Recursion. A problem solving technique where an algorithm is defined in terms of itself. A recursive method is a method that calls itself

Transcription

1 Recursio 1 A probem sovig techique where a agorithm is defied i terms of itsef A recursive method is a method that cas itsef A recursive agorithm breaks dow the iput or the search space ad appies the same ogic to a smaer ad smaer piece of the probem uti the remaiig piece is sovabe without recursio. Sometimes caed divide ad coquer

2 Recursio vs. Iteratio 2 i geera, ay agorithm that is impemeted usig a oop ca be trasformed ito a recursive agorithm movig i the reverse directio is ot aways possibe uess you maitai a additioa data structure (stack) yousef.

3 Recursio Aaysis 3 i geera, recursive agorithms are more efficiet more readabe (but occasioay quite the opposite!) more eegat side effects mismaagemet of memory over head costs

4 Recursio Compoets 4 Soutio to the base case probem for what vaues ca we sove without aother recursive ca? Reducig the iput or the search space modify the vaue so it is coser to the base case The recursive ca Where do we make the recursive ca? What do we pass ito that ca?

5 How recursio works 5 Whe a method cas itsef it is just as if that method is caig some other method. It is just a coicidece that the method has the same ame args ad code. A recursive method ca created a idetica copy of the caig method ad everythig ese behaves as usua. Thik of the method as a rectage of code ad data, ad recursio is just a ayerig or tiig of those rectages with iformatio passig to with each ca ad iformatio returig from each ca as the method fishes.

6 GCD Agorithm 6 give two positive itegers X ad Y, where X >= Y, the GCD(X,Y) is equa to Y if X mod Y = = 0 s ese equa to the GCD(Y, X mod Y) Agorithm termiates whe the X % Y is zero. Notice that each time the fuctio cas it sef, the 2 d arg gets coser to zero ad must evetuay reach zero.

7 What is the output of this program? 7 pubic void foo( it x) if (x ==0) retur; ese System.out.prit( x ); foo( x - 1 ); pubic static void mai( Strig args[]) foo( 7 ); ** Idetify the Base case, recursive ca ad reductio / modificatio of the iput toward the base case.

8 What is the output of this program? 8 pubic it foo( it x) if (x ==0) retur 0; ese retur x + foo(x-1); pubic static void mai( Strig args[]) System.out.prit( foo(7) ); ** Idetify the Base case, recursive ca ad reductio / modificatio of the iput toward the base case.

9 What is the output of this program? 9 pubic it foo( it x, it y) if (x == 0) retur y; ese retur foo( x-1, y+1 ); pubic static void mai( Strig args[] ) System.out.prit( foo( 3, 4 ) ); ** Idetify the Base case, recursive ca ad reductio or modificatio of the iput toward the base case.

10 What is the output of this program? 10 pubic it foo( it x, it y ) if (x == 0) retur y; ese retur foo( x-1, y+x ); pubic static void mai( Strig args[]) System.out.prit( foo( 3, 4 ) );

11 Now.. You hep me write this 11 Write a recursive fuctio that accepts a it ad prits that iteger out i reverse o 1 ie What is the base case? How do I reduce the iput toward base case? What do I pass to the recursive ca?

12 Oe more try! 12 Write a recursive fuctio that accepts a strig ad prits that strig out i reverse o 1 ie. What is the base case? How do I reduce the iput toward base case? What do I pass to the recursive ca?

13 Other Exampes Bad exampes (but for iustratio/treachig) factoria expoetia Fiboacci umbers power

14 Other Exampes Good exampes Towers of Haoi GCD Eight Quees Biary Search Trees Maze traversa (I.e recovery from dead eds, backtrackig)

15 Tai Recursio optimizatio 15 Recursio ca use up a ot of memory very quicky! The compier ca geerate assemby code that is iterative but guarateed to compute the exact same operatio as the recursive source code. It oy works if the very ast statemet i your method is the recursive ca. This is tai recursio.