math_cms/app/Support/OptionLayoutDecider.php

<?php

namespace App\Support;

class OptionLayoutDecider
{
    public function normalizeCompactMathForDisplay(string $option): string
    {
        $trimmed = trim($option);
        if ($trimmed === '') {
            return $option;
        }

        $text = preg_replace('/^\$(.*)\$$/u', '$1', $trimmed) ?? $trimmed;
        $parts = $this->extractSingleFractionParts($text);
        if ($parts === null) {
            return $option;
        }

        [$num, $den] = $parts;
        $compactPart = '/^[\-+0-9a-zA-Z\x{221A}\\\\{}]+$/u';
        if (
            preg_match($compactPart, $num) !== 1
            || preg_match($compactPart, $den) !== 1
            || preg_match('/[=<>]/u', $num.$den) === 1
            || $this->hasBinaryOperator($num)
            || $this->hasBinaryOperator($den)
        ) {
            return $option;
        }

        return str_replace($text, $num.'/'.$den, $trimmed);
    }

    /**
     * @param array<int|string, mixed> $options
     * @return array{class:string,layout:string,max_length:int,max_width_units:float,avg_width_units:float,width_std_dev:float,has_complex_formula:bool,opt_count:int}
     */
    public function decide(array $options, string $context = 'exam'): array
    {
        $optCount = count($options);
        $maxOptionLength = 0;
        $maxWidthUnits = 0.0;
        $widthUnitsList = [];
        $sumWidthUnits = 0.0;
        $compactMathCount = 0;
        $plainCompactCount = 0;
        $optionMetas = [];
        $hasComplexFormulaOption = false;

        foreach ($options as $option) {
            $optionMeta = $this->analyzeOption((string) $option);
            $maxOptionLength = max($maxOptionLength, $optionMeta['effective_length']);
            $maxWidthUnits = max($maxWidthUnits, $optionMeta['width_units']);
            $widthUnitsList[] = $optionMeta['width_units'];
            $sumWidthUnits += $optionMeta['width_units'];
            if ($optionMeta['is_compact_math']) {
                $compactMathCount++;
            }
            if ($optionMeta['is_plain_compact']) {
                $plainCompactCount++;
            }
            $optionMetas[] = $optionMeta;
            $hasComplexFormulaOption = $hasComplexFormulaOption || $optionMeta['is_complex_formula'];
        }

        [$grid4Threshold, $grid2Threshold, $grid4WidthCap, $grid2WidthCap, $grid1WidthCap] = $this->thresholdsFor($context);
        $avgWidthUnits = $optCount > 0 ? ($sumWidthUnits / $optCount) : 0.0;
        $widthVariance = $this->variance($widthUnitsList, $avgWidthUnits);
        $widthStdDev = sqrt($widthVariance);
        $maxAvgRatio = $avgWidthUnits > 0 ? ($maxWidthUnits / $avgWidthUnits) : 0.0;

        // 4列仅在“整体紧凑 + 选项宽度分布均匀”时启用，避免单个长选项把 D 挤换行
        $allowGrid4ByWidth = $maxWidthUnits <= ($grid4WidthCap * 0.92)
            && $maxAvgRatio <= 1.42
            && $widthStdDev <= 1.65;
        $allCompactMath = $optCount > 0 && $compactMathCount === $optCount;
        $allowGrid4ByCompactMath = $optCount === 4
            && $allCompactMath
            && $maxWidthUnits <= ($grid4WidthCap * 1.04)
            && $widthStdDev <= 2.1;
        $allowGrid4ByPlainCompact = $optCount === 4
            && $plainCompactCount === $optCount
            && $maxOptionLength <= 9
            && $maxWidthUnits <= ($grid4WidthCap * 1.20)
            && $widthStdDev <= 2.4;
        $forceGrid4ByPlainShort = $optCount === 4
            && $plainCompactCount === $optCount
            && $maxOptionLength <= 8
            && ! $hasComplexFormulaOption;

        $canTryGrid4 = $optCount <= 4
            && ! $hasComplexFormulaOption
            && (
                (
                    $maxOptionLength <= $grid4Threshold
                    && $allowGrid4ByWidth
                )
                || $allowGrid4ByCompactMath
                || $allowGrid4ByPlainCompact
                || $forceGrid4ByPlainShort
            );
        $canTryGrid2 = $maxOptionLength <= $grid2Threshold && $maxWidthUnits <= ($grid2WidthCap * 1.18);

