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<!DOCTYPE html>
<html lang="zh-CN">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Hacker's Delight Ch02 - 快速记忆卡片</title>
<style>
:root {
--g: #00ff88;
--b: #00d4ff;
--p: #b14fff;
--o: #ff8c00;
--r: #ff4466;
--dark: #050810;
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--border: rgba(0,255,136,.18);
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.container { max-width: 1400px; margin: 0 auto; position: relative; z-index: 1; }
.header {
text-align: center;
margin-bottom: 40px;
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.header h1 {
font-size: clamp(1.5rem, 4vw, 2rem);
color: #f1f5f9;
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.header p { color: #94a3b8; font-size: 0.95rem; }
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border-radius: 12px;
padding: 20px;
cursor: pointer;
transition: all 0.25s ease;
min-height: 200px;
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flex-direction: column;
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box-shadow: 0 0 20px rgba(0,255,136,.15);
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.flashcard-front {
font-size: 0.9em;
font-weight: bold;
color: #e2e8f0;
margin-bottom: 20px;
border-bottom: 1px solid rgba(0,255,136,.2);
padding-bottom: 10px;
}
.flashcard.flipped .flashcard-front { border-bottom-color: var(--g); color: var(--g); display: none; }
.flashcard-back {
font-size: 0.85em;
color: #94a3b8;
line-height: 1.6;
background: rgba(0,0,0,.25);
padding: 15px;
border-radius: 6px;
display: none;
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.flashcard.flipped .flashcard-back {
display: block;
border: 1px solid rgba(0,255,136,.15);
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.flashcard.flipped .flashcard-hint { display: none; }
.flashcard-hint { font-size: 0.75em; color: #64748b; margin-top: 10px; text-align: center; }
.category-section { margin-bottom: 40px; }
.category-title {
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border: 1px solid #1e293b;
padding: 15px 20px;
border-radius: 8px;
border-left: 4px solid var(--g);
font-size: 1.1em;
font-weight: bold;
color: #f1f5f9;
margin-bottom: 20px;
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.category-title:hover { border-color: rgba(0,255,136,.3); }
.quick-ref {
background: var(--card);
border: 1px solid #1e293b;
border-radius: 12px;
padding: 30px;
margin-bottom: 40px;
}
.quick-ref:hover { border-color: rgba(0,255,136,.25); }
.quick-ref h2 {
color: var(--g);
margin-bottom: 20px;
border-bottom: 1px solid rgba(0,255,136,.2);
padding-bottom: 10px;
font-family: 'JetBrains Mono', monospace;
font-size: 1rem;
}
.ref-grid {
display: grid;
grid-template-columns: repeat(auto-fit, minmax(300px, 1fr));
gap: 20px;
}
.ref-item {
background: #010409;
border: 1px solid #1e293b;
padding: 15px;
border-radius: 8px;
border-left: 3px solid var(--b);
}
.ref-item:hover { border-color: rgba(0,212,255,.25); }
.ref-formula {
font-family: 'JetBrains Mono', monospace;
background: rgba(0,255,136,.08);
border: 1px solid rgba(0,255,136,.2);
padding: 10px;
border-radius: 4px;
color: var(--g);
margin: 10px 0;
font-size: 0.95em;
}
.tip-box {
background: rgba(0,255,136,.04);
border: 1px solid rgba(0,255,136,.15);
border-left: 4px solid var(--g);
padding: 20px;
border-radius: 8px;
margin-bottom: 20px;
color: #94a3b8;
}
.tip-box strong { color: var(--g); }
.star { color: var(--o); font-size: 1.1em; }
@media (max-width: 768px) {
.flashcard-grid { grid-template-columns: 1fr; }
.header h1 { font-size: 1.5em; }
}
.print-button {
background: transparent;
