SpreadQuiz/class/Tasks/NumberConversionTask.php

<?php

require_once "OpenEndedTask.php";

class NumberConversionTask extends OpenEndedTask
{
    protected string $instruction; // instruction word
    protected string $source; // source

    // runtime variables -----
    private int $src_base; // source number system
    private string $src_rep; // source representation
    private int $src_n_digits; // minimum number of digits in the source
    private int $dst_base; // destination number system
    private string $dst_rep; // destination representation
    private int $dst_n_digits; // number of digits in the destination

    // -------------------------
    public function __construct(array &$a = null)
    {
        parent::__construct($a);

        $this->setType("numberconversion");

        // get instruction word
        $this->instruction = strtolower(trim($a["instruction"] ?? "10u:2->2u:4"));

        // expand it
        $pattern = "/([0-9]+)([suc]):([0-9]+)->([0-9]+)([suc]):([0-9]+)/";
        preg_match($pattern, $this->instruction, $matches);

        // if the instruction was meaningful
        if (count($matches) == 7) {
            $this->src_base = (int)$matches[1];
            $this->src_rep = $matches[2];
            $this->src_n_digits = $matches[3];
            $this->dst_base = (int)$matches[4];
            $this->dst_rep = $matches[5];
            $this->dst_n_digits = $matches[6];
        } else { // no valid instruction word has been passed
            $this->src_base = 10;
            $this->src_rep = "u";
            $this->src_n_digits = 2;
            $this->dst_base = 2;
            $this->dst_rep = "u";
            $this->dst_n_digits = 4;

            $this->instruction = $this->src_base . $this->src_rep . ":" . $this->src_n_digits . "->" . $this->dst_base . $this->dst_rep . ":" . $this->dst_n_digits;
        }

        $this->source = $a["source"] ?? "---";
        $this->correct_answer = $a["correct_answer"] ?? "---";
    }

    public function toArray(): array
    {
        $a = parent::toArray();

        $a["instruction"] = $this->instruction;
        $a["source"] = $this->source;
        $a["correct_answer"] = $this->correct_answer;

        return $a;
    }

    private static function extend(string $num, int $base, int $exnd, bool $comp): string
    {
        $fd = (int)(base_convert($num[0], $base, 10)); // get first digit as a number
        $extd = (string)(($comp && ($fd >= ($base / 2))) ? ($base - 1) : 0); // get the extension digit
        return str_pad((string)($num), $extd, $extd, STR_PAD_LEFT); // extend to the left
    }

    private static function complement(string $num, int $base): string
    {
        // convert to an integer
        $M = (int)(base_convert($num, $base, 10));

        // check if the highest digit is less than the half of the base, if not, add a zero prefix
        $fd = (int)(base_convert($num[0], $base, 10));

        // create the basis for forming the complement
        $H = (string)($base - 1);
        $K_str = (int)(str_repeat($H, strlen($num)));
        if ($fd >= ($base / 2)) { // if one more digit is needed...
            $K_str = $H . $K_str; // prepend with a zero digit
        }

        // convert to integer
        $K = (int)(base_convert($K_str, $base, 10));

        // form the base's complement
        $C = $K - $M + 1;

        // convert to the final base
        return base_convert((string)$C, 10, $base);
    }

    private static function changeRepresentation(int $num, int $base, string $rep, int $digits): string {
        $neg = $num < 0; // store if the value is negative
        $numa_str = (string)(abs($num)); // create the absolute value as a string
        $numa_str = base_convert($numa_str, 10, $base); // convert to specific base
        if ($neg) {
            if ($rep === "s") {
                $numa_str = self::extend($numa_str, $base, $digits, false);
                $numa_str = "-" . $numa_str;
            } else if ($rep === "c") {
                $numa_str = self::complement($numa_str, $rep);
                $numa_str = self::extend($numa_str, $base, $digits, true);
            }
        } else {
            $numa_str = self::extend($numa_str, $base, $digits, false);
        }
        return $numa_str;
    }

    public function randomize(): void
    {
        // validate representation marks
        $invalid = in_array($this->src_rep . $this->dst_rep, ["us", "su"]);
        if ($invalid) { // fix invalid representation pairs
            $this->dst_rep = "u";
            $this->src_rep = "u";
        }

        // specify the range
        $max = 1;
        $min = 0;
        switch ($this->dst_rep) {
            case "u":
                $max = pow($this->dst_base, $this->dst_n_digits) - 1;
                $min = 0;
                break;
            case "s":
                $max = pow($this->dst_base, $this->dst_n_digits) - 1;
                $min = -$max;
                break;
            case "c":
                $max = pow($this->dst_base, $this->dst_n_digits - 1) - 1;
                $min = -($max + 1);
                break;
        }

        // randomize a value
        $m = random_int($min, $max);

        // create the question and the answer
        $this->correct_answer = self::changeRepresentation($m, $this->dst_base, $this->dst_rep, $this->dst_n_digits);
        $this->source = self::changeRepresentation($m, $this->src_base, $this->src_rep, $this->src_n_digits);
    }

    public function getMark(): float
    {
        if ($this->hasFlag("acceptwithoutleadingzeros")) {
            return (ltrim($this->player_answer, " 0") === ltrim($this->correct_answer, "0")) ? 1.0 : 0.0;
        } else {
            return (trim($this->player_answer) === trim($this->correct_answer)) ? 1.0 : 0.0;
        }
    }
}