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• Data Structures & Algorithms

• Tower Of Hanoi Using Recursion

• Algorithm

Mar 07, 2016  Move N-1 Disks from Temporary Tower To Destination Tower (using Source Tower as Temporary Tower) For a total of n disks, 2 n – 1 moves or disk shift are required. Note: This code To Solve Towers of Hanoi Problem using Recursion in C Programming Language is developed in Linux Ubuntu Operating System and compiled with GCC Compiler.

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Tower Of Hanoi Using Recursion

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Tower of Hanoi, is a mathematical puzzle which consists of three towers (pegs) and more than one rings is as depicted −

These rings are of different sizes and stacked upon in an ascending order, i.e. the smaller one sits over the larger one. There are other variations of the puzzle where the number of disks increase, but the tower count remains the same.

Rules

The mission is to move all the disks to some another tower without violating the sequence of arrangement. A few rules to be followed for Tower of Hanoi are −

• Only one disk can be moved among the towers at any given time.
• Only the 'top' disk can be removed.
• No large disk can sit over a small disk.

Following is an animated representation of solving a Tower of Hanoi puzzle with three disks.

Tower of Hanoi puzzle with n disks can be solved in minimum 2ⁿ−1 steps. This presentation shows that a puzzle with 3 disks has taken 2³ - 1 = 7 steps.

Algorithm

To write an algorithm for Tower of Hanoi, first we need to learn how to solve this problem with lesser amount of disks, say → 1 or 2. We mark three towers with name, source, destination and aux (only to help moving the disks). If we have only one disk, then it can easily be moved from source to destination peg.

If we have 2 disks −

• First, we move the smaller (top) disk to aux peg.
• Then, we move the larger (bottom) disk to destination peg.
• And finally, we move the smaller disk from aux to destination peg.

So now, we are in a position to design an algorithm for Tower of Hanoi with more than two disks. We divide the stack of disks in two parts. The largest disk (n^th disk) is in one part and all other (n-1) disks are in the second part.

Our ultimate aim is to move disk n from source to destination and then put all other (n1) disks onto it. We can imagine to apply the same in a recursive way for all given set of disks.

The steps to follow are −

A recursive algorithm for Tower of Hanoi can be driven as follows −

To check the implementation in C programming, click here.

C Program To Solve Tower of Hanoi without Recursion

Learn How To Solve Tower of Hanoi without Recursion in C Programming Language. This Non Recursive C Program makes use of an Iterative method using For Loop to solve Tower of Hanoi Problem. The Tower of Hanoi Algorithm in Data Structures is a very famous Interview Question for Beginners. The C Program For Tower of Hanoi Program using Iteration can be solved by using For, While and Do While Loop.

To know more about Tower of Hanoi, you can read this guide: Tower of Hanoi Problem in C Programming

Note: This Code To Solve Tower of Hanoi using Iterative method in C Programming Language is developed in Linux Ubuntu Operating System and compiled with GCC Compiler.

If you try to compile this C Program for Tower of Hanoi without using Recursion in Linux, you will get the following error:

2	test.c:(.text+0x2cd): undefined reference to `pow'

This is because the pow() method cannot be found in the library files. To overcome this error, you will have to explicitly include the math.h header file. Compile the program using the following command:

Also Read: Tower of Hanoi in C using Recursion

C Program To Solve Tower of Hanoi without Recursion

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#include <limits.h> #include <math.h> structStack_Structure inttop; intmax; { structStack_Structure*stack_object=(structStack_Structure*)malloc(sizeof(structStack_Structure)); stack_object->top=-1; stack_object->array=(int*)malloc(stack_object->max*sizeof(int)); } intisEmpty(structStack_Structure*stack_object) return(stack_object->top-1); { } voiddisplay_shift(charfromTower,chartoTower,intdisk) printf('Move Disk %d from '%c' to '%c'n',disk,fromTower,toTower); voidadd_element(structStack_Structure *stack_object,intitem) if(isFull(stack_object)) return; stack_object->array[++stack_object->top]=item; intremove_element(structStack_Structure*stack_object) if(isEmpty(stack_object)) returnINT_MIN; returnstack_object->array[stack_object->top--]; voidshift_Disks(structStack_Structure *source_tower,structStack_Structure *destination_tower,charsource,chardestination) inttower1=remove_element(source_tower); if(tower1INT_MIN) add_element(source_tower,tower2); } { display_shift(source,destination,tower1); elseif(tower1>tower2) add_element(source_tower,tower1); display_shift(destination,source,tower2); else add_element(destination_tower,tower2); display_shift(source,destination,tower1); } voidtower_of_hanoi(intlimit,structStack_Structure *source_tower,structStack_Structure *temporary_tower,structStack_Structure *destination_tower) intcount,shift; if(limit%20) charx=destination; temporary=x; shift=pow(2,limit)-1; { } { { shift_Disks(source_tower,destination_tower,source,destination); elseif(count%32) shift_Disks(source_tower,temporary_tower,source,temporary); elseif(count%30) shift_Disks(temporary_tower,destination_tower,temporary,destination); } { structStack_Structure *source_tower,*destination_tower,*temporary_tower; scanf('%d',&limit); source_tower=createStack(limit); destination_tower=createStack(limit); tower_of_hanoi(limit,source_tower,temporary_tower,destination_tower); return0;

Must Read: C Program For FCFS Algorithm

Output

If you have any compilation errors or doubts in this C Program for Tower of Hanoi without Recursion, let us know about in the Comment Section below.