Warm-Up! Coding Bat Ap-1

Transcription

1 Recursion

2 Warm-Up! Coding Bat Ap-1

3 Lecture: Recursion!

4 What will this code output? public int mystery(int max) { int answer = 1; for (int n = 1; n <= max; n++) answer *= n; return answer; } //MAIN System.out.println(this.mystery(5));

5 What will this code output? 120 public int mystery(int max) { int answer = 1; for (int n = 1; n <= max; n++) answer *= n; return answer; } //MAIN System.out.println(this.mystery(5)); n answer 1 1* 1 = * 1 = 2 3 3*2 = 6 4 4*6 = * 5 = 120 What math operation did we just duplicate?

6 What will this code output? n! public int mystery(int max) { int answer = 1; for (int n = 1; n <= max; n++) answer *= n; return answer; } //MAIN System.out.println(this.mystery(5)); n answer 1 1* 1 = * 1 = 2 3 3*2 = 6 4 4*6 = * 5 = 120 5! = 5 x 4 x 3 x 2 x 1 = 120

7 Now, what will this code output? public int fact(int n) { if (n == 1) return 1 else return fact(n-1) * n; } //MAIN System.out.println(this.fact(5));

8 Now, what will this code output? public int fact(int n) { } if (n == 1) return 1 else return fact(n-1) * n; We build a stack like pancakes until we get to the end case fact (1) = 1 fact (2) = fact(1) *2 fact(3) = fact(2) * 3 fact(4) = fact(3) * 4 fact(5) = fact(4) * 5 //MAIN System.out.println(this.fact(5));

9 Now, what will this code output? public int fact(int n) { } if (n == 1) return 1 else return fact(n-1) * n; Now we go BACK down the stack. RECURSION! fact (1) = 1 fact (2) = fact(1) *2 = 1 * 2 = 2 fact(3) = fact(2) * 3 = 2 * 3 = 6 fact(4) = fact(3) * 4 = 6 * 4 = 24 fact(5) = fact(4) * 5 = 24 * 5 = 120 //MAIN System.out.println(this.fact(5));

10 Recursion Recursion happens when a method calls itself A recursive method must have a stop condition/ base case. Recursive calls will continue until the stop condition is met. A+ Computer Science -

11 public class RecursionOne { } public void run(int x) { out.println(x); run(x+1); } public static void main(string args[] ) { RecursionOne test = new RecursionOne(); test.run(1); } Will it stop? A+ Computer Science - Recursion OUTPUT

12 public class RecursionTwo { } public void run(int x ) { out.println(x); if(x<5) run(x+1); } public static void main(string args[] ) { RecursionTwo test = new RecursionTwo(); test.run(1); } base case It will stop! Recursion OUTPUT A+ Computer Science -

13 AP Problem - try int fun(int x, int y) { OUTPUT if ( x == 0 ) return x; else return x+fun(y-1,x); } What would fun(4,4) return? A+ Computer Science -

14 AP Problem - try int fun(int x, int y) { OUTPUT if ( x == 0 ) 16 return x; else return x+fun(y-1,x); } What would fun(4,4) return? A+ Computer Science -

15 What is tail end recursion? Difference? REGULAR RECURSION public int sumdigits(int n) { if (n <= 0 ) return 0; else return sumdigits(n/10) + n%10; } TAIL-END RECURSION public int sumdigits(int n) { if (n <= 0 ) return 0; else return sumdigits(n/10); }

16 Homework: Recursion Packet Worksheets #1,2

17 Today - Recursion and STRINGS

18 Warm-Up:

19 The Stack call out.println(recur("abc")) public String recur(string s) { int len = s.length(); if(len>0) return recur(s.substring(0,len-1)) + s.charat(len-1); return ""; } A+ Computer Science -

20 The Stack call out.println(recur("abc")) AR stands for activation record. An AR is placed on the stack every time a method is called. AR1 s="abc" return AR2 + c A+ Computer Science -

21 The Stack AR2 s="ab" return AR3 + b AR1 s="abc" return AR2 + c A+ Computer Science -

22 The Stack AR3 s="a" return AR4 + a AR2 s="ab" return AR3 + b AR1 s="abc" return AR2 + c A+ Computer Science -

23 The Stack AR4 s="" return "" AR3 s="a" return AR4 + a AR2 s="ab" return AR3 + b AR1 s="abc" return AR2 + c A+ Computer Science -

24 The Stack AR3 s="a" return a AR2 s="ab" return AR3 + b AR1 s="abc" return AR2 + c A+ Computer Science -

25 The Stack AR2 s="ab" return ab AR1 s="abc" return AR2 + c A+ Computer Science -

26 The Stack call out.println(recur("abc")) OUTPUT abc AR1 s="abc" return abc A+ Computer Science -

27 What is the point? If recursion is just a loop, why would you just not use a loop? Recursion is a way to take a block of code and spawn copies of that block over and over again. This helps break a large problem down into smaller A+ pieces. Computer Science -

28 Advanced Topic - using recursion to look around you

29 Counting Spots If checking 0 0, you would find are @ A+ Computer Science - at spot at spot at spot at spot at spot [1,2] The exact same checks are made at each spot.

30 Counting Spots if ( r and c are in bounds and current spot is ) mark spot as visited bump up current count by one recur up recur down recur left recur right This same block of code is recreated with each recursive call. The exact same code is used to check many different locations. A+ Computer Science -

31 Counting Spots if ( r and c are in bounds and current spot is ) mark spot as visited bump up current count by one recur up recur down recur left recur - @ A+ Computer Science -

32 Homework: Worksheet #3 In CANVAS

33 HW: Coding Bat

34 Today - Recursion o Rama

35 Recursion Kahoot Recursion Kahoot

36 Fibonacci Numbers

37 HomeWork#11! Coding Bats, recursion Do 12 of these 15 (more for extra credit)

38 HW #12 Code Step By Step

39 Extra Credit : Towers of Hanoi Explanation by MIT Professor of Computer Science