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Recursion Ch 14 Recursion There are two important parts of recursion: -A stopping case that ends the recursion -A reduction case that reduces the problem What are the base and stopping cases for the Fibonacci numbers? (sum of the previous

  1. Recursion Ch 14

  2. Recursion There are two important parts of recursion: -A stopping case that ends the recursion -A reduction case that reduces the problem What are the base and stopping cases for the Fibonacci numbers? (sum of the previous two numbers) (see last time: fibonacciRecursion.cpp)

  3. Recursion: Root finding Find a root of: (see: rootFind.cpp) Method: 1. Find one positive y and 1 neg. y 2. Find midpoint (of x values) 3. update y-pos/neg

  4. Recursion: Dictionary search Open the dictionary to the middle - If the word is not on that page, reopen in the middle of the unsearched side (See: dictionarySearch.cpp)

  5. Recursion How would you sum the numbers 1 to n using recursion (not a loop)? For example sumToN(5) = 15, as 1+2+3+4+5 = 15 What is the stopping case? How do you reduce the problem? (see: sumToN.cpp)

  6. Recursion What if we defined tangent recursively as: Assume we take an input for how many times to do this recursion What is the pattern? What is the stopping case? How do we move towards the stopping case (see: tangent.cpp)

  7. Recursion: Tower or Hanoi https://www.youtube.com/watch?v=2SUvWfNJSsM

  8. Recursion: Tower or Hanoi The tower of Hanoi is played by: 1. Moving a single ring to another stack 2. Smaller rings cannot have larger rings on top of them (see: towerHanoi.cpp)

  9. Recursion How would you solve a sudoku problem? Rules: 1. Every row has numbers 1-9 2. Every column has numbers 1-9 3. The nine 3x3 boxes have numbers 1-9 Reduce problem? Stopping case? (see: sudokuSolver.cpp)

  10. Recursion Do not try to solve chess in this manner! You will segfault (you will also not finish computing before the sun burns the earth to a crisp)

  11. Miscellaneous notes Try googling “recursion” and click on the spelling suggestion Recursion is very powerful and used in many advanced algorithms It will give you a headache for a while... =(

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