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<div class="output_wrapper" id="output_wrapper_id" style="font-size: 15px; color: rgb(62, 62, 62); line-height: 1.8; word-spacing: 2px; letter-spacing: 2px; font-family: 'Helvetica Neue', Helvetica, 'Hiragino Sans GB', 'Microsoft YaHei', Arial, sans-serif; background-image: linear-gradient(90deg, rgba(50, 0, 0, 0.05) 3%, rgba(0, 0, 0, 0) 3%), linear-gradient(360deg, rgba(50, 0, 0, 0.05) 3%, rgba(0, 0, 0, 0) 3%); background-size: 20px 20px; background-position: center center;">有些算法題目，只要掌握了思路就可以用很短的代碼來實(shí)現(xiàn)它。比如下面這幾道題目：
<h3 id="h" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; border-bottom: 2px solid rgb(239, 112, 96); font-size: 1.3em;"><span style="font-size: inherit; line-height: inherit; margin: 0px; display: inline-block; font-weight: normal; background: rgb(239, 112, 96); color: rgb(255, 255, 255); padding: 3px 10px 1px; border-top-right-radius: 3px; border-top-left-radius: 3px; margin-right: 3px;">二的冪 </h3>
<h4 id="h-1" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; font-size: 1.2em;">問題</h4>
判斷一個(gè)數(shù)字是否是2的n次方
<h4 id="h-2" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; font-size: 1.2em;">解答</h4>
遇到2的冪次方，要建立位移操作的思想，如果n是二的冪，即最高位為1其他位置為0，那么n-1就是最高位為0，其余位置為1，那么n&(n-1)就是0
<pre style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px;"><code class="hljs java" style="overflow-wrap: break-word; margin: 0px 2px; line-height: 18px; font-size: 14px; font-weight: normal; word-spacing: 0px; letter-spacing: 0px; font-family: Consolas, Inconsolata, Courier, monospace; border-radius: 0px; overflow-x: auto; padding: 0.5em; color: rgb(51, 51, 51); background: rgb(248, 248, 248); white-space: pre !important; word-wrap: normal !important; word-break: normal !important; overflow: auto !important; display: -webkit-box !important;"><span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">1<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">boolean?isPowerOfTow(<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">int?n){
<span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">2????<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">return?(n>0)%%(n&(n-1))==0;
<span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">3}
</code></pre>
<h3 id="h-3" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; border-bottom: 2px solid rgb(239, 112, 96); font-size: 1.3em;"><span style="font-size: inherit; line-height: inherit; margin: 0px; display: inline-block; font-weight: normal; background: rgb(239, 112, 96); color: rgb(255, 255, 255); padding: 3px 10px 1px; border-top-right-radius: 3px; border-top-left-radius: 3px; margin-right: 3px;">三的冪 </h3>
<h4 id="h-4" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; font-size: 1.2em;">問題</h4>
判斷一個(gè)數(shù)字是否為3的n次方
<h4 id="h-5" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; font-size: 1.2em;">解答</h4>
int類型中不溢出情況下3的最高次方即為1162261467，那么只要這個(gè)數(shù)去約n為0，那么說明n的約數(shù)只有三，即為3的n次方.