        $layoutCandidates = [];
        if ($canTryGrid4) {
            $layoutCandidates['options-grid-4'] = $this->layoutScore($optionMetas, 4, $grid4WidthCap);
        }
        if ($canTryGrid2) {
            $layoutCandidates['options-grid-2'] = $this->layoutScore($optionMetas, 2, $grid2WidthCap);
        }
        $layoutCandidates['options-grid-1'] = $this->layoutScore($optionMetas, 1, $grid1WidthCap);

        // 如果2列可行，尽量避免退化到1列（除非1列显著更优）
        if (isset($layoutCandidates['options-grid-2'], $layoutCandidates['options-grid-1'])) {
            $s2 = $layoutCandidates['options-grid-2']['score'];
            $s1 = $layoutCandidates['options-grid-1']['score'];
            if ($s2 <= ($s1 + 1.6)) {
                $layoutCandidates['options-grid-2']['score'] -= 0.35;
            }
        }

        $selectedClass = 'options-grid-1';
        $selectedScore = PHP_FLOAT_MAX;
        foreach ($layoutCandidates as $class => $meta) {
            if ($meta['score'] < $selectedScore) {
                $selectedClass = $class;
                $selectedScore = $meta['score'];
            }
        }

        if ($selectedClass === 'options-grid-4') {
            return [
                'class' => 'options-grid-4',
                'layout' => '4列布局',
                'max_length' => $maxOptionLength,
                'max_width_units' => $maxWidthUnits,
                'avg_width_units' => $avgWidthUnits,
                'width_std_dev' => $widthStdDev,
                'has_complex_formula' => $hasComplexFormulaOption,
                'opt_count' => $optCount,
            ];
        }

        if ($selectedClass === 'options-grid-2') {
            return [
                'class' => 'options-grid-2',
                'layout' => '2列布局',
                'max_length' => $maxOptionLength,
                'max_width_units' => $maxWidthUnits,
                'avg_width_units' => $avgWidthUnits,
                'width_std_dev' => $widthStdDev,
                'has_complex_formula' => $hasComplexFormulaOption,
                'opt_count' => $optCount,
            ];
        }

        return [
            'class' => 'options-grid-1',
            'layout' => '1列布局',
            'max_length' => $maxOptionLength,
            'max_width_units' => $maxWidthUnits,
            'avg_width_units' => $avgWidthUnits,
            'width_std_dev' => $widthStdDev,
            'has_complex_formula' => $hasComplexFormulaOption,
            'opt_count' => $optCount,
        ];
    }

    /**
     * @return array{effective_length:int,raw_length:int,width_units:float,height_units:float,is_complex_formula:bool,is_compact_math:bool,is_plain_compact:bool,has_stacked_fraction:bool}
     */
    private function analyzeOption(string $option): array
    {
        $optionText = html_entity_decode(strip_tags($option), ENT_QUOTES | ENT_HTML5, 'UTF-8');
        $optionText = preg_replace('/\s+/u', '', $optionText) ?? '';
        $optionTextNoDollar = preg_replace('/^\$(.*)\$$/u', '$1', $optionText) ?? $optionText;
        $rawLength = mb_strlen($optionText, 'UTF-8');
        $optionLength = $rawLength;
        $isSimpleCompactMath = preg_match('/^-?[0-9a-zA-Z\x{221A}]+(?:\/[0-9a-zA-Z\x{221A}]+)?$/u', $optionTextNoDollar) === 1;
        $isCompactLatexFraction = preg_match(
            '/^\\\\d?frac\{[-+0-9a-zA-Z\\\\\x{221A}\^\(\)]+\}\{[-+0-9a-zA-Z\\\\\x{221A}\^\(\)]+\}$/u',
            $optionTextNoDollar
        ) === 1;
        $isCompactLatexDegree = preg_match(
            '/^-?[0-9]+(?:\.[0-9]+)?(?:\^\{?\\\\circ\}?|°)$/u',
            $optionTextNoDollar
        ) === 1;
        $isCompactMath = $isSimpleCompactMath || $isCompactLatexFraction || $isCompactLatexDegree;
        $isSimpleSymbolLatex = preg_match('/^\\\\(pm|mp)\s*[0-9]+$/u', $optionTextNoDollar) === 1;
        $isPlainCompact = (
            preg_match('/\\\\[a-zA-Z]+/u', $optionTextNoDollar) !== 1
            || $isSimpleSymbolLatex
        ) && mb_strlen($optionTextNoDollar, 'UTF-8') <= 10;

