Tuesday, December 8, 2009

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 + ................. + xn-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 + ................. + xn-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 nth fibonacci number. 1st and 2nd 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 nth 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!!!


27 comments:

  1. need some critical recursion?

    ReplyDelete
  2. Haha, I have plenty :) I think these are enough for beginners to give them a head start, after these, they can practice on their own.

    But If you think that you can help them further, you can post here the problems, or source links or whatever you have.

    ReplyDelete
  3. Truly Helpful Brother...May Allah Bless you :)

    ReplyDelete
  4. ইনফিনিটিভ(অসংখ্য) ধন্যবাদ।অনেক কিছু প্রেক্টিস করতে পারলাম।
    সাকিব হাসান,ইবি,কুস্টিয়া,বাংলাদেশ।

    ReplyDelete
    Replies
    1. I am really glad that it helped, my best wishes for you :)

      Delete
  5. I am trying to learn recursion.I can write easy recursion.But when I am trying to write a recursion for backtracking problem or dp, most of the time I failed.But if I see a medium hard recursive func I relaize it easily.But if I try to write a new recusion most of the time I failed.

    ReplyDelete
    Replies
    1. Actually, after solving lots of dp and recursive problem, this is what I would say: If you want to learn dp / backtracking algorithm, you have to solve as many dp as possible, the only way to improve dp skill is to solving more and more. Frustrating at some points, but I don't think there is any other options.

      Delete
  6. wow!! It is very helpful for me and anyone . Thank you so much for this good job.

    ReplyDelete
  7. thank u so much vai..............really helpful!

    ReplyDelete
  8. That's damn important and fun ........................... Had a lot of fum :D

    ReplyDelete
  9. I have tested the following code and it give me correct result But the answer script has one extra line before recursive call. the line is "if(*sbest < a[i]) *sbest = a[i];". Is it necessary? If necessary, would you kindly explain to me.

    void sMax(int i, int n, int *a, int *fbest, int *sbest)
    {
    if (i == n - 1)
    {
    *fbest = a[i];
    return;

    }


    sMax((i + 1), n, a, fbest, sbest);

    if (a[i] > *fbest)
    {
    *sbest = *fbest;
    *fbest = a[i];
    }
    else if (a[i] > *sbest)
    *sbest = a[i];

    return;

    }

    ReplyDelete
  10. কিছু কিছু Problem বুঝতে পারলাম না !

    ReplyDelete
  11. int main(){
    printf("Thank you\n");
    main();
    }

    ReplyDelete
    Replies
    1. haha, nice recursion, (but your program cannot call main() )
      you're welcome!

      Delete
  12. Can u plz tell me what's wrong with my code? All the time, it returns the correct ans with an extra value. why is there an extra?
    int call(int i,int n,int a[])
    {
    if(i<=n)
    {

    cout<>n;
    {
    for(int i=0; i>a[i];
    cout<<call(0,n-1,a)<<endl;
    return 0;
    }

    }

    ReplyDelete
    Replies
    1. Hi, your code is broken because of HTML characters. Can you post your code here and then give me the link?
      http://codepad.org/

      Delete
  13. Thanks so so so so so sooooooooooooooooooooooooooooooooooooooooooo much <3

    ReplyDelete
  14. how i can write a recursive problem to generate all permutations of a given n numbers?

    ReplyDelete
  15. //============================================================================
    // Name : TowerOfHanoiRecursion.cpp
    // Author : Nitish Raj, Scientist, DRDO, raj.nitp@gmail.com
    // Version :
    // Copyright : No Copyright
    // Description : Ansi-style
    //============================================================================

    #include
    #include
    #include

    #include
    using namespace std;


    /*
    | | |
    ___|___ __|__ __|__
    Source Auxilary Destination

    */
    /*Function say whenever you call this second argument will be always from where
    you have to element and fourth argument says where you need to put and third used as
    spare */

    stack A,B,C;

    void moveData(char Src, char Des){

    switch(Src)
    {
    case 'a':
    {
    if(Des == 'b') B.push(A.top());
    if(Des == 'c') C.push(A.top());
    A.pop();
    break;
    }
    case 'b':
    {
    if(Des == 'a') A.push(B.top());
    if(Des == 'c') C.push(B.top());
    B.pop();
    break;
    }
    case 'c':
    {
    if(Des == 'b') B.push(C.top());
    if(Des == 'a') A.push(C.top());
    C.pop();
    break;
    }
    }

    }
    void ShowDataofStack(){
    stack temp;
    cout<<"TOWER A :: ";
    temp = A;

    while(!temp.empty()){
    cout<0)
    {
    HanoiTowerRec(n-1, Source,Destination, Aux); //

    // Now nth element left on Source so put this to Destination;
    cout<<"______________________________________ "<"<>n;
    for(int i =0 ; i<n;i++) A.push(n-i);
    HanoiTowerRec(n, 'a', 'b', 'c');



    return 0;
    }

    ReplyDelete
  16. /**
    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 + ................. + xn-1 = 31

    Input:
    2 5
    Output:
    31

    **/

    #include
    using namespace std;
    int print(int i,int x,int n,int sum)
    {
    if(i==1)
    {
    sum=1;
    }
    if(i>1)
    {
    sum+=pow(x,i-1);
    }
    if(i==n)
    return sum;
    print(i+1,x,n,sum);
    }
    int main()
    {
    cout<<print(1,2,5,0)<<endl;;
    return 0;
    }

    ভাইয়া আমি এইভাবে করছি। আমারটা কি হইছে? নাকি কোন বাগ আছে? জানালে ভালো হত।

    ReplyDelete
  17. sakhawatshamim35@gmail.com এই ইমেইল ও জানাতে পারেন।

    ReplyDelete