同樣的做法也可以適用于5的冪,7的冪,X的冪（X是一個(gè)素?cái)?shù)）之類的題目。
<pre style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px;"><code class="hljs java" style="overflow-wrap: break-word; margin: 0px 2px; line-height: 18px; font-size: 14px; font-weight: normal; word-spacing: 0px; letter-spacing: 0px; font-family: Consolas, Inconsolata, Courier, monospace; border-radius: 0px; overflow-x: auto; padding: 0.5em; color: rgb(51, 51, 51); background: rgb(248, 248, 248); white-space: pre !important; word-wrap: normal !important; word-break: normal !important; overflow: auto !important; display: -webkit-box !important;"><span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">1<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">boolean?isPowerOfThree(<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">int?n){
<span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">2????<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">return?(n>0)&&(116261467%n)==0;
<span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">3}
</code></pre>
<h3 id="h1" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; border-bottom: 2px solid rgb(239, 112, 96); font-size: 1.3em;"><span style="font-size: inherit; line-height: inherit; margin: 0px; display: inline-block; font-weight: normal; background: rgb(239, 112, 96); color: rgb(255, 255, 255); padding: 3px 10px 1px; border-top-right-radius: 3px; border-top-left-radius: 3px; margin-right: 3px;">二進(jìn)制1的個(gè)數(shù) </h3>
<h4 id="h-6" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; font-size: 1.2em;">問題</h4>
給定一個(gè)數(shù)字n，求n轉(zhuǎn)換為二進(jìn)制表示中1的個(gè)數(shù)
<h4 id="h-7" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; font-size: 1.2em;">解答</h4>
JDK大法好，直接使用自帶的方法：
<ul style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; padding-left: 32px; list-style-type: disc;">
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">bitCount：返回二進(jìn)制中1的個(gè)數(shù)</li>
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">lowestOneBit：返回二進(jìn)制表示中最低位1的位置</li>
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">highestOneBit：返回二進(jìn)制表示中最高位1的位置</li>
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">numberOfLeadingZeros：返回二進(jìn)制表示中高位0的數(shù)目</li>
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">numberOfTrailingZeros：返回二進(jìn)制表示中低位0的數(shù)目</li>
</ul>
<pre style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px;"><code class="hljs dart" style="overflow-wrap: break-word; margin: 0px 2px; line-height: 18px; font-size: 14px; font-weight: normal; word-spacing: 0px; letter-spacing: 0px; font-family: Consolas, Inconsolata, Courier, monospace; border-radius: 0px; overflow-x: auto; padding: 0.5em; color: rgb(51, 51, 51); background: rgb(248, 248, 248); white-space: pre !important; word-wrap: normal !important; word-break: normal !important; overflow: auto !important; display: -webkit-box !important;"><span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">1?int?bitCount(int?num)?{
<span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">2????????<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">return?Integer.bitCount(num);
<span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">3????}
</code></pre>
或者也可以不使用jdk類庫(kù)的解法
<pre style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px;"><code class="hljs dart" style="overflow-wrap: break-word; margin: 0px 2px; line-height: 18px; font-size: 14px; font-weight: normal; word-spacing: 0px; letter-spacing: 0px; font-family: Consolas, Inconsolata, Courier, monospace; border-radius: 0px; overflow-x: auto; padding: 0.5em; color: rgb(51, 51, 51); background: rgb(248, 248, 248); white-space: pre !important; word-wrap: normal !important; word-break: normal !important; overflow: auto !important; display: -webkit-box !important;"><span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">1int?bitOfOne(int?num)?{
<span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">2????????<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">return?num?==?0???0?:?1?+?bitOfOne(num?&?(num?-?1));
<span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">3????}
</code></pre>
<h3 id="h-8" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; border-bottom: 2px solid rgb(239, 112, 96); font-size: 1.3em;"><span style="font-size: inherit; line-height: inherit; margin: 0px; display: inline-block; font-weight: normal; background: rgb(239, 112, 96); color: rgb(255, 255, 255); padding: 3px 10px 1px; border-top-right-radius: 3px; border-top-left-radius: 3px; margin-right: 3px;">階乘后的零 </h3>
<h4 id="h-9" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; font-size: 1.2em;">問題</h4>
