Rekursif. Overview. Tujuan Instruksional

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Rekursif

Pertemuan : 6 - 7 Disusun oleh : Danang Junaedi

Jurusan Teknik Informatika – Universitas Widyatama

Jurusan Teknik Informatika VI-VII - 2 Universitas Widyatama

Pemrograman II (Terstruktur II)

Tujuan Instruksional

Review Fungsi & Prosedur

Introduction of Recursion

Definition

Recursion Method

Contoh Kasus

Recursion vs Iteration

Kasus

Tugas Presentasi

Overview

Menjelaskan pengertian dan manfaat rekursif, serta

cara penulisannya dalam program

Menjelaskan kelebihan dan kekurangan rekursif dalam

pemrograman

Menjelaskan penggunaan rekursif dalam program

Menggunakan rekursif dalam program

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Review Fungsi dan Prosedur

Fungsi

tipe_fungsi nama_Fungsi(argumen1, argumen2,....) definisi Fungsi

{ xxxx xxxx tubuh Fungsi

xxxx }

contoh : double Absolut(double X) {

if (X,0) X=-X; return(X); }

Prosedur

void nama_Prosedur(argumen1, argumen2,....) definisi Prosedur

{ xxxx

xxxx tubuh Prosedur

xxxx }

contoh : void Tampil(char Nama[15], int Kali) {

int I;

for(I=0;I<Kali;I++) printf(Nama); }

Introduction of Recursion

So far, we have seen methods that call other methods.

For example, the main() method calls the square() method.

Recursive Method:

A recursive method is a method that calls itself.

main()

square()

compute()

Definition

A recursive function

is a function that calls itself either

directly or indirectly through another function.

The function launches (calls) a fresh copy of itself to work on

the smaller problem – this is referred to as

recursive call

and

is also called as

recursion step

.

The recursion step often includes the keyword

return

The function recognizes the base case and returns a result to

the previous copy of the function and a sequence of returns

ensues all the way up the line until the original function call

eventually returns the final result to

main

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Recursion Method

The important thing to remember when creating a recursive function

is to give an 'end-condition'. We don't want the function to keep

calling itself forever, now, do we? Somehow, it should know when to

stop. There are many ways of doing this. One of the simplest is by

means of an 'if condition' statement

A recursive method generally has two parts.

A termination part that stops the recursion.

This is called the base case.

The base case should have a simple or trivial solution.

One or more recursive calls.

This is called the recursive case.

The recursive case calls the same method but with simpler or

smaller arguments.

Example

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Fungsi Faktorial

C++

Secara Iterasi

atau n! = n * (n - 1) * (n - 2) * ... * 1

Secara Rekursif

atau n! = n * (n - 1)! dan 0! = 1 int Fakt(int n) { Fak=1; if (n > 1) { for(i=1;i<=n;i++) { Fak=Fak*I;} } return Fak; } int Fakt(int n) { if (n == 1 || n == 0) { return 1;}

else {return n * Fakt(n-1);} }

Example

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Ilustration

a. Process of recursive calls

b. Values returned from each recursive calls

5! 5 * 4! 4 * 3! 3 * 2! 2 * 1! 1 5! 5 * 4! 4 * 3! 3 * 2! 2 * 1! 1 5! = 5 * 24 = 120 returned 4! = 4 * 6 = 24 returned 3! = 3 * 2 = 6 returned 2! = 2 * 1 = 2 returned 1 returned

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Recursion vs Iteration

Iteration

Uses repetition structures (for, whileor do…while) Repetition through explicitly use of repetition structure

Terminates when loop-continuation condition fails

Controls repetition by using a counter

Recursion

Uses selection structures (if, if…elseor switch) Repetition through repeated method calls

Terminates when base case is satisfied

Controls repetition by dividing problem into simpler one

More overhead than iteration More memory intensive than iteration Can also be solved iteratively

Often can be implemented with only a few lines of code

Studi Kasus

Towers of Hanoi game

(Game invented by French mathematician Edouard Lucas in 1883)

Rules for the Towers of Hanoi game

1.

Move one disk at a time. Each disk you move must be a topmost disk.

2.

No disk may rest on top of a disk smaller than itself.

3.

You can store disks on the second pole temporarily, as long as you

observe the previous two rules.

Fibonacci

(F(n)=F(n-1) + F(n-2) + ……)

Binary Search secara rekursif

Tugas

Buat Laporan berdasarkan kasus yang sudah kelompok anda pilih

dengan susunan

Bab I Pendahuluan (Latar Belakang, Tujuan, Batasan Masalah) Bab II Dasar Teori

Bab III Analisa & Perancangan

Bab IV Implementasi (Listing Program dan Hasil Running Program)

Bab V Penutup (Kesimpulan & Saran)

Referensi

Laporan (Tidak perlu dijilid)

Bahan presentasi dan program dikumpulkan dalam bentuk file

(maksimum 4 hari sebelum presentasi dilaksanakan)

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