stepped up or down.
5. The untilM function repeatedly calls step until the step function returns False (indicating that the robot stepped down).
6. The final position of the robot is then printed.

stepUp :: Robot ()
stepUp = untilM step stepUp

untilM :: Monad m => m Bool -> m () -> m ()
untilM test action = do
    result <- test
    if result then return () else action >> untilM test action


import Control.Monad.State
import System.Random (StdGen, getStdGen, random)

type Robot = State (Int, StdGen)

step :: Robot Bool
step = do
    (i, g) <- get
    let (succeeded, g') = random g
    put (if succeeded then i + 1 else i - 1, g')
    return succeeded

startingPos = 20 :: Int

main = do
    g <- getStdGen
    putStrLn $ "The robot is at step #" ++ show startingPos ++ "."
    let (endingPos, _) = execState stepUp (startingPos, g)
    putStrLn $ "The robot is at step #" ++ show endingPos ++ "."