Question

A python algorithm written for Tower Of Hanoi.

class Towers:

    hasItMoved = []

    toDest = []

    def __init__(self):

        self.current = 1

        self.n = int(input("Enter the number of disks: "))

        self.hasItMoved = [None] * 12

        self.toDest = [1] * 12

        for i in range(self.n):

            self.toDest[i] = 0

        self.r = self.n

        self.hanoiStart(self.n, "Start", "Aux1", "Aux3", "Aux2", "Dest", self.current)

# function to start

    def hanoiStart(self, numOfDisks, start, source, dest, aux, last, current):

        self.move(1, start, source, self.current)

        self.current += 1

        self.H1(self.n, "Start", "Aux1", "Aux3", "Aux2", "Dest", self.current)

        self.move(1, dest, last, self.current)

        self.current += 1

# helper function

    def H1(self, numOfDisks, start, source, dest, aux, last, current):

        if numOfDisks == 1:

            self.move(numOfDisks, source, aux, self.current)

            self.current += 1

            self.move(numOfDisks, aux, dest, self.current)

            self.current += 1

        elif numOfDisks == 2:

            self.move(numOfDisks-1, source, aux, self.current)

            self.current += 1

            self.move(numOfDisks-1, aux, dest, self.current)

            self.current += 1

            if self.current == 4:

                self.move(numOfDisks, start, source, self.current)

                self.current += 1

                self.move(numOfDisks, source, aux, self.current)

                self.current += 1

                self.move(numOfDisks-1, dest, aux, self.current)

                self.current += 1

                self.move(numOfDisks-1, aux, source, self.current)

                self.current += 1

                self.move(numOfDisks, aux, dest, self.current)

                self.current += 1

        if self.r == 2:

            self.move(2, dest, last, self.current)

            self.current += 1

            self.move(numOfDisks-1, source, aux, self.current)

            self.current += 1

            self.move(numOfDisks-1, aux, dest, self.current)

            self.current += 1

        elif numOfDisks > 2:

            self.current = self.H1(numOfDisks-1, start, source, dest, aux, last, self.current)

            if self.hasItMoved[numOfDisks] != 1:

                self.move(numOfDisks, start, source, self.current)

                self.current += 1

                self.hasItMoved[numOfDisks] = 1

                self.move(numOfDisks, source, aux, self.current)

                self.current += 1

                self.current = self.H1(numOfDisks-1, start, dest, source, aux, last, self.current)

                self.move(numOfDisks, aux, dest, self.current)

                self.current += 1

            if self.toDest[numOfDisks+1] != 0:

                self.move(numOfDisks, dest, last, self.current)

                self.current += 1

                self.toDest[numOfDisks] = 1

                if numOfDisks == self.r:

                    self.r -= 1

            self.current = self.H1(numOfDisks-1, start, source,

                                dest, aux, last, self.current)

        return self.current

    # function to print the move performed

    def move(self, aDisk, source, dest, currentStep):

        print("Move ", self.current, ": Move disk ", aDisk, " from ", source, " to ", dest)

Main File

import hanoi

if __name__=="__main__":

    test = hanoi.Towers()

Please rewrite this so that it accounts for an additional auxilary. Like Start, Aux1,Aux 2, Aux 3, Aux 4, Destination.

And if you can, please provide Time and space comlexity.

Answer 1

Sol:-

I have written code for you, which is very understandable

Code:-

#include <stdio.h>
void towerOfHanoi(int n, char from_rod, char to_rod,
                      char aux_rod1, char aux_rod2)
{
    if (n == 0)
        return;
    if (n == 1) {
        printf("\n Move disk %d from rod %c to rod %c",
                            n, from_rod, to_rod);
        return;
    }

    towerOfHanoi(n - 2, from_rod, aux_rod1, aux_rod2,
                                            to_rod);
    printf("\n Move disk %d from rod %c to rod %c ",
                       n - 1, from_rod, aux_rod2);
    printf("\n Move disk %d from rod %c to rod %c ",
                          n, from_rod, to_rod);
    printf("\n Move disk %d from rod %c to rod %c ",
                       n - 1, aux_rod2, to_rod);
    towerOfHanoi(n - 2, aux_rod1, to_rod, from_rod,
                                        aux_rod2);
}
int main()
{
    int n = 4; // Number of disks

    // A, B, C and D are names of rods
    towerOfHanoi(n, 'A', 'D', 'B', 'C');
    return 0;
}

Output:-

We know that for any recursive function, the space complexity is O(n) so space complexity of tower of hanoi is O(n).

Time complexity for tower of hanoi problem is O(2ⁿ⁺¹-1)or simply O(n) where n is no.of rods or disks.

Move disk 1 from rod A to rod D Move disk 2 from rod A to rod B Move disk 1 from rod D to rod B Move disk 3 from rod A to rod C Move disk 4 from rod A to rod D Move disk 3 from rod C to rod D Move disk 1 from rod B to rod C Move disk 2 from rod B to rod D Move disk 1 from rod C to rod D Process exited after 0.03206 seconds with return value o Press any key to continue ...