Recursion என்பது Python functions-ல் மிகவும் முக்கியமான concept. Simple……
Recursion
Recursion is a programming technique in which a function calls itself to solve a problem by reducing it into smaller versions of the same problem. தமிழில்: ஒரு பெரிய problem-ஐ அதே வகையிலான சிறிய-small problem-களாக reduce செய்து, ஒரு functi…
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Program
Example
Explanation
இங்கே show() function உள்ளே மீண்டும் show() call ஆகிறது. இதுதான் recursion-ன் basic idea. ஆனா……
List
1. Recursive Call 2. Base Case…
Definition
Recursion is a programming technique in which a function calls itself to solve a problem by reducing it into ……
Simple Explanation
Suppose நாம்: 5 4 3 2 1 print செய்ய வேண்டும். Normal method: for i in……
இங்கே function என்ன செய்கிறது? count(5) ↓ count……
Concept
Main concept
Recursion-ஐ ஒரு staircase போல நினைத்துக்கொள்ளுங்கள். count(5) ↓ count(4) ↓ cou……
Important
Two most important parts
Recursion-ல் இரண்டு parts com……
Important
1. Base Case…
Important
Function எப்போது stop ஆக வேண்……
Program
Example
Explanation
இதுதான் stopping condition.…
List
1. Recursive Case…
Explanation
Function தன்னையே மீண்டும் call ச……
Memory Trick
Recursion = Base Case + Self Call Very important: Bas……
Syntax
General syntax
Explanation
function_name(smaller_value) ……
Explanation
return function_name(n - 1)…
Explanation
count(5)…
Flow
count(5) ↓ Print 5 ↓ count(4) ↓ Print 4 ↓ count(3) ↓ Prin……
Explanation
Why base case is needed
இதோ base case இல்லாத recursion: def count(n): print(n) count(n - 1) count(5) ……
Common Mistake
Recursion error
Common message concept: RecursionError: maximum recursion depth ex……
Important
Very important
Recursion என்பது technically infinite loop அல்ல. ஆனால் stopping condition இல்……
Flow
Call stack
Recursion புரிய Call Stack concept ரொம்ப முக்கியம். Suppose: def test(n): if n == 0: return print(n) test(n -……
Explanation
Call and return
Recursion-ல் இரண்டு phases இர……
Explanation
1. Going Down / Calling Phase……
Explanation
இதுதான் recursion-ன் most imp……
Real Life Example
Example
def show(n): if n == 0: return pr……
இதுதான் recursion-ன் real bea……
Explanation
Why output reverses
Let's understand inch by inch. show(3) Print Before 3 Call show(2) After 3 இன்னும் execute ஆகவில்லை. Wait செய……
Flow
Visual stack
Calling phase: show(3) ↓ show(2) ↓ show(1) ↓ show(0) Returning……
Concept
Most important exam concept
Recursion uses: Stack data structure / Call Stack Reason: F……
Real Life Example
Stack example
Calls: test(3) test(2) test(1) L……
Explanation
Factorial using recursion
Recursion-க்கு classic example:……
Output
Result
Recursive formula: n! = n × (……
Explanation
return n * factorial(n - 1)…
Concept
This line: return n * factorial(n - 1) means: factorial(5) = 5 ×……
Dry Run
Factorial dry run
Important
Very important
Recursion-ல் result immediately கிடைக்காமல் இருக்கலாம். Function calls first stack-ல் build ஆகு……
Flow
Factorial flow
factorial(5) ↓ 5 * factorial(4) ↓ 4 * factorial(3) ↓ 3 * ……
Explanation
Sum using recursion
Find: 1 + 2 + 3 + 4 + 5…
Explanation
return n + total(n - 1)…
Explanation
Print 1 to n
Recursion பயன்படுத்தி 1 to 5 print செய்யலாம். def p……
Explanation
Why ascending
Notice: print_numbers(n - 1) comes before: print(n) So function first dee……
Explanation
Print n to 1
def print_numbers(n): if n == 0: ……
Concept
Very important concept
இந்த இரண்டு programs compare செய்யுங்கள். Print before recursive call print(n) function(n - 1) Outp……
Explanation
Fibonacci using recursion
Fibonacci sequence: 0, 1, 1, ……
Formula
F(n) = F(n-1) + F(n-2) Base c……
Explanation
return fib(n - 1) + fib(n - 2)…
Explanation
Why two recursive calls
For: fib(5) Python calculates: fib(4) + f……
Concept
fib(5) / \ fib(4) fib(3) / \ / \ fib(3)……
Important
Simple recursive Fibonacci is easy to understand.……
Explanation
Example
fib(3) multiple times calculate ஆகலாம். ……
Explanation
String recursion
Recursion numbers மட்டும் அல்ல. String processing-க்கும் use செய்யலாம். Exampl……
Dry Run
reverse("ABC") = reverse("BC") + "A"
Explanation
Direct recursion
ஒரு function தன்னையே direct-ஆ……
Program
Example
Explanation
show(n - 1)…
Explanation
Indirect recursion
Function A → Function B → மீண்டும் ……
Program
Example
Explanation
a(4) Flow: a() ↓ b() ↓ a() ↓ ……
Explanation
Tail recursion
Recursive call function-ன் last oper……
Program
Example
Explanation
Recursive call: count(n - 1) ……
Important
Important python point
Some programming languages tail recursion optimization செய்யலாம். ஆனால் ……
Comparison
Recursion vs iteration
Recursion மற்றும் Loop இரண்டு……
