Recursion
Any questions before we start?
Recursion Basics
Recursion
Recursion is the process of defining a problem (or the solution to a problem) in terms of (a simpler version of) itself.
Example
we can define the operation "Go to Home" as:
Base Case
1. If you are at home, stop moving.
Recursive Case
2. Take one step toward home.
3. "Go To Home".
Code
Text
//A Simple Recursive Function
static void goHome(x,Home){
if(x == Home){
print("Reached Home")
return;
}
x = x + 1
goHome(x,Home)
}
//Main
int x = 1
int Home = 10
goHome(x,Home);Recursion = Principal of Mathematical Induction
1. Figure of the Smallest Case
2. Always Assume the Subproblem Can be Solved
3. Solve the current problem assuming subproblem solution exists
Factorial of Number
Input
5
Output
120
Call Stack! 👨💻
Time & Space Utilisation 👨💻
Fibonacci Number
Write a program to compute the nth Fibonacci Number.
Fibonacci Series:
0, 1, 1, 2, 3, 5, 8 , ........
Increasing Numbers
Given N, print numbers from 1 to N without using a Loop (Use Recursion)
Input
5
Output
1, 2, 3, 4, 5
Decreasing Numbers
Given N, print numbers from 1 to N without using a Loop (Use Recursion)
Input
5
Output
5, 4, 3, 2, 1
Sum the Digits
Given N, print the sum of digits of that number using recursion.
Input
512
Output
8
More Problems
Climbing Ladder
Given a ladder containing N Steps, you can take a jump of 1,2 or 3 at each step. Find the number of ways to climb the ladder.
Sample Input
N = 4
Sample Output
7
Tiling Problem
Given Given a “4 x n” board and tiles of size “4 x 1”, count the number of ways to tile the given board using the 4 x 1 tiles.
A tile can either be placed horizontally i.e., as a 1 x 4 tile or vertically i.e., as 4 x 1 tile.
Input
N
Output
No of ways
Binary Strings
Count the number of binary strings with no consecutive ones that can be formed using a binary string of Length N.
Input
N
Output
Count of Strings
Friend's Pairing Problem
Given n friends who want to go to party, each one can remain single or can be paired up with some other friend. Each friend can be paired only once. Find out the total number of ways in which friends can remain single or can be paired up.
Examples:
Copy of [Java 07] Recursion - II
By Prateek Narang
