Recursion, Fixed Schedule - Lecture Slides | CMSC 433, Study Guides, Projects, Research of Programming Languages

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Recursion

CMSC 433

Bill Pugh and

Nelson Padua-Perez

Fixed schedule

• Project 5 - Dense bags and Markov text
  • Due next Thursday, April 6th
• 2nd Midterm, Monday, April 10th
• Readings from now to midterm:
  • Chapter 7: Recursion
  • Section 8.1: Tree terminology

How many ways are there to

order the numbers 1..n?

• permutation(1) = 1
• permutation(n) =
  • n different numbers that could occur first
  • remaining elements could appear in permutation(n-1) different orders
• thus, permutation(n) = n * permutation(n-1)

= n!

Iteration/Recursion

• Iteration over a list/sequence is very similar to using recursion to combine the result from the first element with the result from the rest of the list - int countVowels(String s) { if (s.length() == 0) return 0; int tailResult = countVowels(s.substring(1)); switch (s.charAt(1)) { case ‘a’: case ‘e’: case ‘i’: case ‘o’: case ‘u’: return tailResult+1; default: return tailResult; }}

Boring recursion

• Using recursion where iteration would work

just as well isn’t that exciting

• sometimes, a little to think about it as a recursive problem
• In Java, it isn’t particularly efficient for long lists or deep recursion
• In some languages (such as Scheme) that support tail recursion, it is as efficient as iteration. In fact, it can be the only/preferred way to implement iteration - has to be a special kind of recursion, called tail recursion

Some interesting recursion

• Binary search
• Quicksort
• Mergesort

recursive permutation

generation

• Define a function calculatePermutations(int [] a)
• that generates each permutation of a and calls handlePermutation(int [] a)
• with each generated permutation
• Hint: define a recursive helper function calculatePermutations(int [] a, int k)
• permutes the values in a[k ... a.length-1]

Change making

• We’ve been asked to help devise a new set of coins for a country ruled by a mathematician.
• Our task is to figure out what the denominations of the coins should be. - For example, in the US, the coins have denominations (in pennies) of: 1, 5, 10, 25 (we'll ignore half dollars for now)
• Assume we want to have only three coins.
• What values should the coins have so as to minimize the average number of coins needed to make any number of cents from 0 to 99.