5-Recursion

# 5-Recursion - CMPT 225 Recursion CMPT 225 Objectives At the...

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CMPT 225 Recursion

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CMPT 225 Objectives At the end of this unit, we will be able to … Develop recursive algorithms and implement them Hand (box) trace recursive calls and compute their final result(s) Describe some advantages of tail recursion 2
CMPT 225 3 Iteration versus Recursion In order to solve a problem, we may have to repeat (or iterate) some statements several times This can be done using loops Another way of repeating statements is to repeat the whole algorithm or operation itself Recursion

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CMPT 225 4 Recursive Algorithm/Operation Definition: To solve a problem, a recursive algorithm/operation can achieve iteration (repeated statements) by calling itself either … Directly: Indirectly: recursive call operation recursive call recursive call operation 2 operation 1
CMPT 225 Base Case: Part of the problem (the algorithm is trying to solve) for which we know the answer Its purpose is to stops the algorithm from calling itself indefinitely Also called “terminating case” Recursive Case : Part of the problem for which we do not know the answer Therefore, in this step, the problem needs to be “modified” such that eventually, it does reach the point where it becomes “the part of the problem for which we know the answer” i.e., the base case This is where the algorithm/operation calls itself with a different (often smaller) version of the problem 5 Designing a Recursive Algorithm - 1

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CMPT 225 Other components to consider: name parameters and their type returned value type 6 Designing a Recursive Algorithm - 2
CMPT 225 Mystery Operation (Java) import java.io.*; class mysteryTestDriver { static public void main ( String [ ] args ) { System.out.println( "Calling mystery with n = 1 and max = 5." );

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