Penjelasan Algoritma Rekursif
Summary
TLDRIn this educational video, the presenter explores the concept of recursive algorithms, which they consider one of the most challenging yet beautiful topics in the study of algorithms. The script explains that recursion is a technique where a problem's solution involves the problem itself, often implemented within a function that calls itself. Using the analogy of mirrors facing each other to illustrate the self-referential nature of recursion, the presenter then delves into the practical example of calculating factorials. They demonstrate how each factorial calculation is dependent on the previous one, showcasing the recursive pattern. The video aims to clarify the recursive approach by contrasting it with iterative methods and encouraging viewers to pause and reflect on the presented examples.
Takeaways
- 🧠 The script discusses the concept of recursive algorithms, which the speaker considers one of the most challenging yet beautiful parts of the study of algorithms.
- 🔍 Recursive algorithms are defined as techniques for solving problems where the solution to the problem involves the problem itself, either in its definition or in its implementation.
- 💡 The speaker uses the analogy of mirrors facing each other in a corridor to illustrate the concept of recursion, where an image within a mirror reflects another image, and so on, indefinitely.
- 📚 The script mentions that recursion is not only implemented within functions but can also be used in procedures, although it is commonly implemented within functions.
- 🌐 The speaker gives a real-world example of recursion by describing the experience of looking at mirrors in a barbershop or an elevator, where one's reflection is seen within multiple layers of mirrors.
- 🔢 The script provides an example of recursion in the context of calculating factorials, where the factorial of a number is defined in terms of the factorial of a smaller number.
- 📉 The script explains that factorials are a classic example of recursion, with factorial n being n times factorial of n-1, and factorial 0 being defined as 1.
- 📝 The speaker encourages viewers to pause the video and compare the recursive pattern on the left with the iterative pattern on the right to understand the recursive nature of factorials.
- 🔄 The script highlights that recursion is a powerful tool for solving problems that have a self-similar structure, and it is essential for understanding certain types of algorithms.
- 🎯 The speaker concludes by emphasizing the importance of recognizing the recursive nature within problems and how it can be mathematically represented, such as in the case of factorials.
Q & A
What is the main topic discussed in the script?
-The main topic discussed in the script is the concept of recursive algorithms, specifically focusing on their definition, implementation, and examples like the factorial function.
What is the definition of a recursive algorithm according to the script?
-A recursive algorithm is defined as a technique for solving a problem where the solution to the problem involves the problem itself, either in its definition or in its implementation.
How does the script explain the concept of recursion using mirrors?
-The script uses the analogy of standing between two facing mirrors to explain recursion. It describes how each mirror reflects the other, creating an infinite sequence of reflections, which is similar to how a recursive function calls itself.
What is the example given for a recursive problem in the script?
-The example given for a recursive problem in the script is the calculation of factorials, where the factorial of a number n is defined as n times the factorial of n-1.
How is the factorial function described as recursive in the script?
-The factorial function is described as recursive because it involves the factorial of the previous number (n-1) multiplied by n, which in turn involves the factorial of n-2, and so on, until it reaches the base case of factorial 0 which is 1.
What is the base case for the factorial function as mentioned in the script?
-The base case for the factorial function mentioned in the script is when n is 0, at which point the factorial is defined as 1.
How does the script differentiate between recursive and iterative solutions?
-The script differentiates between recursive and iterative solutions by showing that a recursive solution involves a function calling itself, while an iterative solution uses a loop to achieve the same result.
What is the significance of the script's comparison between the left and right sides of an equation?
-The script compares the left and right sides of an equation to illustrate the recursive pattern, where the right side shows the recursive definition of the factorial function, and the left side might represent an iterative approach.
What does the script suggest about the implementation of recursive algorithms?
-The script suggests that recursive algorithms are not only implemented in functions but can also be implemented in procedures, and they are commonly implemented in functions for everyday examples like the factorial calculation.
Why are recursive algorithms considered both difficult and beautiful according to the script?
-Recursive algorithms are considered difficult because they involve a complex concept of a function calling itself, which can be confusing. They are also considered beautiful because they provide a clean and elegant solution to problems like calculating factorials.
What advice does the script give for understanding recursive algorithms?
-The script advises to pause and carefully observe the examples given, such as the mirror analogy and the factorial function, to fully understand the concept of recursion.
