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Recursion

Recursion. Alice. Repetition. In some situations, we don’t know exactly how many times a block of instructions should be repeated. All we know is that repetition is needed

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Recursion

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  1. Recursion Alice

  2. Repetition • In some situations, we don’t know exactly how many times a block of instructions should be repeated. • All we know is that repetition is needed • For example, in a board game like chess or checkers, we don’t know exactly how many moves it will take for a player to win or lose the game – all we know is that several moves will be needed.

  3. Indefinite Repetition • In programs where a count of repetitions is not known (indefinite), we can use one of two repetition control mechanisms: • Recursion • While statement • This session focuses on Recursion.

  4. Recursion • Many of the pieces we use to create a program are identified by using special words. For example, • Do in order • Do together • If/Else • Loop • Recursion is not a program statement with a special word that identifies it as part of the programming language. Recursion means that a method (or a question) calls itself.

  5. Example – horse race A carnival style horse race. In repeated moves, one horse is randomly selected to move forward. The selected horse “runs” straight ahead to the finish line. A horse is the winner if it gets to the finish line before any other horse. When one horse wins, the game ends.

  6. Storyboard "do everything again" means that the entire method should be repeated – this is where recursion occurs. race If one of the horses has won the winner says, “I won!!!” Else randomly choose one horse and move it forward a small amount do everything again

  7. Question • How do we implement “do everything again” ? • Create a call to the race method itself. • Recursion means that a method calls itself. race If one of the horses has won the winner says, “I won!!!” Else randomly choose one horse and move it forward a small amount call the race method

  8. Stepwise Refinement race If one of the horses has won the winner says, “I won!!!” Else randomly choose one horse and move it forward a small amount call the race method moveRandomHorseForward whichHorseWon? isGameOver?

  9. isGameOver To determine whether the game is over, ask the question: Is the finish line < 0.5 meters (arbitrary distance) in front of a horse?

  10. moveRandomHorseForward To randomly choose a horse and move it forward, use the built-in random selection question.

  11. whichHorseWon • To determine the winner, we ask the question: "Which horse is within 0.5 meters of the finish line?"

  12. Putting together the pieces Recursive call. Note: The winning horse says "I won!!!" -- a lame ending, we know.

  13. Demo!

  14. Testing • Testing a program that used random numbers requires extra caution. • In this example, we ran the program 20 times and found that • racehorse1 won 7 times • racehorse2 won 3 times • racehorse3 won 10 times • Something is wrong! Each horse should win approximately 1/3 of the time.

  15. Removing the bug • The bug in this code is that we have • nested If statements, and • we used a 33% probability for each If statement • What we didn't consider is that if racehorse1 was not selected, then we have a 50% probability of selecting either racehorse2 or racehorse3.

  16. Revised moveRandomHorseForward • The corrected code:

  17. Assignment • Read Chapter 8-1, Recursion • Lab 8-1

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