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<!DOCTYPE HTML>
<html lang="zh" class="sidebar-visible no-js light">
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<title>示例: Bit数组 - Go语言圣经</title>
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<nav id="sidebar" class="sidebar" aria-label="Table of contents">
<div class="sidebar-scrollbox">
<ol class="chapter">
<li class="chapter-item expanded ">
<a href="../index.html" >Go语言圣经</a>
</li>
<li class="chapter-item expanded ">
<a href="../preface-zh.html" >译者序</a>
</li>
<li class="chapter-item expanded ">
<a href="../preface.html" >前言</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch1/ch1.html" ><strong aria-hidden="true">1.</strong> 入门</a>
</li>
<ol class="section">
<li class="chapter-item expanded ">
<a href="../ch1/ch1-01.html" ><strong aria-hidden="true">1.1.</strong> Hello, World</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch1/ch1-02.html" ><strong aria-hidden="true">1.2.</strong> 命令行参数</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch1/ch1-03.html" ><strong aria-hidden="true">1.3.</strong> 查找重复的行</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch1/ch1-04.html" ><strong aria-hidden="true">1.4.</strong> GIF动画</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch1/ch1-05.html" ><strong aria-hidden="true">1.5.</strong> 获取URL</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch1/ch1-06.html" ><strong aria-hidden="true">1.6.</strong> 并发获取多个URL</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch1/ch1-07.html" ><strong aria-hidden="true">1.7.</strong> Web服务</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch1/ch1-08.html" ><strong aria-hidden="true">1.8.</strong> 本章要点</a>
</li>
</ol>
<li class="chapter-item expanded ">
<a href="../ch2/ch2.html" ><strong aria-hidden="true">2.</strong> 程序结构</a>
</li>
<ol class="section">
<li class="chapter-item expanded ">
<a href="../ch2/ch2-01.html" ><strong aria-hidden="true">2.1.</strong> 命名</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch2/ch2-02.html" ><strong aria-hidden="true">2.2.</strong> 声明</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch2/ch2-03.html" ><strong aria-hidden="true">2.3.</strong> 变量</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch2/ch2-04.html" ><strong aria-hidden="true">2.4.</strong> 赋值</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch2/ch2-05.html" ><strong aria-hidden="true">2.5.</strong> 类型</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch2/ch2-06.html" ><strong aria-hidden="true">2.6.</strong> 包和文件</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch2/ch2-07.html" ><strong aria-hidden="true">2.7.</strong> 作用域</a>
</li>
</ol>
<li class="chapter-item expanded ">
<a href="../ch3/ch3.html" ><strong aria-hidden="true">3.</strong> 基础数据类型</a>
</li>
<ol class="section">
<li class="chapter-item expanded ">
<a href="../ch3/ch3-01.html" ><strong aria-hidden="true">3.1.</strong> 整型</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch3/ch3-02.html" ><strong aria-hidden="true">3.2.</strong> 浮点数</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch3/ch3-03.html" ><strong aria-hidden="true">3.3.</strong> 复数</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch3/ch3-04.html" ><strong aria-hidden="true">3.4.</strong> 布尔型</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch3/ch3-05.html" ><strong aria-hidden="true">3.5.</strong> 字符串</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch3/ch3-06.html" ><strong aria-hidden="true">3.6.</strong> 常量</a>
</li>
</ol>
<li class="chapter-item expanded ">
<a href="../ch4/ch4.html" ><strong aria-hidden="true">4.</strong> 复合数据类型</a>
</li>
<ol class="section">
<li class="chapter-item expanded ">
<a href="../ch4/ch4-01.html" ><strong aria-hidden="true">4.1.</strong> 数组</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch4/ch4-02.html" ><strong aria-hidden="true">4.2.</strong> Slice</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch4/ch4-03.html" ><strong aria-hidden="true">4.3.</strong> Map</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch4/ch4-04.html" ><strong aria-hidden="true">4.4.</strong> 结构体</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch4/ch4-05.html" ><strong aria-hidden="true">4.5.</strong> JSON</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch4/ch4-06.html" ><strong aria-hidden="true">4.6.</strong> 文本和HTML模板</a>
</li>
</ol>
<li class="chapter-item expanded ">