Outlines
🧠 Introduction to Recursive Algorithms
The paragraph introduces the concept of recursive algorithms, which the speaker considers one of the most challenging yet beautiful parts of the study of algorithms. It explains that a recursive algorithm is a method of solving a problem where the solution depends on solutions to smaller instances of the same problem. The speaker uses the analogy of standing between two facing mirrors to illustrate the self-referential nature of recursion, where an image within a frame contains the frame itself. The paragraph also mentions that recursion is not limited to functions but can also be implemented in procedures. It then transitions into explaining the recursive nature of factorial calculations, a common example used to demonstrate recursion, where the factorial of a number is defined in terms of the factorial of a smaller number.
🔍 Deep Dive into Factorial Recursion
This paragraph delves deeper into the recursive nature of factorial calculations. It explains that the factorial of a number 'n' is defined as 'n' times the factorial of 'n-1'. The speaker uses the mathematical formula to illustrate this, showing that factorial 'n' equals 'n' times factorial 'n-1'. The paragraph highlights the recursive definition where the base case is when 'n' is zero, in which case the factorial is 1. For all other values of 'n', the factorial is calculated by multiplying 'n' by the factorial of 'n-1'. The speaker emphasizes the self-referential aspect of the factorial function, which is a quintessential example of recursion in algorithmic problems.
Mindmap
Keywords
💡Algorithm
💡Recursion
💡Function
💡Procedure
💡Factorial
💡Base Case
💡Recursive Case
💡Mirror Image
💡Problem Solving
💡Mathematical Formula
Highlights
Introduction to the concept of recursive algorithms in the field of algorithms.
Definition of recursion as a technique where the solution to a problem includes the problem's definition itself.
Explanation that recursion is not only implemented in functions but can also be in procedures.
Analogy of recursion to mirrors facing each other, illustrating the self-similarity in recursive problems.
Example of a barbershop with mirrors to explain the concept of recursion in everyday life.
The concept of recursion in the context of algorithms, specifically with the factorial problem.
Recursive nature of factorial calculation, where the factorial of a number is the product of all positive integers up to that number.
Recursive definition of factorial where n! = n * (n-1)! with the base case being 0! = 1.
Comparison between iterative and recursive patterns in solving factorial problems.
The importance of understanding recursion for solving problems that have a self-similar structure.
Recursive implementation of factorial function in programming.
Explanation of how recursion can be used to solve problems that are not easily solvable through iteration.
The significance of base cases in recursion to terminate the recursive calls.
Recursive approach to solving problems as a fundamental concept in algorithm design.
The beauty of recursion in solving complex problems with elegant and simple code.
Practical examples of recursion in programming, such as calculating the factorial of a number.
The importance of understanding both iterative and recursive approaches to problem-solving in algorithms.
Transcripts
e-cash Assalamualaikum warahmatullahi
wabarakatuh teman-teman semua kita akan
belajar satu buah materi yang saya pikir
dalam
mata pelajarannya atau dalam ilmu
pelajaran algoritma ini adalah
eh bagian yang menurut saya paling sulit
itu ya Selama saya belajar algoritma
namun ini adalah bagian paling indah
dalam tanda kutip dari
ei5 algoritma itu sendiri yaitu adalah
rekursif ya algoritma rekursif ini eh 1
bab terakhir kalau kita mau belajar
tentang
agoritma
na rekursif itu apa Jadi secara definisi
tekstual ya ini mohon maaf agak membumi
membingungkan mungkinnya dari
definisinya rekursif adalah teknik
menyelesaikan persoalan dimana didalam
nah di dalam menyelesaikan persoalan itu
mengandung definisi persoalan itu
sendiri ya
eh atau dalam bentuk implementasinya
nanti rekursif ini diimplementasikan
