Factorial Calculation: Recursion is great for figuring out factorials. For example, the factorial of a number ( n ) (written as ( n! )) is found by multiplying ( n ) by the factorial of ( n-1 ). And remember, ( 0! = 1 ). This shows how recursive functions work.
Fibonacci Series: You can make Fibonacci numbers using recursion. In this series, the number at position ( n ) (written as ( F(n) )) is the sum of the two numbers before it. So, ( F(n) = F(n-1) + F(n-2) ). The starting points are ( F(0) = 0 ) and ( F(1) = 1 ). This example shows how neat and efficient recursive solutions can be.
Permutations: This is about finding all the different ways you can arrange a string of letters. This problem really shows how powerful recursion can be for creating combinations.
Tower of Hanoi: This classic challenge is all about moving disks between three pegs while following some specific rules. The solution to this problem also uses recursion and has a running time of ( O(2^n) ), which means it can take a bit longer for bigger numbers.
Maze Solving: With recursion, you can find your way through a maze. It demonstrates how recursive backtracking can help you figure out complex paths.
These problems help us understand recursion better and show how important it is when designing algorithms.
Factorial Calculation: Recursion is great for figuring out factorials. For example, the factorial of a number ( n ) (written as ( n! )) is found by multiplying ( n ) by the factorial of ( n-1 ). And remember, ( 0! = 1 ). This shows how recursive functions work.
Fibonacci Series: You can make Fibonacci numbers using recursion. In this series, the number at position ( n ) (written as ( F(n) )) is the sum of the two numbers before it. So, ( F(n) = F(n-1) + F(n-2) ). The starting points are ( F(0) = 0 ) and ( F(1) = 1 ). This example shows how neat and efficient recursive solutions can be.
Permutations: This is about finding all the different ways you can arrange a string of letters. This problem really shows how powerful recursion can be for creating combinations.
Tower of Hanoi: This classic challenge is all about moving disks between three pegs while following some specific rules. The solution to this problem also uses recursion and has a running time of ( O(2^n) ), which means it can take a bit longer for bigger numbers.
Maze Solving: With recursion, you can find your way through a maze. It demonstrates how recursive backtracking can help you figure out complex paths.
These problems help us understand recursion better and show how important it is when designing algorithms.