This is not a unique approach but something I personally used when I had to shave off a few kilobytes off the contract size and also reduce the gas usage. In my use-case, I needed multiple sorting to decide certain winners, rankings, price distributions and such.

Now, I don't have access to a backend code to try this on when writing this, maybe I could update this later with some scaffold-eth, but this is how I would possible implement this.

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.10;

contract Array {
    uint[] public arr;
    uint[] public arrSorted;
    address payable public _admin;

    constructor()
    {
        _admin = payable(msg.sender);
    }

    event sort(uint[]);

    function sortOffChain() public returns (uint[] memory)
    {
        emit sort(arr);
        return arrSorted;
    }

    function getSortedData(uint[] memory arrData) public
    {
        require(msg.sender == _admin);
        arrSorted = arrData;
    }
}

On the backend, the algorithm would look something like this -

1. event listener listening for sort()
2. calls bubbleSort() [Or whatever suits you] upon getting triggered
3. calls getSortedData() function with returned value of bubbleSort()

This of course shouldn't be used everywhere, but it is a quick and easy way of sorting data.