Recursion [click]
Telerik Academy Alpha
DSA
Table of contents
What is Recursion?
- Function that calls itself
What is Recursion?
- Recursion is when a methods calls itself
- Very powerful technique for implementing algorithms
- Recursion should have
-
Exit criteria (bottom)
- Prevents infinite recursion
- Direct or indirect recursive call
- Оr through other methods
- The method calls itself directly
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Exit criteria (bottom)
Why Recursion?
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Used in algorithms
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Merge Sort
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Binary Search
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Typical for various operations related to Trees and other non-linear data structures
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OS Folder structure traversal
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HTML/DOM trees and other “Visual Trees” – WPF, WinForms
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Why Recursion?
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Used in algorithms
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DFS – graphs, also trees
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Math - Factorial, Fibonacci, Combinatorial problems
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Develops analytical thinking
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High chance to be asked on interviews!
Examples
Example: Factorial
- Recursive definition of n! (n factorial):
for n > 0
for n = 0
Example: Factorial
- Recursive definition of n! (n factorial):
- Don't try this at home!
- Use iteration instead
- Don't try this at home!
static decimal Factorial(decimal num)
{
if (num == 0)
{
return 1;
}
var result = num * Factorial(num - 1);
return result;
}Where is the bottom?
Demo: Factorial
Explain: Factorial
- Diagram of recursive factorial function
- every time we call it the function is executed with different parameters
- when the bottom is hit (n<=1) it returns the stored values back
Where is the bottom?
Example: String Reverse
Where is the bottom?
- Debug the example in Visual Studio to understand how it is working
Example: String Reverse
Where is the bottom?
- You are already familiar with Binary Search
- Now we need a volunteer to write pseudo-code Binary Search with the help of the Mentor
Backtracking
Backtracking?
Solving Computational Problems by Generating All Candidates
- What is backtracking?
- Backtracking is a class of algorithms for finding all solutions to some computational problem
- E.g. find all paths from Sofia to Varna
- How does backtracking work?
- Usually implemented recursively
- At each step we try all perspective possibilities to generate a solution
- Backtracking has exponential running time!
Backtracking?
Path finder - demo
Recursion vs Iteration
Recursion is harmful?
- When used incorrectly the recursion could take too much memory and computing power
- Example:
Recursion is harmful?
- The same value is calculated many, many times!
Recursion done right
- Each Fibonacci sequence member can be remembered once it is calculated (memoization)
Can be returned directly when needed again- Example:
When to use recursion?
-
Avoid recursion when an obvious iterative algorithm exists
- Examples: factorial, Fibonacci numbers
- Use recursion for combinatorial algorithm where at each step you need to recursively explore more than one possible continuation
- Examples: permutations, all paths in labyrinth
- If you have only one recursive call in the body of a recursive method, it can directly become iterative (like calculating factorial)
Questions?
[C# DSA] Recursion
By telerikacademy
