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Lecture 12

COP3502: Introduction to CIS I. Lecture 12. r ecursion “defining a program in terms of itself”. “find your way home”. f ind your way home: if (you are at home) { stop moving } else { take one step towards home “find your way home” } . “find your way home”.

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Lecture 12

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  1. COP3502: Introduction to CIS I Lecture 12

  2. recursion “defining a program in terms of itself”

  3. “find your way home” find your way home: if (you are at home) { stop moving } else { take one step towards home “find your way home” }

  4. “find your way home” find your way home (stepsAway) : if (stepsAway == 0) { stop moving } else { take one step towards home “find your way home”(stepsAway – 1) }

  5. recursion requirements base case – recursion ends recursive call – function call on smaller problem EVERY RECURSIVE CALL SHOULD BRING YOU CLOSER TO THE BASE CASE!

  6. factorial n! = n x (n-1) x (n-2) …. x 2 x 1 Ex. 5! = 5 x 4 x 3 x 2 x 1 = 120

  7. factorial n! = n x (n-1)! 5! = 5 x 4! = 5 x (4 x 3!) = 5 x (4 x (3 x 2!)) = 5 x (4 x (3 x (2 x 1!)))

  8. FACTORIAL(5) = 5 * FACTIORIAL(4)

  9. FACTORIAL(5) = 5 * FACTIORIAL(4) FACTORIAL(4) = 4 * FACTIORIAL(3)

  10. FACTORIAL(5) = 5 * FACTIORIAL(4) FACTORIAL(4) = 4 * FACTIORIAL(3) FACTORIAL(3) = 3 * FACTIORIAL(2)

  11. FACTORIAL(5) = 5 * FACTIORIAL(4) FACTORIAL(4) = 4 * FACTIORIAL(3) FACTORIAL(3) = 3 * FACTIORIAL(2) FACTORIAL(2) = 2 * FACTIORIAL(1)

  12. FACTORIAL(5) = 5 * FACTIORIAL(4) FACTORIAL(4) = 4 * FACTIORIAL(3) FACTORIAL(3) = 3 * FACTIORIAL(2) FACTORIAL(2) = 2 * FACTIORIAL(1) FACTORIAL(1) = 1 * FACTIORIAL(0)

  13. FACTORIAL(5) = 5 * FACTIORIAL(4) FACTORIAL(4) = 4 * FACTIORIAL(3) FACTORIAL(3) = 3 * FACTIORIAL(2) FACTORIAL(2) = 2 * FACTIORIAL(1) FACTORIAL(1) = 1 * FACTIORIAL(0) FACTORIAL(0) = 1 BASE CASE!

  14. Fibonacci Fib(0) = 0 Fib(1) = 1 Fib(2) = 1 Fib(3) = 2 … Fib(n) = Fib(n-1) + Fib(n-2)

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