color: var(--g);
border: 1px solid var(--g);
padding: 12px 24px;
border-radius: 8px;
cursor: pointer;
font-size: 0.9rem;
margin-bottom: 30px;
font-family: 'JetBrains Mono', monospace;
transition: all 0.2s;
}
.print-button:hover {
background: rgba(0,255,136,.1);
box-shadow: 0 0 12px rgba(0,255,136,.3);
}
@media print {
body { background: #fff; color: #111; }
body::after { display: none; }
.flashcard { background: #fff; border-color: #ddd; color: #333; }
.flashcard-back { background: #f5f5f5; color: #333; }
.category-title { background: #f5f5f5; color: #333; border-left-color: #00ff88; }
.quick-ref { background: #fff; border-color: #ddd; }
.quick-ref h2 { color: #00aa55; }
.ref-item { background: #f9f9f9; border-left-color: #00d4ff; }
.ref-formula { background: #eee; color: #c00; }
.tip-box { background: #f0fff4; border-left-color: #00ff88; color: #333; }
.print-button { display: none; }
}
</style>
</head>
<body>
<nav class="ch02-nav" style="position:fixed;left:0;top:0;bottom:0;width:180px;background:rgba(0,0,0,0.92);padding:1rem 0.5rem;display:flex;flex-direction:column;gap:0.25rem;font-family:monospace;font-size:0.8rem;border-right:1px solid rgba(0,255,136,0.2);z-index:90;overflow-y:auto;"><a href="ch02.html" style="color:#00ff88;text-decoration:none;padding:0.35rem 0.6rem;">← 返回 Ch.02 主章</a><div style="height:1px;background:rgba(255,255,255,0.1);margin:0.25rem 0;"></div><a href="ch02_quickref.html" style="color:#94a3b8;text-decoration:none;padding:0.35rem 0.6rem;">快速参考</a><a href="ch02_interactive.html" style="color:#94a3b8;text-decoration:none;padding:0.35rem 0.6rem;">交互演示</a><a href="ch02_anaylze.html" style="color:#94a3b8;text-decoration:none;padding:0.35rem 0.6rem;">深度分析</a><a href="ch02_mindmap.html" style="color:#94a3b8;text-decoration:none;padding:0.35rem 0.6rem;">思维导图</a><a href="ch02_check.html" style="color:#94a3b8;text-decoration:none;padding:0.35rem 0.6rem;">练习检查</a><a href="ch02_game.html" style="color:#94a3b8;text-decoration:none;padding:0.35rem 0.6rem;">趣味游戏</a><a href="ch02_Gosper's Hack.html" style="color:#94a3b8;text-decoration:none;padding:0.35rem 0.6rem;">Gosper算法</a><a href="ch02_summary.html" style="color:#94a3b8;text-decoration:none;padding:0.35rem 0.6rem;">章节总结</a></nav>
<div style="margin-left:180px;">
<div class="container">
<div class="header">
<h1>🎓 Hacker's Delight Ch02 - 快速记忆卡片</h1>
<p>点击卡片翻转 | 打印成便签随身携带</p>
</div>
<button class="print-button" onclick="window.print()">🖨️ 打印记忆卡片</button>
<!-- 第一部分：最右位操纵 -->
<div class="category-section">
<div class="category-title">🔧 第一部分：最右位操纵 TRICKS (8个)</div>
<div class="flashcard-grid">
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">TRICK 01: 清除最右边的1</div>
<div class="flashcard-back">
<div class="ref-formula">x & (x - 1)</div>
<p>判断 2 的幂：<br/>(x & (x-1)) == 0</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">TRICK 06: 最右边的1掩码 <span class="star">⭐⭐⭐</span></div>
<div class="flashcard-back">
<div class="ref-formula">x & (-x)</div>
<p>棋盘引擎必用！Kernighan 位计数。</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">TRICK 02: 置位最右边的0</div>
<div class="flashcard-back">
<div class="ref-formula">x | (x + 1)</div>
<p>连续 0 检测</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">TRICK 03: 清除尾部连续的1</div>
<div class="flashcard-back">
<div class="ref-formula">x & (x + 1)</div>
<p>判断 2ⁿ-1 形式</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">TRICK 04: 置位尾部连续的0</div>
<div class="flashcard-back">
<div class="ref-formula">x | (x - 1)</div>
<p>内存对齐、取整</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">TRICK 05: 最右边的0掩码</div>
<div class="flashcard-back">
