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Pertemuan 1

Pertemuan 1. Rekursi. Fungsi Rekursif. Definisi fungsi rekursif . Contoh 1 : Triangle Contoh 2 : Faktorial Contoh 3 : Perkalian Contoh 4 : Fibonacci Contoh 5 : Tower of Hanoi. Fibonacci. 0,1,1,2,3,5,8,13,21,34,55,89,144,..

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Pertemuan 1

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  1. Pertemuan 1 Rekursi

  2. Fungsi Rekursif • Definisifungsirekursif. • Contoh 1 : Triangle • Contoh2 : Faktorial • Contoh3 : Perkalian • Contoh4 : Fibonacci • Contoh5 : Tower of Hanoi

  3. Fibonacci • 0,1,1,2,3,5,8,13,21,34,55,89,144,.. • The Fibonacci seriesfn≥0 is a famous series defined by:f0 :≡ 0, f1 :≡ 1, fn≥2 :≡ fn−1 + fn−2 • f2 = f0 + f1 = 0 + 1 = 1 • f3 = f1 + f2 = 1 + 1 = 2 • f4 = f2 + f3 = 1 + 2 = 3 • f5 = f3 + f4 = 2 + 3 = 5 • …. Leonardo Fibonacci1170-1250

  4. Fibonacci

  5. Tracing Fibonacci • fibo (4) = ? F(4) F(2) F(3) F(2) F(0) F(1) F(1) F(0) F(1)

  6. Towers of Hanoi • Sebuah game /puzzle matematikakunodimanaadaadatigabuahtiang, dimanasalahsatutiangterdapatbeberapapiringan • Piringanakandipindahkanketiang yang lain dengansalahsatutiangmenjaditiang bantu • Untukmemindahkanadabeberapsyarat • Hanyaadasatupiringan yang berpindahdalamsatulangkah • Tidakbolehadapiringan yang beradadiataspiringan yang lebihkecil • Total langkah yang dibutuhkanuntukmenyelesaikan puzzle secaramatematikaadalah 2n -1 dengan n adalahbanyaknyapiringan

  7. Tracing Towers of Hanoi • towers(3, A, C, B) = ?

  8. resume • Kelebihan : • Program menjadilebihsingkat/sederhana • Dalambeberapakasuskasusmemangdibutuhkanpenggunaanrekursi • Kekurangan : • Kurangefektifdalamhalkecepatan • Membutuhkahmemorilebih, karenaketikasatufungsi / method memanggildirinya , dibutuhkantambahanalokasimemori. Sehinggaalokasimemori total menjadilebihbesar

  9. Tugas Rumah : TRACING 1. NPM genap : towers (4, A, C, B) = ? NPM ganjil : towers (4, C, A, B ) = ? 2. fibo(6) = ?

  10. http://coding-n-inspiring.blogspot.com • wikipedia

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