Recursion – java tutorial

Recursion – Java tutorial • Learn about recursive definitions • Explore the base case and the general case of a recursive definition • Learn about recursive algorithms Lecture Objectives • Learn about recursive methods • Become aware of direct and indirect recursion • Explore how to use recursive methods to implement recursive algorithms Lecture Objectives (Cont’d) • Recursion  Process of solving a problem by reducing it to smaller versions of itself • Recursive definition  Definition in which a problem is expressed in terms of a smaller version of itself  Has one or more base cases Recursive Definitions Recursive Definitions (Cont’d) 0! = 1 (By Definition!) n! = n x (n – 1) ! If n > 0 3! = 3 x 2! 2! = 2 x 1! 1! = 1 x 0! 0! = 1 (Base Case!) 1! = 1 x 0! = 1 x 1 = 1 2! = 2 x 1! = 2 x 1 = 2 3! = 3 x 2! = 3 x 2 = 6 • Recursive algorithm  Algorithm that finds the solution to a given problem by reducing the problem to smaller versions of itself  Has one or more base cases  Implemented using recursive methods • Recursive method  Method that calls itself • Base case  Case in recursive definition in which the solution is obtained directly  Stops the recursion Recursive Definitions (Cont’d) • General solution  Breaks problem into smaller versions of itself • General case  Case in recursive definition in which a smaller version of itself is called  Must eventually be reduced to a base case Recursive Definitions (Cont’d) • Directly recursive: a method that calls itself • Indirectly recursive: a method that calls another method and eventually results in the original method call • Tail recursive method: recursive method in which the last statement executed is the recursive call • Infinite recursion: the case where every recursive call results in another recursive call Recursive Definitions (Cont’d) Tracing a Recursive Method • Recursive method  Logically, you can think of a recursive method having unlimited copies of itself  Every recursive call has its own • Code • Set of parameters • Set of local variables • After completing a recursive call  Control goes back to the calling environment  Recursive call must execute completely before control goes back to previous call  Execution in previous call begins from point immediately following recursive call Tracing a Recursive Method (Cont’d) [...]... needle1); } } Recursion or Iteration? • Two ways to solve particular problem  Iteration  Recursion • Both iteration and recursion use a control statement  Iteration uses a repetition statement  Recursion uses a selection statement Recursion or Iteration? (Cont’d) • Iteration and recursion both involve a termination test  Iteration terminates when the loop-continuation condition fails  Recursion terminates... of stack Recursion and the Method Call Stack (Cont’d) Figure 6: Method calls on the program execution stack Towers of Hanoi Problem with Three Disks Figure 7: Tower of Hanoi Problem with three disks Towers of Hanoi: Three Disk Solution Figure 8: Tower of Hanoi Problem with three disks – Solution 1 Towers of Hanoi: Three Disk Solution (Cont’d) Figure 9: Tower of Hanoi Problem with three disks – Solution... case(s) • Provide solutions to general cases in terms of smaller versions of general cases Recursive Factorial Method public static int fact(int num) { if (num = = 0) return 1; else return num * fact(num – 1); } Recursive Factorial Method (Cont’d) Figure 1: Execution path of fact(4) Largest Value in Array Figure 2: Array with six elements Largest Value in Array (Cont’d) • • • • if the size of the list... rFibNum(int a, int b, int n) { if (n == 1) return a; else if (n == 2) return b; else return rFibNum(a, b, n -1) + rFibNum(a, b, n - 2); } Recursive Fibonacci (Cont’d) Figure 5: Execution of rFibNum(2, 3, 5) Recursion and the Method Call Stack • Method call stack used to keep track of method calls and local variables within a method call • Just as with nonrecursive programming, recursive method calls are placed... or Iteration? (Cont’d) • Iteration and recursion both involve a termination test  Iteration terminates when the loop-continuation condition fails  Recursion terminates when a base case is reached • Recursion can be expensive in terms of processor time and memory space, but usually provides a more intuitive solution Programming Example: Decimal to Binary public static void decToBin(int num, int base)... midP1P2,midP3P1); drawSierpinski(g, lev - 1, p2, midP2P3, midP1P2); drawSierpinski(g, lev - 1, p3, midP3P1, midP2P3); } L! } NA OP IO T Programming Example: Sierpinski Gasket (Cont’d) Figure 12: Sierpinski Gaskets: Recursion depth of 3 PT O ON I L! A . Recursion – Java tutorial • Learn about recursive definitions • Explore the base case and the general case. methods • Become aware of direct and indirect recursion • Explore how to use recursive methods to implement recursive algorithms Lecture Objectives (Cont’d) • Recursion  Process of solving a problem. cases Recursive Definitions Recursive Definitions (Cont’d) 0! = 1 (By Definition!) n! = n x (n – 1) ! If n > 0 3! = 3 x 2! 2! = 2 x 1! 1! = 1 x 0! 0! = 1 (Base Case!) 1! = 1 x 0! = 1 x 1 =