<a href="../ch5/ch5.html" ><strong aria-hidden="true">5.</strong> 函数</a>
</li>
<ol class="section">
<li class="chapter-item expanded ">
<a href="../ch5/ch5-01.html" ><strong aria-hidden="true">5.1.</strong> 函数声明</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch5/ch5-02.html" ><strong aria-hidden="true">5.2.</strong> 递归</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch5/ch5-03.html" ><strong aria-hidden="true">5.3.</strong> 多返回值</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch5/ch5-04.html" ><strong aria-hidden="true">5.4.</strong> 错误</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch5/ch5-05.html" ><strong aria-hidden="true">5.5.</strong> 函数值</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch5/ch5-06.html" ><strong aria-hidden="true">5.6.</strong> 匿名函数</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch5/ch5-07.html" ><strong aria-hidden="true">5.7.</strong> 可变参数</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch5/ch5-08.html" ><strong aria-hidden="true">5.8.</strong> Deferred函数</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch5/ch5-09.html" ><strong aria-hidden="true">5.9.</strong> Panic异常</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch5/ch5-10.html" ><strong aria-hidden="true">5.10.</strong> Recover捕获异常</a>
</li>
</ol>
<li class="chapter-item expanded ">
<a href="../ch6/ch6.html" ><strong aria-hidden="true">6.</strong> 方法</a>
</li>
<ol class="section">
<li class="chapter-item expanded ">
<a href="../ch6/ch6-01.html" ><strong aria-hidden="true">6.1.</strong> 方法声明</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch6/ch6-02.html" ><strong aria-hidden="true">6.2.</strong> 基于指针对象的方法</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch6/ch6-03.html" ><strong aria-hidden="true">6.3.</strong> 通过嵌入结构体来扩展类型</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch6/ch6-04.html" ><strong aria-hidden="true">6.4.</strong> 方法值和方法表达式</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch6/ch6-05.html" class="active"><strong aria-hidden="true">6.5.</strong> 示例: Bit数组</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch6/ch6-06.html" ><strong aria-hidden="true">6.6.</strong> 封装</a>
</li>
</ol>
<li class="chapter-item expanded ">
<a href="../ch7/ch7.html" ><strong aria-hidden="true">7.</strong> 接口</a>
</li>
<ol class="section">
<li class="chapter-item expanded ">
<a href="../ch7/ch7-01.html" ><strong aria-hidden="true">7.1.</strong> 接口是合约</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch7/ch7-02.html" ><strong aria-hidden="true">7.2.</strong> 接口类型</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch7/ch7-03.html" ><strong aria-hidden="true">7.3.</strong> 实现接口的条件</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch7/ch7-04.html" ><strong aria-hidden="true">7.4.</strong> flag.Value接口</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch7/ch7-05.html" ><strong aria-hidden="true">7.5.</strong> 接口值</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch7/ch7-06.html" ><strong aria-hidden="true">7.6.</strong> sort.Interface接口</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch7/ch7-07.html" ><strong aria-hidden="true">7.7.</strong> http.Handler接口</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch7/ch7-08.html" ><strong aria-hidden="true">7.8.</strong> error接口</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch7/ch7-09.html" ><strong aria-hidden="true">7.9.</strong> 示例: 表达式求值</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch7/ch7-10.html" ><strong aria-hidden="true">7.10.</strong> 类型断言</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch7/ch7-11.html" ><strong aria-hidden="true">7.11.</strong> 基于类型断言识别错误类型</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch7/ch7-12.html" ><strong aria-hidden="true">7.12.</strong> 通过类型断言查询接口</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch7/ch7-13.html" ><strong aria-hidden="true">7.13.</strong> 类型分支</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch7/ch7-14.html" ><strong aria-hidden="true">7.14.</strong> 示例: 基于标记的XML解码</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch7/ch7-15.html" ><strong aria-hidden="true">7.15.</strong> 补充几点</a>
</li>
</ol>
<li class="chapter-item expanded ">
<a href="../ch8/ch8.html" ><strong aria-hidden="true">8.</strong> Goroutines和Channels</a>
</li>
<ol class="section">
<li class="chapter-item expanded ">