<div class="ref-formula">~x & (x + 1)</div>
<p>在最低位 0 处产生单个 1</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">TRICK 07: 尾部0的掩码</div>
<div class="flashcard-back">
<div class="ref-formula">~x & (x - 1)</div>
<p>所有尾部 0 位置产生 1</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">TRICK 08: 尾部1右对齐传播</div>
<div class="flashcard-back">
<div class="ref-formula">x | (x - 1)</div>
<p>内存对齐、子集枚举</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
</div>
</div>
<!-- 第二部分：加减法恒等式 -->
<div class="category-section">
<div class="category-title">➕ 第二部分：加减法恒等式 (7个)</div>
<div class="flashcard-grid">
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">(a) 王牌恒等式 <span class="star">⭐⭐⭐</span></div>
<div class="flashcard-back">
<div class="ref-formula">x+y = (x^y)+((x&y)<<1)</div>
<p>加法 = 无进位 + 进位传播</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">(f) Dietz无溢出平均 <span class="star">⭐⭐⭐</span></div>
<div class="flashcard-back">
<div class="ref-formula">avg = (x&y)+((x^y)>>1)</div>
<p>永不溢出！JDK 的救星</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">(b) OR/AND分解</div>
<div class="flashcard-back">
<div class="ref-formula">x+y = (x|y)+(x&y)</div>
<p>等价分解形式</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">(e) AND表示法 <span class="star">⭐⭐</span></div>
<div class="flashcard-back">
<div class="ref-formula">x&y = (x|y)-(x^y)</div>
<p>对偶性质，三个操作互推</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">(c) 反向推导</div>
<div class="flashcard-back">
<div class="ref-formula">x^y = (x+y)-((x&y)<<1)</div>
<p>从加法反向推导 XOR</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">(d) OR表示法</div>
<div class="flashcard-back">
<div class="ref-formula">x|y = (x+y)-(x&y)</div>
<p>OR 用加减表示</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">(g) XOR分解</div>
<div class="flashcard-back">
<div class="ref-formula">x^y = (x|y)&~(x&y)</div>
<p>4 指令分解形式</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
</div>
</div>
<!-- 第三部分：无分支算术 -->
<div class="category-section">
<div class="category-title">⚡ 第三部分：无分支算术 (6个)</div>
<div class="flashcard-grid">
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">符号掩码 <span class="star">⭐⭐</span></div>
<div class="flashcard-back">
<div class="ref-formula">mask = x >> 31</div>
<p>x≥0: 0x00 | x<0: 0xFF<br/>所有无分支操作基础</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">abs(x) - 绝对值 <span class="star">⭐⭐⭐</span></div>
<div class="flashcard-back">
<div class="ref-formula">abs = (x + mask) ^ mask</div>
<p>3 指令，0 分支<br/>快 5-10 倍</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">min(x,y) <span class="star">⭐⭐</span></div>
<div class="flashcard-back">
<div class="ref-formula">min = y+((x-y)&((x-y)>>31))</div>
<p>3 指令，无分支</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">max(x,y) <span class="star">⭐⭐</span></div>
<div class="flashcard-back">
<div class="ref-formula">max = x-((x-y)&((x-y)>>31))</div>
<p>3 指令，无分支</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">avg(x,y) <span class="star">⭐⭐⭐</span></div>
<div class="flashcard-back">
<div class="ref-formula">avg = (x&y)+((x^y)>>1)</div>
<p>永不溢出！SIMD 必用</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">sign(x)</div>
<div class="flashcard-back">
<div class="ref-formula">sign = (x>>31)|((-x)>>31)</div>
<p>结果：-1/0/+1<br/>3 指令</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
</div>
</div>
<!-- 第四部分：Gosper's Hack -->
<div class="category-section">
<div class="category-title">🌟 第四部分：Gosper's Hack <span class="star">⭐⭐⭐</span> (100倍加速)</div>
<div class="flashcard-grid">
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">Step 1: 提取最低1</div>
