Question

void phase05(){

int n = atoi(next_input());

int m = atoi(next_input());

int t = (hash % 30) + 21;

int s = 0;

while(n>1){

if(n & 1){

n = (n<<2) - n + 1;

}

else {

n = n >> 1;

}

if(s == t && m == t){

return;

}

s++;

}

failure("Seems you forgatz the essence of Collatz");

}

Hash value: 2002296385

what input values should n, m have in order for the function phase05 to work?

Answer 1

#include <iostream>
using namespace std;
#define hash 2002296385
void phase05(){

int n;
cin>>n;
int m ;
cin>>m;
int t = (hash % 30) + 21; // Line 9
cout<<t<<endl;
int s = 0;
while(n>1) // Line 12
    {
    if(n & 1) // Line 14
    {    n = (n<<2) - n + 1;  }  // Line 15
    else
    {   n = n >> 1;    } //Line 17
    if(s == t && m == t) //Line 18
            {  
                cout<<"program worked";
                return; 
                
            }
    
    s++;
    
    }
    
    cout<<"Seems you forgatz the essence of Collatz"; // error line 
    
    }
int main() {
    
    phase05();

    return 0;
}

This program is based on Collatz conjecture, which generates Collatz sequence for any natural number, the Collatz sequence eventually reach 1 for all positive integer, Main crux of choosing n in this program is that, it's Collatz sequence should have 46 or more terms before it reaches to 1.

Line 9 of Code snippet sets the value of t = 46

Program works if it returns before executing the error line, so the value of m should be 46 ( In order to satisfy the second condition of the if Statement (m == t)

Now to satisfy the first condition, we have to make s = 46 and every time while loop runs it increases the value of s by 1 so we have to make while loop run 46 times and then it will go inside the if condition in line 18 and program returns, s depends on the value of n

• n >1 (to enter in while loop)

Line 14 checks if n is odd,

• if n is odd then, the execution will go inside the if condition and the value of n will be updated

Line 17 checks if n is even,

• if the value of n is even then it will go inside else condition and then n will get updated to

So the value of m should be 46 and the value of n can be any natural number which has more than 46 terms in its Collatz sequence before it reaches to 1. some value of n can be { 27, 31,46,47,54,55,62,63,71,73,82,83,91,94,95, 97 etc}