How can you concatenate uints in Solidity?

Question

I want to generate tokenIDs based on the properties generated in the contract.

         uint256[5] memory tokenID;
    
         for (uint i = 0; i < 5; i++) {
             tokenID[i] =  1 + item[i] + property[i] + level[i];
         }

So if the item is 14, the property is 4, and the level is 51, then the combined uint would 114451.

As I see it now I need to convert every uint to a bytes32, convert bytes32 to a string, and then I'm not even sure if there is a simple way to converts string to a uint. Is there a way to do this without much gas, or do I need to look at a more complicated naming convention?

Edit: Forgot to add the current solution which doesn't allow for scaling:

tokenID[i] = (((item[i]+1) * 10**5) + (property[i] * 10**4)) + level[i]

Item goes up to 1000, property goes up to 100, and level is always under 10.

Answer 1

Try this:

for (uint256 i = 0; i < tokenID.length; i++) {
    uint256 levelLen    = numOfDigits(level[i]);
    uint256 propertyLen = numOfDigits(property[i]);
    uint256 itemLen     = numOfDigits(item[i]);
    tokenID[i] =
        level[i] +
        property[i] * 10 ** levelLen +
        item[i] * 10 ** (propertyLen + levelLen) +
        10 ** (itemLen + propertyLen + levelLen);
}

Where a simple implementation of function numOfDigits can be:

function numOfDigits(uint256 _x) private pure returns (uint256) {
    uint256 y = 0;
    for (uint256 x = _x; x > 0; x /= 10) {
        y++;
    }
    return y;
}

Note that this method can map several different inputs to the same output.

For example, both [14, 4, 51] and [14, 45, 1] are mapped to 114451.

In that sense, the correct way is to do what you've mentioned as "doesn't allow for scaling".

So I would recommend you to reconsider exactly what scaling issue you're concerned with.