Data Structures 605'202'92 Recursion

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Data Structures 605.202.92Recursion

• Robert Holder
• robert.holder_at_jhuapl.edu

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Agenda

• Recursion
• Examples
• Backtracking

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Recursion

• solves a problem by breaking it into smaller
  problem of the same type
• calls itself

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Recursion vs Iteration

• both utilize divide and conquer
• recursion divides problem into smaller problems
  of the same type
• iteration divides problem into smaller problems
  of different types

.
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Writing recursive solutions

• define the problem in terms of smaller problems
  of the same type
  
  determine the base case
• make sure each recursive call diminishes the size
  of the problem
• make sure the base case is reached as the problem
  size diminishes

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Examples

• factorial
• writing a string backwards
• picking k things from n choices
• Hanoi Towers

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Recursion tradeoffs

• benefits
• simple solutions to complex problems
• elegant solutions to complex problems
• helpful in transitioning to iterative solutions
• disadvantages
• method call overhead
• possible recalculation of sub-steps

n! ------------ k! (n-k)!
C (n,k)
see Multiplying Rabbits, p 69 and p 93
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Backtracking

• trial-and-error problem solving method
• when a solution consists of a number of
  decisions, guess at the solution until a conflict
  is reached. At that point, go back to the last
  decision and guess differently.

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Backtracking using recursion

• recursion with no guarantee of success, but with
  a contingency plan.