Question

**C++ only, standard library.

We are supposed to create a tower of hanoi program and do a sequence of 100 disks. We are supposed to run the program and then answer two questions:

1) How long does your computer take to run(time)?

2) If I could move 1 disk per second how long would it take?

Here is my program so far:

void towerOfHanoi(int numDisks, char from_rod, char to_rod, char aux_rod)
{
int count=0;
if (numDisks == 1)
{
//cout << "Move disk 1 from rod " << from_rod <<
// " to rod " << to_rod<<endl;
return;
}
towerOfHanoi(numDisks - 1, from_rod, aux_rod, to_rod);

//cout << "Move disk " << numDisks << " from rod " << from_rod <<
//" to rod " << to_rod << endl;
towerOfHanoi(numDisks - 1, aux_rod, to_rod, from_rod);
}
  
// Driver code
int main()
{
int numDisks; // Number of disks
  
cout<<"This program solves the Hanoi Tower puzzle"<<endl<<endl;
  
cout<<"Enter the number of disks to calculate: ";
cin>>numDisks;
  
towerOfHanoi(numDisks, 'A', 'C', 'B'); // A, B and C are names of rods
return 0;
}
  

Answer 1

#include <iostream>
#include <algorithm>
#include <chrono>

using namespace std;
using namespace std::chrono;

int moves = 0;

void towerOfHanoi(int numDisks, char from_rod, char to_rod, char aux_rod)
{
    moves++;
    int count=0;
    if (numDisks == 1)
    {
        //cout << "Move disk 1 from rod " << from_rod <<
        // " to rod " << to_rod<<endl;
        return;
    }
    towerOfHanoi(numDisks - 1, from_rod, aux_rod, to_rod);

    //cout << "Move disk " << numDisks << " from rod " << from_rod <<
    //" to rod " << to_rod << endl;
    towerOfHanoi(numDisks - 1, aux_rod, to_rod, from_rod);
}
  
// Driver code
int main()
{
    int numDisks; // Number of disks
    
    cout<<"This program solves the Hanoi Tower puzzle"<<endl<<endl;
    
    cout<<"Enter the number of disks to calculate: ";
    cin>>numDisks;
    
    // Get starting timepoint
    auto start = high_resolution_clock::now();
    towerOfHanoi(numDisks, 'A', 'C', 'B'); // A, B and C are names of rods
    auto stop = high_resolution_clock::now();
    auto duration = duration_cast<microseconds>(stop - start);
    cout << "Time taken: "
         << duration.count() << " microseconds" << endl;

    cout << "Number of disk movements: " << moves << endl;
    return 0;
}

**************************************************
The above code can be used to measure the time taken in reality.. And also it shows how many disk movements happen.
If you notice below, for n = 10, We get (2^n - 1) movements.

Similarly, For n = 3,

Hence, For n = 100 disks, (2^100 - 1) movements will be required, which is 1267650600228229401496703205375 movements.

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