LECTURE 20:RECURSIONCSC 212 – Data Structures

Humorous Asides

“A journey begins with a single step”

“A journey begins with a single step”

Large problems hard to solve Thinking about & solving small problems

easier Split large problems into smaller ones

Before you start coding, plan each assignment

Break up large methods with many ifs and loops

Action in many methods into small (private) methods

Solving Problems

(At least for programming)

Smaller is Better

CENSORED

Should be boring, monotonous drone Given its parameters, perform the expected

action Only perform the action defined for its

parameters Should not cure cancer

Do not worry about the larger problem This greater solution is not this method’s concern

Solving entire programming assignment is hard Why we divide up tasks in the first place!

Goal of a Java Method

re-cur-sion: Method of solving problem by combining solutions to identical, smaller problems

Recursion

Keep dividing until base case(s) reached Base cases are cases that are trivial to solve4! = 4 * 3! = 4 * (3 * 2!) = 4 * (3 * (2 * 1!))

After base case, combine solutions to complete work = 4 * (3 * (2 * 1)) = 4 * (3 * 2) = 4 * 6 = 24

See Recursion Work

Begin by figuring out what are the base case(s) Simple subproblem that is solved

immediately A base case will always be reached solving

problem Recursive step can then be generated

Create easier problem(s) which splits original problem

Combine subproblems’ solutions for final answer

Writing Recursive Solution

Will your solution work? Each step moves toward base case All possible inputs must be considered Otherwise, get infinite recursion

Working Recursive Solutions

A method is recursive if it calls itself:public static int factorial(int i) { if (i <= 1) {

return 1; } else {

return i * factorial(i - 1); }

}

Recursion in Java

public method starts the recursive process Usually only calls recursive method

private recursive method has 1+ parameter Results should only depend on the parameters if or switch selects from different cases

Using fields can avoid parameters… … but not recursive approach to solving the

problem Cheating recursion with fields does not scale

Designing Recursion

Should have immediately check for base case(s) Cannot have recursive calls within this code

Include 1+ method calls in recursive step(s) Assume recursion works when writing these Take 1 step toward base case (not 2, 3, or

10482)

Writing Recursive Method

Each call gets frame created for it Within frame, place all local variables &

parameters (Real frames include line being executed)

Trace shows frames solving their single step NO CURING CANCER

Tracing Recursion

X

private static void rev(int[] a, int j) {int opposite = a.length - (j + 1);if (j < opposite) { rev(a, j + 1); int temp = a[j]; a[j] = a[opposite]; a[opposite] = temp;}

}public static void reverse(int[] a) { rev(a,0);

}

int[] example1 = { 0 };reverse(example1);

Trace This, Buddy!

private static void rev(int[] a, int j) {int opposite = a.length - (j + 1);if (j < opposite) { rev(a, j + 1); int temp = a[j]; a[j] = a[opposite]; a[opposite] = temp;}

}public static void reverse(int[] a) { rev(a,0);

}

int[] example2 = { 0, 1, 2, 3, 4 };reverse(example2);

Trace This, Buddy!

Divide array in two parts First element & everything after

Last element & all preceding elements

Left & right halves of the array

Base case when working with 0 (or 1) entries

Recursive Array Handling

Complete week #7 assignment Due by 5PM next Wednesday

Finish programming assignment #2 Due before next lecture (Wednesday)

Review sections 3.1-3.5 in book before class How do linked lists, arrays & recursion

work together? How do they work?

Before Next Lecture…