Combine two numbers into one. Example: 123 and 456 become 123456

Question

In C++, how do I combine (note: not add) two integers into one big integer?

For example:

int1 = 123;
int2 = 456;

Is there a function to take the two numbers and turn intCombined into 123456?

EDIT:

My bad for not explaining clearly. If int2 is 0, then the answer should be 123, not 1230. In actuality though, int1 (the number on the left side) would only have a value if int2 goes over the 32 bit limit. So when int2 is 0, then int1 is 0 (or garbage, i'm not sure).

Solution 1

The power of ten, that you need to multiply the first number with, is the smallest one, that is bigger than the second number:

int combine(int a, int b) {
   int times = 1;
   while (times <= b)
      times *= 10;
   return a*times + b;
} 

Solution 2

You could convert them into strings, combine them and then convert them back to an int?

Solution 3

If the numbers you are trying to combine are positive integers you can use pairing Functions.

Pairing function creates a unique number from two. It is also a reversible function.

x,y -> z
z -> x,y

z = (x+y)(x+y+1)/2 + y

Then the reverse is:

w = floor((sqrt(8z+1)-1)/2)
t = (w*w + w)/2
y = z - t
x = w - y

Note. The above is not in any specific language. Just some math...

Solution 4

For each digit in int2, you can multiple int1 by 10 and then add int2:

// merge(123, 0) => 1230
int merge(int int1, int int2)
{
    int int2_copy = int2;
    do
    {
        int1 *= 10;
        int2_copy /= 10;
    } while (int2_copy);

    return int1 + int2;
}

You could get rid of the loop using log10 and ceil.

Solution 5

Assuming both ints are non-negative, and int1 goes on the left and int2 goes on the right, you need to figure out how many digits long int2 is, multiply int1 by 10 a bunch of times, and then add them.

unsigned int int1 = blah;
unsigned int int2 = blah;

unsigned int temp = int2;

do
{
    temp /= 10;
    int1 *= 10;
} while (temp >0)

unsigned int newInt = int1 + int2;

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