Wiki Article · Cinematic

Recursion Tree

Recursion tree ek visual analysis tool hai jo dikhata hai ke koi recursive algorithm apne execution…

Overview

Recursion Tree — Quick Facts

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Property: Detail

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Concept Name: Recursion Tree

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Type: Algorithm Analysis Tool /…

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Domain: Computer Science / Algorithm…

Topic 1

Infobox

📚 | Property | Detail | |---|---| | Concept Name | Recursion Tree | | Type | Algorithm…

Topic 2

Kyun Zaroori Hai

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Root: $n$ kaam

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Level 1: 2 nodes, har ek me $n/2$…

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Level 2: 4 nodes, har ek me $n/4$…

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...har level pe total $n$ kaam ho…

Topic 3

What is a Recursion Tree

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Har node ek recursive function…

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Node ka label/cost woh kaam hai jo…

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Node ke children woh sub-calls…

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Leaves (patte) base cases hain…

Topic 4

Anatomy of a Recursion Tree

Topic 5

How to Draw a Recursion Tree

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Root node cost = $n$…

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Root has 2 children (because…

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Each child has cost = $n/2$…

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Each child again has 2 children

Topic 6

Using Recursion Trees for Complexity Analysis

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Standard form: $T(n) = aT(n/b) +…

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$a$ = number of sub-problems…

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$n/b$ = size of each sub-problem

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$f(n)$ = non-recursive work (cost…

Topic 7

Classic Examples

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Level 0: 1 node, cost $n$ → total…

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Level 1: 2 nodes, each cost $n/2$…

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Level 2: 4 nodes, each cost $n/4$…

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Level $i$: $2^i$ nodes, each cost…

Topic 8

Recursion Tree Properties aur Patterns

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Sab branches same depth tak jaati…

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Har level pe same total cost

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Total = levels × cost_per_level

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Signature: $T(n) = aT(n/b) +…

Topic 9

Recursion Tree vs Master Theorem

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Sub-problems unequal size ke hon:…

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Non-polynomial $f(n)$: $T(n) =…

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$T(n) = T(n-1) + T(n-2)$ type…

Topic 10

Recursion Tree vs Call Stack

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Recursion tree ka height = call…

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Recursion tree ka total nodes =…

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Tree ki width runtime me…

Topic 11

Common Mistakes

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Decreasing geometric series: Sum ≈…

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Increasing geometric series: Sum ≈…

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Constant (equal terms): Sum = term…

Topic 12

Glossary

⭐ | # | Term | Meaning | |---|---|---| | 1 | Recursion Tree | Recursive algorithm ke calls…

Comparison

Recursion Tree vs Master Theorem

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1: Approach

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2: Applicable To

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3: Ease of Use

Comparison

Recursion Tree vs Call Stack

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Purpose: Algorithm analysis (complexity)

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Scope: Saari recursive calls…

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Width: Branching factor ke hisaab se…

Diagram

Visual Flow

📊 Diagram visualization — details in narration

Quiz — Question 1

Recursion Tree ka sabse sahi definition kya hai?

Quick Quiz

Quiz — Question 2

Recursion Tree ka 'Concept Name' kya hai?

Complete! 🎉

Recursion Tree Complete!

Aliens Wiki · Hinglish · Cinematic Knowledge

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Recursion Tree Complete

➡️

Recursion Tree

Recursion Tree — Quick Facts

Property: Detail

Concept Name: Recursion Tree

Type: Algorithm Analysis Tool /…

Domain: Computer Science / Algorithm…

Infobox

Kyun Zaroori Hai

Root: $n$ kaam

Level 1: 2 nodes, har ek me $n/2$…

Level 2: 4 nodes, har ek me $n/4$…

...har level pe total $n$ kaam ho…

What is a Recursion Tree

Har node ek recursive function…

Node ka label/cost woh kaam hai jo…

Node ke children woh sub-calls…

Leaves (patte) base cases hain…

Anatomy of a Recursion Tree

How to Draw a Recursion Tree

Root node cost = $n$…

Root has 2 children (because…

Each child has cost = $n/2$…

Each child again has 2 children

Using Recursion Trees for Complexity Analysis

Standard form: $T(n) = aT(n/b) +…

$a$ = number of sub-problems…

$n/b$ = size of each sub-problem

$f(n)$ = non-recursive work (cost…

Classic Examples

Level 0: 1 node, cost $n$ → total…

Level 1: 2 nodes, each cost $n/2$…

Level 2: 4 nodes, each cost $n/4$…

Level $i$: $2^i$ nodes, each cost…

Recursion Tree Properties aur Patterns

Sab branches same depth tak jaati…

Har level pe same total cost

Total = levels × cost_per_level

Signature: $T(n) = aT(n/b) +…

Recursion Tree vs Master Theorem

Sub-problems unequal size ke hon:…

Non-polynomial $f(n)$: $T(n) =…

$T(n) = T(n-1) + T(n-2)$ type…

Recursion Tree vs Call Stack

Recursion tree ka height = call…

Recursion tree ka total nodes =…

Tree ki width runtime me…

Common Mistakes

Decreasing geometric series: Sum ≈…

Increasing geometric series: Sum ≈…

Constant (equal terms): Sum = term…

Glossary

Recursion Tree vs Master Theorem

1: Approach

2: Applicable To

3: Ease of Use

Recursion Tree vs Call Stack

Purpose: Algorithm analysis (complexity)

Scope: Saari recursive calls…

Width: Branching factor ke hisaab se…

Visual Flow

See Also

Recursion

Algorithm

Time Complexity

Master Theorem

Divide and Conquer

Merge Sort

Quiz — Question 1

Quiz — Question 2

Recursion Tree Complete!

Recursion Tree Complete

Recursion