Practice Recursions

Recursions are fun

You may like to try out some simple problems to practice recursions. Try to solve all of them without using any global variables. And try on your own before looking at the solutions. Also please notify any error to me ( zobayer1[at]gmail[dot]com ). Before looking at the problems, you may like to read this post about how to attack recursive problems.

Problem 1:

You will be given an array of integers, write a recursive solution to print it in reverse order.

Input:
5
69 87 45 21 47
Output:
47 21 45 87 69

see answer

Problem 2:

Write a recursive function to print an array in the following order. [0] [n-1] [1] [n-2] ......... ......... [(n-1)/2] [n/2]

Input:
5
1 5 7 8 9
Output:
1 9
5 8
7 7

see answer

Problem 3:

Write a recursive program to remove all odd integers from an array. You must not use any extra array or print anything in the function. Just read input, call the recursive function, then print the array in main().

Input:
6
1 54 88 6 55 7
Output:
54 88 6

see answer

Problem 4:

Write a recursive solution to print the polynomial series for any input n: 1 + x + x² + ................. + x^n-1

Input:
5
Output:
1 + x + x^2 + x^3 + x^4

see answer

Problem 5:

Write a recursive solution to evaluate the previous polynomial for any given x and n. Like, when x=2 and n=5, we have 1 + x + x² + ................. + x^n-1 = 31

Input:
2 5
Output:
31

see answer

Problem 6:

Write a recursive program to compute n!

Input:
5
Output:
120

see answer

Problem 7:

Write a recursive program to compute n^th fibonacci number. 1^st and 2^nd fibonacci numbers are 1, 1.

Input:
6
Output:
8

see answer

Problem 8:

Write a recursive program to determine whether a given integer is prime or not.

Input:
49
999983
1
Output:
not prime
prime
not prime

see answer

Problem 9:

Write a recursive function that finds the gcd of two non-negative integers.

Input:
25 8895
Output:
5

see answer

Problem 10:

Write a recursive solution to compute lcm of two integers. You must not use the formula lcm(a,b) = (a x b) / gcd(a,b); find lcm from scratch...

Input:
23 488
Output:
11224

see answer

Problem 11:

Suppose you are given an array of integers in an arbitrary order. Write a recursive solution to find the maximum element from the array.

Input:
5
7 4 9 6 2
Output:
9

see answer

Problem 12:

Write a recursive solution to find the second maximum number from a given set of integers.

Input:
5
5 8 7 9 3
Output:
8

see answer

Problem 13:

Implement linear search recursively, i.e. given an array of integers, find a specific value from it. Input format: first n, the number of elements. Then n integers. Then, q, number of query, then q integers. Output format: for each of the q integers, print its index (within 0 to n-1) in the array or print 'not found', whichever is appropriate.

Input:
5
2 9 4 7 6
2
5 9
Output:
not found
1

see answer

Problem 14:

Implement binary search recursively, i.e. given an array of sorted integers, find a query integer from it. Input format: first n, the number of elements. Then n integers. Then, q, number of query, then q integers. Output format: for each of the q integers, print its index (within 0 to n-1) in the array or print 'not found', whichever is appropriate.

Input:
5
1 2 3 4 5
2
3 -5
Output:
2
not found

see answer

Problem 15:

Write a recursive solution to get the reverse of a given integer. Function must return an int

Input:
123405
Output:
504321

see answer

Problem 16:

Read a string from keyboard and print it in reversed order. You must not use any array to store the characters. Write a recursive solutions to solve this problem.

Input:
helloo
Output:
oolleh

see answer

Problem 17:

Write a recursive program that determines whether a given sentence is palindromic or not just considering the alpha-numeric characters ('a'-'z'), ('A'-'Z'), ('0'-'9').

Input:
madam, i'm adam
hulala
Output:
palindromic
not palindromic

see answer

Problem 18:

Implement strcat(), stracpy(), strcmp() and strlen() recursively.

Input:
test on your own
Output:
test on your own

see answer

Problem 19:

If you already solved the problem for finding the n^th fibonacci number, then you must have a clear vision on how the program flow works. So now, in this problem, print the values of your fibonacci function in pre-order, in-order and post-order traversal. For example, when n = 5, your program calls 3 and 4 from it, from the call of 3, your program calls 1 and 2 again....... here is the picture:

Input:
5
Output:
Inorder: 1 3 2 5 2 4 1 3 2
Preorder: 5 3 1 2 4 2 3 1 2
Postorder: 1 2 3 2 1 2 3 4 5

see answer

Problem 20:

All of you have seen the tower of Hanoi. You have 3 pillars 'a', 'b' and 'c', and you need transfer all disks from one pillar to another. Conditions are, only one disk at a time is movable, and you can never place a larger disk over a smaller one. Write a recursive solution to print the moves that simulates the task, a -> b means move the topmost of tower a to tower b.

Input:
3
Output:
a -> c
a -> b
c -> b
a -> c
b -> a
b -> c
a -> c

see answer

Good Luck!!!