dalam sebuah fungsi tentu Sebelumnya kan
kita sudah belajar apa itu fungsi Apa
itu prosedur yang tidak langsung si
tersebut nanti memanggil fungsi itu
sendiri gitu
itu rekursif secara implementasi
sebenarnya eh tidak hanya dalam sebuah
fungsi sih dalam prosedur pun juga tentu
nanti implementasinya bisa hanya
lazimnya ekskursif ini diimplementasikan
dalam sebuah fungsi na dalam contoh
keseharian misalkan kita berdiri di satu
lorong Gimana Di Dinding antar dua
lorong itu ada cermin yang saling
berhadapan Ketika kita melihat cermin
itu maka cermin ini akan memantulkan
cermin di dalam kita Ed sang Kita dimana
di belakang di cermin di belakang kita
itu ada kita dengan cermin yang di depan
kita lagi kalau kemudian di cermin yang
di depan kita ada kita lagi
terus ini dan seterusnya ada di dalam
satu buah cermin ada kita yang ada
cerminnya lagi lalu kemudian dicermin
tuada kita lagi dengan cermin lagi dan
seterusnya teman-teman kalau datang anak
cowok misalkan nya pergi ke
apa namanya Barbershop di teater tukang
cukur di depan wajah kita ada cermin di
belakang kita ada cermin Maka kalau kita
melihat
cermin yang ada di belakang kita itu ada
cermin kita lagi GTA tentu culture
minyak benar-benar berhadapan atau non
bisa coba-coba hadapan dua buah cermin
atau kalau kita misalkan ada di lift
yang dimana live itu Sisinya adalah
cermin pasti kita akan melihat Sisi
cermin itu ada kita dan cermin lagi
terus dan seterusnya Nah itu gambaran
bagaimana rekursif di dalam dunia
jadi dalam satu buah bingkai persoalan
di dalamnya ada persoalan itu sendiri
dan di dalamnya ada persoalan itu
sendiri begitu ya Nah nanti kita coba
lihat dalam konteks algoritma
contoh misalkan kita punya persoalan
perulangan faktorial ya factorials Nol
itu satu faktorial satu itu satu
faktorial 2 itu satu kali dua faktorial
tiga itu satu kali dua kali tiga
faktorial 4 itu satu kali dua kali tiga
kali empat dan faktor ya lima itu satu
kali dua kali tiga kali empat kali lima
nah ini contoh tentang faktorial ini
sudah sering dibahas di video-video
sebelumnya temen-temen silahkan cek
video-video saya yang algoritma soal
faktorial baik itu di Sumba perulangan
ataupun F fungsi Kalau enggak salah daya
bisa cek lagi di sana Nah ternyata
Wow
proses melakukan faktorial ini ini juga
sebenarnya memiliki sifat rekursif
Kenapa karena kalau kita lihat Oke
faktorial nol itu memang satu Ternyata
faktorial satu itu adalah faktor yang
nol dikali satu dan faktorial 2 itu
adalah faktorial satu dikali faktorial 2
faktorial tiga itu adalah faktorial 2
dikali dengan tiga faktorial 4 itu
adalah faktorial tiga dikali dengan 4G
dan faktorial 5 itu adalah
faktorial 4 dikali lima silakan
teman-teman di pos video ini lalu Coba
lihat antara kiri dan kanan lihat ya Ini
satu adalah faktorial satu kali dua
inhaled nih mulai tiga kelihatan Ya
gimana tiga itu adalah faktorial 2
sebenarnya satu kali dua itulah
faktorial 2 jadi yang kanan ini adalah
pola rekursif yang kiri perulangan
ada biasanya Eh rekursif ini nanti kita
menyelesaikan persoalan-persoalan yang
bentuknya juga perlu dan ya cukup
silakan di-pause dipandangi antara kiri
dengan kanan
oke kalau sudah di Paus sudah bisa
dipahami dari contoh ini kita lanjut nah
di dalam persoalan faktorial terdapat
persoalan faktorial itu sendiri lihat di
dalam faktor yang empat itu terdapat
persoalan faktorial 3gnya jadi dalam
faktorial ada persoalan faktorial itu
sendiri nah kalau kita Tuliskan dalam
bentuk eh matematika faktorial dari n
itu kan satu kali dua kali seterusnya
sampai dengan n min1 dikalikan dengan n
ya jadi faktorial dari mitos adalah n
kurang satu faktorial dikalikan dengan
seperti ini ya faktorial 4 itu adalah
empat kurang satu faktorial yaitu tiga
faktorial dikalikan dengan empat dia
Jadi ini korelasinya dengan rumus yang
ada di bawah sini aku
Iya nah jadi kita lihat di sini n
faktorial itu dia akan bernilai 1
jika
n-nya itu adalah nol
lalu kemudian ia akan bernilai n
caliente in 1 faktorial yang ini dengan
posisinya ditukar aja jadi nw-1
faktorialnya pindah ke kanan kalau NY
itu lebih besar dari nol ya jadi dia
akan bernilai 1 kalau NY itu nol
sedangkan dia akan bernilai n * n
faktorial kalau dia lebih besar dari
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