I am unable to find the Time Complexity and Space Complexity of Tower of Hanoi problem using iterative algorithm. Can anyone help, please?
Iterative Algorithm:
code -
// C Program for Iterative Tower of Hanoi
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <limits.h>
// A structure to represent a stack
struct Stack
{
unsigned capacity;
int top;
int *array;
};
// function to create a stack of given capacity.
struct Stack* createStack(unsigned capacity)
{
struct Stack* stack =
(struct Stack*) malloc(sizeof(struct Stack));
stack -> capacity = capacity;
stack -> top = -1;
stack -> array =
(int*) malloc(stack -> capacity * sizeof(int));
return stack;
}
// Stack is full when top is equal to the last index
int isFull(struct Stack* stack)
{
return (stack->top == stack->capacity - 1);
}
// Stack is empty when top is equal to -1
int isEmpty(struct Stack* stack)
{
return (stack->top == -1);
}
// Function to add an item to stack. It increases
// top by 1
void push(struct Stack *stack, int item)
{
if (isFull(stack))
return;
stack -> array[++stack -> top] = item;
}
// Function to remove an item from stack. It
// decreases top by 1
int pop(struct Stack* stack)
{
if (isEmpty(stack))
return INT_MIN;
return stack -> array[stack -> top--];
}
//Function to show the movement of disks
void moveDisk(char fromPeg, char toPeg, int disk)
{
printf("Move the disk %d from \'%c\' to \'%c\'\n",
disk, fromPeg, toPeg);
}
// Function to implement legal movement between
// two poles
void moveDisksBetweenTwoPoles(struct Stack *src,
struct Stack *dest, char s, char d)
{
int pole1TopDisk = pop(src);
int pole2TopDisk = pop(dest);
// When pole 1 is empty
if (pole1TopDisk == INT_MIN)
{
push(src, pole2TopDisk);
moveDisk(d, s, pole2TopDisk);
}
// When pole2 pole is empty
else if (pole2TopDisk == INT_MIN)
{
push(dest, pole1TopDisk);
moveDisk(s, d, pole1TopDisk);
}
// When top disk of pole1 > top disk of pole2
else if (pole1TopDisk > pole2TopDisk)
{
push(src, pole1TopDisk);
push(src, pole2TopDisk);
moveDisk(d, s, pole2TopDisk);
}
// When top disk of pole1 < top disk of pole2
else
{
push(dest, pole2TopDisk);
push(dest, pole1TopDisk);
moveDisk(s, d, pole1TopDisk);
}
}
//Function to implement TOH puzzle
void tohIterative(int num_of_disks, struct Stack
*src, struct Stack *aux,
struct Stack *dest)
{
int i, total_num_of_moves;
char s = 'S', d = 'D', a = 'A';
//If number of disks is even, then interchange
//destination pole and auxiliary pole
if (num_of_disks % 2 == 0)
{
char temp = d;
d = a;
a = temp;
}
total_num_of_moves = pow(2, num_of_disks) - 1;
//Larger disks will be pushed first
for (i = num_of_disks; i >= 1; i--)
push(src, i);
for (i = 1; i <= total_num_of_moves; i++)
{
if (i % 3 == 1)
moveDisksBetweenTwoPoles(src, dest, s, d);
else if (i % 3 == 2)
moveDisksBetweenTwoPoles(src, aux, s, a);
else if (i % 3 == 0)
moveDisksBetweenTwoPoles(aux, dest, a, d);
}
}
// Driver Program
int main()
{
// Input: number of disks
unsigned num_of_disks = 3;
struct Stack *src, *dest, *aux;
// Create three stacks of size 'num_of_disks'
// to hold the disks
src = createStack(num_of_disks);
aux = createStack(num_of_disks);
dest = createStack(num_of_disks);
tohIterative(num_of_disks, src, aux, dest);
return 0;
}
The code of Tower of Hanoi iterative algorithm is above. Please, help me.
Let's define as the number of discs.
The time complexity is O(2 ), because that is the number of iterations done in the only loops present in the code, while all other code runs in constant time.
The space complexity can be split up in two parts:
So combined this has a O() space complexity.
It depends, because the question is fundamentally ambiguous. The most interesting part of the tower-of-Hanoi algorithm is that it is a pseudo-random irrational structure with an exponential information, but if you move the tower from left to right, and then move it from right to left, the time complexity is exactly 0.
For example, there is no fast algorithm that can compute the square root of 5.
This means that the question is fundamentally subjective based on what you mean by the tower of Hanoi and how much information you really want to extract.
The technical post webpages of this site follow the CC BY-SA 4.0 protocol. If you need to reprint, please indicate the site URL or the original address.Any question please contact:yoyou2525@163.com.