<a href="../ch8/ch8-01.html" ><strong aria-hidden="true">8.1.</strong> Goroutines</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch8/ch8-02.html" ><strong aria-hidden="true">8.2.</strong> 示例: 并发的Clock服务</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch8/ch8-03.html" ><strong aria-hidden="true">8.3.</strong> 示例: 并发的Echo服务</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch8/ch8-04.html" ><strong aria-hidden="true">8.4.</strong> Channels</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch8/ch8-05.html" ><strong aria-hidden="true">8.5.</strong> 并发的循环</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch8/ch8-06.html" ><strong aria-hidden="true">8.6.</strong> 示例: 并发的Web爬虫</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch8/ch8-07.html" ><strong aria-hidden="true">8.7.</strong> 基于select的多路复用</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch8/ch8-08.html" ><strong aria-hidden="true">8.8.</strong> 示例: 并发的目录遍历</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch8/ch8-09.html" ><strong aria-hidden="true">8.9.</strong> 并发的退出</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch8/ch8-10.html" ><strong aria-hidden="true">8.10.</strong> 示例: 聊天服务</a>
</li>
</ol>
<li class="chapter-item expanded ">
<a href="../ch9/ch9.html" ><strong aria-hidden="true">9.</strong> 基于共享变量的并发</a>
</li>
<ol class="section">
<li class="chapter-item expanded ">
<a href="../ch9/ch9-01.html" ><strong aria-hidden="true">9.1.</strong> 竞争条件</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch9/ch9-02.html" ><strong aria-hidden="true">9.2.</strong> sync.Mutex互斥锁</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch9/ch9-03.html" ><strong aria-hidden="true">9.3.</strong> sync.RWMutex读写锁</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch9/ch9-04.html" ><strong aria-hidden="true">9.4.</strong> 内存同步</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch9/ch9-05.html" ><strong aria-hidden="true">9.5.</strong> sync.Once惰性初始化</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch9/ch9-06.html" ><strong aria-hidden="true">9.6.</strong> 竞争条件检测</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch9/ch9-07.html" ><strong aria-hidden="true">9.7.</strong> 示例: 并发的非阻塞缓存</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch9/ch9-08.html" ><strong aria-hidden="true">9.8.</strong> Goroutines和线程</a>
</li>
</ol>
<li class="chapter-item expanded ">
<a href="../ch10/ch10.html" ><strong aria-hidden="true">10.</strong> 包和工具</a>
</li>
<ol class="section">
<li class="chapter-item expanded ">
<a href="../ch10/ch10-01.html" ><strong aria-hidden="true">10.1.</strong> 包简介</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch10/ch10-02.html" ><strong aria-hidden="true">10.2.</strong> 导入路径</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch10/ch10-03.html" ><strong aria-hidden="true">10.3.</strong> 包声明</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch10/ch10-04.html" ><strong aria-hidden="true">10.4.</strong> 导入声明</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch10/ch10-05.html" ><strong aria-hidden="true">10.5.</strong> 包的匿名导入</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch10/ch10-06.html" ><strong aria-hidden="true">10.6.</strong> 包和命名</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch10/ch10-07.html" ><strong aria-hidden="true">10.7.</strong> 工具</a>
</li>
</ol>
<li class="chapter-item expanded ">
<a href="../ch11/ch11.html" ><strong aria-hidden="true">11.</strong> 测试</a>
</li>
<ol class="section">
<li class="chapter-item expanded ">
<a href="../ch11/ch11-01.html" ><strong aria-hidden="true">11.1.</strong> go test</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch11/ch11-02.html" ><strong aria-hidden="true">11.2.</strong> 测试函数</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch11/ch11-03.html" ><strong aria-hidden="true">11.3.</strong> 测试覆盖率</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch11/ch11-04.html" ><strong aria-hidden="true">11.4.</strong> 基准测试</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch11/ch11-05.html" ><strong aria-hidden="true">11.5.</strong> 剖析</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch11/ch11-06.html" ><strong aria-hidden="true">11.6.</strong> 示例函数</a>
</li>
</ol>
<li class="chapter-item expanded ">
<a href="../ch12/ch12.html" ><strong aria-hidden="true">12.</strong> 反射</a>
</li>
<ol class="section">
<li class="chapter-item expanded ">