Program
Example
Explanation
count(5) Both same output.…
Explanation
When recursion is useful
Recursion especially useful when problem itself recursive structure. Examples: Factoria……
Real Life Example
Real time analogy
Folder inside Folder Computer folder: Main Folder │ ├── File ├── Sub Folder │ ├── File │ └── A……
Real Life Example
Tree example
Tree structure: A / \ B C / \ D E Each node-க்கும் child nodes இருக்கலாம். Node……
Comparison
Base case vs recursive case
Base Case Recursion stop cond……
Program
Example
Explanation
Problem smaller செய்து functi……
Explanation
Recursive progress
Base case மட்டும் போதாது. ஒவ்வொரு recursive call-லும் base case-க்கு closer ஆக வேண்டும். Correct: count(n - ……
Explanation
ஒரு good recursive function-க்கு
1. Base Case இருக்க வேண்டும் 2. Recursive ……
Explanation
இதையே முக்கியமான theory point……
Common Mistake
Error 1
No Base Case def test(): test……
Output
Result
Common Mistake
Error 2
Wrong Direction def count(n): if n == 0……
Common Mistake
Error 3
Base Case Never Reached def count(n): if n……
Common Mistake
Error 4
Forgetting return Factorial wrong: def fact(n): if n == ……
Common Mistake
Error 5
Wrong Base Value Factorial: 0! = 1 So correct: if n == 0:……
Explanation
Memory usage
Every recursive call normally requires a new stack frame. Each frame stores things l……
Explanation
Each active call has its own ……
Explanation
Local scope connection
Previous Local Scope concept இங்கே connect ஆகிறது. def fact(n): ஒவ்வொரு recursive call-க்கும் தனி……
Explanation
Return value connection
Recursion return values-ஐ chain ஆக pass செய்யலாம். Factorial: fact(0) returns 1 fact(1) receives 1 return……
Explanation
Recursion limit
Python has recursion depth protection. Current limit பார்க்க: import sys print(sys.ge……
Important
Technically recursion limit change செய்ய: sys.setrecursionlimit(...) possible……
Comparison
Function composition vs recursion
Previous topic-க்கு comparison: Function Composition f(g(x)) ……
Comparison
Recursion vs nested function
Nested function: def outer(): def inner()……
Explanation
Advantages
Recursion advantages: Code short ஆகலாம் Mathematical definitions easy Tree traver……
Explanation
Disadvantages
Recursion disadvantages: Extra memory Function-call overhead Debugging some……
Explanation
When not to use
Simple: 1 முதல் 100 வரை print இதற்கு recursion தேவைய……
Explanation
When to use
Problem naturally breaks into same smaller problem: fact……
Memory Trick
BSR Recursion-க்கு: B → Base Case S → Sel……
Memory Trick
Another memory trick
Recursion: Call yourself, but know when to stop. தம……
TRB Point
1. Recursion என்றால்?…
TRB Point
Function calls itself.…
TRB Point
1. Recursion stop செய்யும் co……
TRB Point
Base Case…
TRB Point
1. Function self-call பகுதி?…
TRB Point
Recursive Case / Recursive Ca……
TRB Point
1. Recursion uses which memor……
TRB Point
Stack / Call Stack…
TRB Point
1. Stack principle?…
TRB Point
LIFO…
TRB Point
1. Base case இல்லையென்றால்?…
TRB Point
RecursionError ஏற்படலாம்.…
TRB Point
1. Function calls itself dire……
TRB Point
Direct Recursion…
TRB Point
1. Function A calls B, B call……
TRB Point
Indirect Recursion…
TRB Point
1. Recursive call last operat……
TRB Point
Tail Recursion…
TRB Point
1. Python tail-call optimizat……
TRB Point
Generally No.…
Interview Point
What is recursion? Recursion is a technique where a function calls itself……
Interview Point
1. Base Case 2. Recursive Case…
Interview Point
Additionally, each recursive call must make progress toward the base case. Why is a base case necessary? It p……
MCQ
Recursion means:…
MCQ
What stops recursion?…
MCQ
Recursion primarily uses:…
MCQ
Stack follows:…
MCQ
What may happen without a bas……
MCQ
2 1 1. What is the base case here? ……
MCQ
factorial(5) returns:…
MCQ
A function directly calling i……
MCQ
Recursive call at the end of ……
MCQ
Which is generally more memor……
MCQ
In recursion, each function c……
Practice
Practice 1
Countdown def count(n): if n ……
Practice
Practice 2
Sum def total(n): if n == 0: ……
Dry Run
4 + 3 + 2 + 1 + 0…
Practice
Practice 3
Factorial def fact(n): if n == ……
Practice
Practice 4
Ascending Print def show(n): ……
Practice
Practice 5
Find the Error def show(n): if n == 0: return show(n + 1)……
Summary
Recursion basic structure: def function(n): if base_case: return function(smaller_problem) Core flow: Problem……
Summary
1. Base Case இருக்க வேண்டும் 2. Recursive C……
Explanation
Short description
Recursion என்பது ஒரு function தன்னையே call செய்து ஒரு பெரிய problem-ஐ அதே வகையிலான smaller problems-ஆக reduce……
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