        $hasLatexCmd = preg_match('/\\\\(frac|dfrac|sqrt|log|sin|cos|tan|cdot|times|left|right|begin|end)/u', $optionText) === 1;
        $hasStackedFraction = preg_match('/\\\\d?frac\{[^{}]+\}\{[^{}]+\}/u', $optionTextNoDollar) === 1;
        // 对可安全转为行内分式的短表达，不计入“堆叠分式”高度惩罚
        if ($isCompactLatexFraction) {
            $hasStackedFraction = false;
        }
        $sqrtCount = preg_match_all('/\\\\sqrt|√/u', $optionText);
        $supCount = preg_match_all('/\^/u', $optionText);
        $operatorCount = preg_match_all('/[=<>+\-*\/\^_]/u', $optionText);
        $hasBrackets = preg_match('/[（）\(\)\[\]\{\}]/u', $optionText) === 1;
        $isComplexFormula = ! $isCompactMath
            && ($hasLatexCmd || $operatorCount >= 2 || ($hasBrackets && $optionLength >= 8));

        if ($isComplexFormula) {
            $optionLength += 6;
        }

        return [
            'effective_length' => $optionLength,
            'raw_length' => $rawLength,
            'width_units' => $this->estimateWidthUnits($optionText),
            'height_units' => 1.0
                + ($hasStackedFraction ? 0.72 : 0.0)
                + min(0.36, ((int) $sqrtCount) * 0.08)
                + min(0.28, ((int) $supCount) * 0.07),
            'is_complex_formula' => $isComplexFormula,
            'is_compact_math' => $isCompactMath,
            'is_plain_compact' => $isPlainCompact,
            'has_stacked_fraction' => $hasStackedFraction,
        ];
    }

    /**
     * 判卷页面中题干+答案区域更紧凑，阈值应更保守。
     *
     * @return array{0:int,1:int,2:float,3:float,4:float}
     */
    private function thresholdsFor(string $context): array
    {
        if ($context === 'grading') {
            return [10, 24, 10.2, 21.0, 44.0];
        }

        return [12, 28, 11.5, 23.5, 48.0];
    }

    private function estimateWidthUnits(string $text): float
    {
        if ($text === '') {
            return 0.0;
        }

        // 简单TeX归一：减少命令名对宽度估计的干扰
        $normalized = preg_replace('/\\\\(left|right|displaystyle)/u', '', $text) ?? $text;
        $normalized = preg_replace('/\\\\(frac|dfrac)\{([^{}]+)\}\{([^{}]+)\}/u', '($2/$3)', $normalized) ?? $normalized;
        $normalized = preg_replace('/\\\\sqrt\{([^{}]+)\}/u', '√($1)', $normalized) ?? $normalized;

        $chars = preg_split('//u', $normalized, -1, PREG_SPLIT_NO_EMPTY) ?: [];
        $units = 0.0;
        foreach ($chars as $ch) {
            if (preg_match('/[\x{4e00}-\x{9fff}]/u', $ch)) {
                $units += 1.0;
            } elseif (preg_match('/[A-Za-z]/u', $ch)) {
                $units += 0.62;
            } elseif (preg_match('/[0-9]/u', $ch)) {
                $units += 0.58;
            } elseif (preg_match('/[=<>+\-*\/\^_]/u', $ch)) {
                $units += 0.45;
            } elseif (preg_match('/[（）\(\)\[\]\{\}]/u', $ch)) {
                $units += 0.35;
            } elseif ($ch === '√') {
                $units += 0.55;
            } else {
                $units += 0.5;
            }
        }

        // 选项标签（A.）和左侧间距补偿
        return $units + 2.2;
    }

    /**
     * @param array<int,array{width_units:float,height_units:float,has_stacked_fraction:bool}> $optionMetas
     * @return array{score:float}
     */
    private function layoutScore(array $optionMetas, int $cols, float $colCap): array
    {
        $count = count($optionMetas);
        if ($count === 0) {
            return ['score' => 0.0];
        }