<a href="../ch12/ch12-01.html" ><strong aria-hidden="true">12.1.</strong> 为何需要反射?</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch12/ch12-02.html" ><strong aria-hidden="true">12.2.</strong> reflect.Type和reflect.Value</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch12/ch12-03.html" ><strong aria-hidden="true">12.3.</strong> Display递归打印</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch12/ch12-04.html" ><strong aria-hidden="true">12.4.</strong> 示例: 编码S表达式</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch12/ch12-05.html" ><strong aria-hidden="true">12.5.</strong> 通过reflect.Value修改值</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch12/ch12-06.html" ><strong aria-hidden="true">12.6.</strong> 示例: 解码S表达式</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch12/ch12-07.html" ><strong aria-hidden="true">12.7.</strong> 获取结构体字段标签</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch12/ch12-08.html" ><strong aria-hidden="true">12.8.</strong> 显示一个类型的方法集</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch12/ch12-09.html" ><strong aria-hidden="true">12.9.</strong> 几点忠告</a>
</li>
</ol>
<li class="chapter-item expanded ">
<a href="../ch13/ch13.html" ><strong aria-hidden="true">13.</strong> 底层编程</a>
</li>
<ol class="section">
<li class="chapter-item expanded ">
<a href="../ch13/ch13-01.html" ><strong aria-hidden="true">13.1.</strong> unsafe.Sizeof, Alignof 和 Offsetof</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch13/ch13-02.html" ><strong aria-hidden="true">13.2.</strong> unsafe.Pointer</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch13/ch13-03.html" ><strong aria-hidden="true">13.3.</strong> 示例: 深度相等判断</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch13/ch13-04.html" ><strong aria-hidden="true">13.4.</strong> 通过cgo调用C代码</a>
</li>
<li class="chapter-item expanded ">
<a href="../ch13/ch13-05.html" ><strong aria-hidden="true">13.5.</strong> 几点忠告</a>
</li>
</ol>
<li class="chapter-item expanded ">
<a href="../appendix/appendix.html" ><strong aria-hidden="true">14.</strong> 附录</a>
</li>
<ol class="section">
<li class="chapter-item expanded ">
<a href="../appendix/appendix-a-errata.html" ><strong aria-hidden="true">14.1.</strong> 附录A：原文勘误</a>
</li>
<li class="chapter-item expanded ">
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<a href="../appendix/appendix-d-translations.html" ><strong aria-hidden="true">14.4.</strong> 附录D：其它语言</a>
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<ul dir="auto"><li><em>凹语言(Go实现, 面向WASM设计): <a href="https://github.com/wa-lang/wa">https://github.com/wa-lang/wa</a></em></li><li><em>WaBook(Go语言实现的MD电子书构建工具): <a href="https://github.com/wa-lang/wabook">https://github.com/wa-lang/wabook</a></em></li></ul><hr>
<h2>6.5. 示例: Bit数组</h2>
<p>Go语言里的集合一般会用map[T]bool这种形式来表示，T代表元素类型。集合用map类型来表示虽然非常灵活，但我们可以以一种更好的形式来表示它。例如在数据流分析领域，集合元素通常是一个非负整数，集合会包含很多元素，并且集合会经常进行并集、交集操作，这种情况下，bit数组会比map表现更加理想。（译注：这里再补充一个例子，比如我们执行一个http下载任务，把文件按照16kb一块划分为很多块，需要有一个全局变量来标识哪些块下载完成了，这种时候也需要用到bit数组。）</p>
<p>一个bit数组通常会用一个无符号数或者称之为“字”的slice来表示，每一个元素的每一位都表示集合里的一个值。当集合的第i位被设置时，我们才说这个集合包含元素i。下面的这个程序展示了一个简单的bit数组类型，并且实现了三个函数来对这个bit数组来进行操作：</p>
<p><!-- raw HTML omitted --><!-- raw HTML omitted -->gopl.io/ch6/intset<!-- raw HTML omitted --><!-- raw HTML omitted --></p>
<pre><code class="language-go">// An IntSet is a set of small non-negative integers.
// Its zero value represents the empty set.
type IntSet struct {
words []uint64
}
// Has reports whether the set contains the non-negative value x.
func (s *IntSet) Has(x int) bool {
word, bit := x/64, uint(x%64)
return word &lt; len(s.words) &amp;&amp; s.words[word]&amp;(1&lt;&lt;bit) != 0
}
// Add adds the non-negative value x to the set.
func (s *IntSet) Add(x int) {
word, bit := x/64, uint(x%64)
for word &gt;= len(s.words) {
s.words = append(s.words, 0)
}
s.words[word] |= 1 &lt;&lt; bit
}
// UnionWith sets s to the union of s and t.
func (s *IntSet) UnionWith(t *IntSet) {
for i, tword := range t.words {
if i &lt; len(s.words) {
s.words[i] |= tword
} else {
s.words = append(s.words, tword)
}
}
}
</code></pre>
<p>因为每一个字都有64个二进制位，所以为了定位x的bit位，我们用了x/64的商作为字的下标，并且用x%64得到的值作为这个字内的bit的所在位置。UnionWith这个方法里用到了bit位的“或”逻辑操作符号|来一次完成64个元素的或计算。（在练习6.5中我们还会有程序用到这个64位字的例子。）</p>
<p>当前这个实现还缺少了很多必要的特性，我们把其中一些作为练习题列在本小节之后。但是有一个方法如果缺失的话我们的bit数组可能会比较难混：将IntSet作为一个字符串来打印。这里我们来实现它，让我们来给上面的例子添加一个String方法，类似2.5节中做的那样：</p>
<pre><code class="language-go">// String returns the set as a string of the form &quot;{1 2 3}&quot;.
