Program crashes and does not display correct output - c++

Question

So I am working on a very "basic" problem for my c++ class and have encountered some errors. The problem is this
An interesting problem in number theory is sometimes called the “necklace problem.” This problem begins with two single-digit numbers. The next number is obtained by adding the first two numbers together and saving only the ones-digit. This process is repeated until the “necklace” closes by returning to the original two numbers. For example, if the starting numbers are 1 and 8, twelve steps are required to close the “necklace”:
18976392134718
Write a program that asks the user for two starting numbers, and then displays the sequence and the number of steps taken. The program output should look similar to:
Enter first number: 1
Enter ssecond number: 8
18976392134718
Your numbers required 12 steps.
What I have done is this:
` #include <iostream>
using namespace std;
int necklace(){
int firstNumber, secondNumber, total = 0, counter = 10, sumOfTwo, tempOne, tempTwo, count;
// 2 single digit numbers
// add first two numbers and save only one digit
// process keeps going until original numbers are found
cout << "Enter the first number: \n";
cin >> firstNumber;
cout << "Enter the second number: \n";
cin >> secondNumber;
sumOfTwo = firstNumber + secondNumber;
while (sumOfTwo >= 10){
sumOfTwo /= 10;
}
int numbersArray[] = {firstNumber, secondNumber, sumOfTwo};
for(int i = 0; i <= 20; i++){
tempOne = numbersArray[i + 1];
tempTwo = numbersArray[i + 2];
sumOfTwo = tempOne + tempTwo;
while (sumOfTwo >= 10){
sumOfTwo %= 10;
}
numbersArray[i + 3] = sumOfTwo;
total++;
if(tempOne == firstNumber && tempTwo == secondNumber){
break;
}
}
for(int i = 0; i < sizeof(numbersArray); i++){
cout << numbersArray[i];
}
cout << endl << "It took " << total << " steps to finish. \n";
return total;
}
int main() {
necklace();
}
`
The problem I am getting is that it will print out all the numbers except the original 2, for example if I use the example with 1 and 8, it will print out 189763921347 and then crash, when it is supposed to print out 18976392134718 with the 1 and 8 at the end of it. Any suggestions? Thanks!

Answer 1

int numbersArray[] = {firstNumber, secondNumber, sumOfTwo};
with three elements on the right hand side makes it an array of size 3. Meaning with indexes 0, 1 and 2.
The use of higher indexes will result in Undefined Behaviour (UB).
On the other hand:
for(int i = 0; i <= 20; i++){
tempOne = numbersArray[i + 1];
tempTwo = numbersArray[i + 2];
[...]
numbersArray[i + 3] = sumOfTwo;
with i up to 20 (included) indexes this very same array from 0 to 23 for the last line!
Next:
for(int i = 0; i < sizeof(numbersArray); i++){
sizeof(numbersArray) returns the size in bytes of the array:
sizeof(numbersArray) = 3 * sizeof(int)
Higher than 3, the real size of the array.
But, if you intend to print the values but not store them, you don't need an array. You just need to "exchange" the values like:
one two // beginning of loop
___|
| __ new_digit
| |
v v
one two // end of loop