        $overflowCount = 0;
        $lineWrapPenalty = 0.0;
        $rowHeights = [];
        $stackedFractionCount = 0;

        foreach ($optionMetas as $idx => $meta) {
            $effectiveWidth = $meta['width_units'] + ($meta['has_stacked_fraction'] ? ($cols === 4 ? 1.6 : 0.6) : 0.0);
            if ($effectiveWidth > $colCap) {
                $overflowCount++;
            }
            $lines = max(1.0, ceil($effectiveWidth / max(1.0, $colCap)));
            $lineWrapPenalty += max(0.0, $lines - 1.0);
            $itemHeight = $meta['height_units'] * $lines;

            $rowIndex = intdiv($idx, $cols);
            if (! isset($rowHeights[$rowIndex])) {
                $rowHeights[$rowIndex] = 0.0;
            }
            $rowHeights[$rowIndex] = max($rowHeights[$rowIndex], $itemHeight);

            if ($meta['has_stacked_fraction']) {
                $stackedFractionCount++;
            }
        }

        $overflowRate = $overflowCount / $count;
        $lineWrapRate = $lineWrapPenalty / $count;
        $rowAvg = array_sum($rowHeights) / max(1, count($rowHeights));
        $rowStd = sqrt($this->variance(array_values($rowHeights), $rowAvg));
        $rowCv = $rowAvg > 0 ? ($rowStd / $rowAvg) : 0.0;
        $stackedRate = $stackedFractionCount / $count;

        $whitespacePenalty = match ($cols) {
            1 => 2.4,
            2 => 0.7,
            default => 0.0,
        };

        $score = ($overflowRate * 120.0)
            + ($lineWrapRate * 10.0)
            + ($rowCv * 5.0)
            + ($stackedRate * ($cols === 4 ? 2.6 : 0.8))
            + $whitespacePenalty;

        return ['score' => $score];
    }

    /**
     * @param array<int,float> $values
     */
    private function variance(array $values, float $avg): float
    {
        if (empty($values)) {
            return 0.0;
        }

        $sum = 0.0;
        foreach ($values as $v) {
            $d = $v - $avg;
            $sum += ($d * $d);
        }

        return $sum / count($values);
    }

    /**
     * @return array{0:string,1:string}|null
     */
    private function extractSingleFractionParts(string $text): ?array
    {
        if (! preg_match('/^\\\\d?frac/u', $text)) {
            return null;
        }
        $offset = preg_match('/^\\\\dfrac/u', $text) ? 6 : 5; // \dfrac or \frac
        $len = mb_strlen($text, 'UTF-8');

        if ($offset >= $len || mb_substr($text, $offset, 1, 'UTF-8') !== '{') {
            return null;
        }

        [$num, $next] = $this->readBalancedBraces($text, $offset);
        if ($num === null || $next >= $len || mb_substr($text, $next, 1, 'UTF-8') !== '{') {
            return null;
        }

        [$den, $end] = $this->readBalancedBraces($text, $next);
        if ($den === null) {
            return null;
        }

        // 必须刚好到结尾，避免把 "\frac{a}{b}\text{cm}" 这类误改坏
        if ($end !== $len) {
            return null;
        }

        return [$num, $den];
    }

    private function hasBinaryOperator(string $expr): bool
    {
        return preg_match('/(?<!^)[+\-*]/u', $expr) === 1;
    }

    /**
     * @return array{0:string|null,1:int}
     */
    private function readBalancedBraces(string $text, int $startOffset): array
    {
        $len = mb_strlen($text, 'UTF-8');
        if ($startOffset >= $len || mb_substr($text, $startOffset, 1, 'UTF-8') !== '{') {
            return [null, $startOffset];
        }

        $depth = 0;
        $buffer = '';
        for ($i = $startOffset; $i < $len; $i++) {
            $ch = mb_substr($text, $i, 1, 'UTF-8');
            if ($ch === '{') {
                $depth++;
                if ($depth > 1) {
                    $buffer .= $ch;
                }
                continue;
            }
            if ($ch === '}') {
                $depth--;
                if ($depth === 0) {
                    return [$buffer, $i + 1];
                }
                if ($depth < 0) {
                    return [null, $i + 1];
                }
                $buffer .= $ch;
                continue;
            }
            $buffer .= $ch;
        }

        return [null, $len];
    }
}