func (s *IntSet) String() string {
var buf bytes.Buffer
buf.WriteByte('{')
for i, word := range s.words {
if word == 0 {
continue
}
for j := 0; j &lt; 64; j++ {
if word&amp;(1&lt;&lt;uint(j)) != 0 {
if buf.Len() &gt; len(&quot;{&quot;) {
buf.WriteByte(' ')
}
fmt.Fprintf(&amp;buf, &quot;%d&quot;, 64*i+j)
}
}
}
buf.WriteByte('}')
return buf.String()
}
</code></pre>
<p>这里留意一下String方法，是不是和3.5.4节中的intsToString方法很相似；bytes.Buffer在String方法里经常这么用。当你为一个复杂的类型定义了一个String方法时，fmt包就会特殊对待这种类型的值，这样可以让这些类型在打印的时候看起来更加友好，而不是直接打印其原始的值。fmt会直接调用用户定义的String方法。这种机制依赖于接口和类型断言，在第7章中我们会详细介绍。</p>
<p>现在我们就可以在实战中直接用上面定义好的IntSet了：</p>
<pre><code class="language-go">var x, y IntSet
x.Add(1)
x.Add(144)
x.Add(9)
fmt.Println(x.String()) // &quot;{1 9 144}&quot;
y.Add(9)
y.Add(42)
fmt.Println(y.String()) // &quot;{9 42}&quot;
x.UnionWith(&amp;y)
fmt.Println(x.String()) // &quot;{1 9 42 144}&quot;
fmt.Println(x.Has(9), x.Has(123)) // &quot;true false&quot;
</code></pre>
<p>这里要注意：我们声明的String和Has两个方法都是以指针类型<code>*IntSet</code>来作为接收器的，但实际上对于这两个类型来说，把接收器声明为指针类型也没什么必要。不过另外两个函数就不是这样了，因为另外两个函数操作的是s.words对象，如果你不把接收器声明为指针对象，那么实际操作的是拷贝对象，而不是原来的那个对象。因此，因为我们的String方法定义在IntSet指针上，所以当我们的变量是IntSet类型而不是IntSet指针时，可能会有下面这样让人意外的情况：</p>
<pre><code class="language-go">fmt.Println(&amp;x) // &quot;{1 9 42 144}&quot;
fmt.Println(x.String()) // &quot;{1 9 42 144}&quot;
fmt.Println(x) // &quot;{[4398046511618 0 65536]}&quot;
</code></pre>
<p>在第一个Println中，我们打印一个<code>*IntSet</code>的指针，这个类型的指针确实有自定义的String方法。第二Println，我们直接调用了x变量的String()方法；这种情况下编译器会隐式地在x前插入&amp;操作符，这样相当于我们还是调用的IntSet指针的String方法。在第三个Println中，因为IntSet类型没有String方法，所以Println方法会直接以原始的方式理解并打印。所以在这种情况下&amp;符号是不能忘的。在我们这种场景下，你把String方法绑定到IntSet对象上，而不是IntSet指针上可能会更合适一些，不过这也需要具体问题具体分析。</p>
<p><strong>练习6.1:</strong> 为bit数组实现下面这些方法</p>
<pre><code class="language-go">func (*IntSet) Len() int // return the number of elements
func (*IntSet) Remove(x int) // remove x from the set
func (*IntSet) Clear() // remove all elements from the set
func (*IntSet) Copy() *IntSet // return a copy of the set
</code></pre>
<p><strong>练习 6.2：</strong> 定义一个变参方法(*IntSet).AddAll(...int)，这个方法可以添加一组IntSet，比如s.AddAll(1,2,3)。</p>
<p><strong>练习 6.3：</strong> (*IntSet).UnionWith会用<code>|</code>操作符计算两个集合的并集，我们再为IntSet实现另外的几个函数IntersectWith（交集：元素在A集合B集合均出现），DifferenceWith（差集：元素出现在A集合，未出现在B集合），SymmetricDifference（并差集：元素出现在A但没有出现在B，或者出现在B没有出现在A）。</p>
<p><strong>练习 6.4：</strong> 实现一个Elems方法，返回集合中的所有元素，用于做一些range之类的遍历操作。</p>
<p><strong>练习 6.5：</strong> 我们这章定义的IntSet里的每个字都是用的uint64类型，但是64位的数值可能在32位的平台上不高效。修改程序，使其使用uint类型，这种类型对于32位平台来说更合适。当然了，这里我们可以不用简单粗暴地除64，可以定义一个常量来决定是用32还是64，这里你可能会用到平台的自动判断的一个智能表达式：32 &lt;&lt; (^uint(0) &gt;&gt; 63)</p>
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