<div class="flashcard-back">
<div class="ref-formula">c = x & (-x)</div>
<p>识别进位点</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">Step 2: 进位传播</div>
<div class="flashcard-back">
<div class="ref-formula">r = x + c</div>
<p>级联翻转低位 1 串</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">Step 3: 计算补充1数</div>
<div class="flashcard-back">
<div class="ref-formula">ones = (((r^x)/c)>>2)+1</div>
<p>保持 popcount 不变</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
<div class="flashcard" onclick="this.classList.toggle('flipped')">
<div class="flashcard-front">Step 4: 合并结果</div>
<div class="flashcard-back">
<div class="ref-formula">result = r | ones</div>
<p>完成！下一个排列</p>
</div>
<div class="flashcard-hint">点击查看答案</div>
</div>
</div>
</div>
<!-- 快速参考表 -->
<div class="quick-ref">
<h2>⚡ 快速参考：最常用公式</h2>
<div class="ref-grid">
<div class="ref-item">
<strong>王牌恒等式</strong>
<div class="ref-formula">x+y = (x^y)+((x&y)<<1)</div>
<p>加法的本质：无进位 + 进位传播</p>
</div>
<div class="ref-item">
<strong>Dietz平均</strong>
<div class="ref-formula">avg = (x&y)+((x^y)>>1)</div>
<p>永不溢出，2006年JDK bug的根源</p>
</div>
<div class="ref-item">
<strong>最右边的1</strong>
<div class="ref-formula">x & (-x)</div>
<p>棋盘引擎和bitboard操作必用</p>
</div>
<div class="ref-item">
<strong>无分支abs</strong>
<div class="ref-formula">abs = (x + (x>>31)) ^ (x>>31)</div>
<p>3指令0分支，快5-10倍</p>
</div>
<div class="ref-item">
<strong>MUX选择器</strong>
<div class="ref-formula">mux = ((x^y)&m) ^ y</div>
<p>3指令优化版本（需ANDC）</p>
</div>
<div class="ref-item">
<strong>Gosper's Hack</strong>
<div class="ref-formula">result = (x+c) | (((r^x)/c)>>2)+1<br/>其中c = x&(-x), r = x+c</div>
<p>组合爆炸救星，100倍加速</p>
</div>
</div>
</div>
<!-- 记忆技巧 -->
<div class="tip-box">
<h3>💡 记忆技巧</h3>
<p><strong>1. x & (x-1)：</strong>减1会触发进位穿透，清除最低的1</p>
<p><strong>2. x & (-x)：</strong>补码性质，提取最低的1（棋盘引擎钥匙）</p>
<p><strong>3. mask = x >> 31：</strong>正数得0，负数得-1，用于无分支条件</p>
<p><strong>4. Dietz平均：</strong>记住 (x&y) 是共同部分，((x^y)>>1) 是不同部分的一半</p>
<p><strong>5. Gosper's Hack：</strong>4个步骤的核心是保持位数不变，只改变排列顺序</p>
</div>
<!-- 学习进度追踪 -->
<div class="quick-ref">
<h2>📈 学习进度追踪</h2>
<div style="display: grid; grid-template-columns: repeat(auto-fit, minmax(250px, 1fr)); gap: 20px;">
<div style="background: #0d1117; padding: 15px; border-radius: 8px; border: 1px solid #1e293b; border-left: 3px solid #00ff88;">
<div style="font-weight: bold; color: #00ff88; margin-bottom: 10px;">第1阶段：基础掌握</div>
<p style="color: #94a3b8;">☐ 8个TRICKS<br/>☐ 7个恒等式<br/>☐ 符号掩码<br/><strong style="color: #e2e8f0;">预计：3天</strong></p>
</div>
<div style="background: #0d1117; padding: 15px; border-radius: 8px; border: 1px solid #1e293b; border-left: 3px solid #00d4ff;">
<div style="font-weight: bold; color: #00d4ff; margin-bottom: 10px;">第2阶段：实战应用</div>
<p style="color: #94a3b8;">☐ 6个无分支操作<br/>☐ Gosper's Hack<br/>☐ MUX优化<br/><strong style="color: #e2e8f0;">预计：5天</strong></p>
</div>
<div style="background: #0d1117; padding: 15px; border-radius: 8px; border: 1px solid #1e293b; border-left: 3px solid #b14fff;">
<div style="font-weight: bold; color: #b14fff; margin-bottom: 10px;">第3阶段：深化理论</div>
<p style="color: #94a3b8;">☐ 特殊技巧合集<br/>☐ 布尔分解定理<br/>☐ 课后习题<br/><strong style="color: #e2e8f0;">预计：7天</strong></p>
</div>
<div style="background: #0d1117; padding: 15px; border-radius: 8px; border: 1px solid #1e293b; border-left: 3px solid #ff8c00;">
<div style="font-weight: bold; color: #ff8c00; margin-bottom: 10px;">第4阶段：应用迁移</div>
<p style="color: #94a3b8;">☐ 20+应用场景<br/>☐ 历史演变理解<br/>☐ 跨领域应用<br/><strong style="color: #e2e8f0;">预计：10天</strong></p>
</div>
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