給定一個(gè)數(shù)字n，求n！位數(shù)中的0的個(gè)數(shù)。
<h4 id="h-10" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; font-size: 1.2em;">解答</h4>
這種問題我們要分析0的產(chǎn)生原因，因?yàn)?0=52，對(duì)于一個(gè)n！的數(shù)字而言，末尾為0的數(shù)字即n！的約數(shù)中包含的52的次數(shù)，因?yàn)?的次數(shù)是足夠的，也就是說這道題等價(jià)于求n！中約數(shù)5的個(gè)數(shù)（注意諸如25這種數(shù)字，約數(shù)中包括了2個(gè)5）。
<pre style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px;"><code class="hljs dart" style="overflow-wrap: break-word; margin: 0px 2px; line-height: 18px; font-size: 14px; font-weight: normal; word-spacing: 0px; letter-spacing: 0px; font-family: Consolas, Inconsolata, Courier, monospace; border-radius: 0px; overflow-x: auto; padding: 0.5em; color: rgb(51, 51, 51); background: rgb(248, 248, 248); white-space: pre !important; word-wrap: normal !important; word-break: normal !important; overflow: auto !important; display: -webkit-box !important;"><span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">1int?zeroAtTheEndCount(int?num)?{
<span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">2????????<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">return?num?/?5?+?zeroAtTheEndCount(num?/?5);
<span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">3????}
</code></pre>
<h3 id="h-11" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; border-bottom: 2px solid rgb(239, 112, 96); font-size: 1.3em;"><span style="font-size: inherit; line-height: inherit; margin: 0px; display: inline-block; font-weight: normal; background: rgb(239, 112, 96); color: rgb(255, 255, 255); padding: 3px 10px 1px; border-top-right-radius: 3px; border-top-left-radius: 3px; margin-right: 3px;">熄滅的燈 </h3>
<h4 id="h-12" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; font-size: 1.2em;">問題</h4>
有x個(gè)燈，一個(gè)開關(guān)控制一個(gè)燈，按下開關(guān)會(huì)使燈熄滅或者打開，現(xiàn)在燈都是熄滅的狀態(tài)，我們進(jìn)行n次操作，每次操作都把編號(hào)為i的倍數(shù)的開關(guān)全部按下，即
<ul style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; padding-left: 32px; list-style-type: disc;">
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">將編號(hào)為1的倍數(shù)的開關(guān)全部按下</li>
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">將編號(hào)為2的倍數(shù)的開關(guān)全部按下</li>
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">…</li>
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">將編號(hào)為x的倍數(shù)的開關(guān)全部按下</li>
</ul>
已知燈的總數(shù)為x，求最后燈亮起來狀態(tài)的數(shù)量
<h4 id="h-13" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; font-size: 1.2em;">解答</h4>
首先任意取燈的編號(hào)n，會(huì)有幾次操作會(huì)影響這個(gè)燈的狀態(tài)呢？答案是n的所有約數(shù)的個(gè)數(shù)次。
好比說編號(hào)為12的燈，12的約數(shù)有1，2，3，4，6，12。也就是說編號(hào)為12的燈的狀態(tài)會(huì)被切換6次，分別在第1，2，3，4，6，12次切換開關(guān)的時(shí)候。
那么從下面2種情況考慮：
<ul style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; padding-left: 32px; list-style-type: disc;">
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">假設(shè)n是一個(gè)非完全平方的數(shù)：因?yàn)闉橐粋€(gè)非平方的數(shù)的約數(shù)個(gè)數(shù)為偶數(shù)個(gè)，也就是說會(huì)切換偶數(shù)次狀態(tài)，也就是說狀態(tài)不會(huì)變。</li>
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">假設(shè)n是一個(gè)完全平方數(shù)：完全平方數(shù)的約數(shù)是奇數(shù)個(gè)，其狀態(tài)會(huì)發(fā)生改變。</li>
</ul>
那么按照題目的要求，一開始全是熄滅狀態(tài)的，求亮起來狀態(tài)的燈數(shù)目，就是說求會(huì)發(fā)生變化的編號(hào)的數(shù)目，也就是相當(dāng)于求1～x之間完全平方數(shù)的個(gè)數(shù)。
<pre style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px;"><code class="hljs cpp" style="overflow-wrap: break-word; margin: 0px 2px; line-height: 18px; font-size: 14px; font-weight: normal; word-spacing: 0px; letter-spacing: 0px; font-family: Consolas, Inconsolata, Courier, monospace; border-radius: 0px; overflow-x: auto; padding: 0.5em; color: rgb(51, 51, 51); background: rgb(248, 248, 248); white-space: pre !important; word-wrap: normal !important; word-break: normal !important; overflow: auto !important; display: -webkit-box !important;"><span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">1<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">int?lightCount(<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">int?num)?{
<span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">2????????<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">return?(<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">int)?Math.sqrt(num);
<span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">3????}
</code></pre>
<h3 id="h-14" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; border-bottom: 2px solid rgb(239, 112, 96); font-size: 1.3em;"><span style="font-size: inherit; line-height: inherit; margin: 0px; display: inline-block; font-weight: normal; background: rgb(239, 112, 96); color: rgb(255, 255, 255); padding: 3px 10px 1px; border-top-right-radius: 3px; border-top-left-radius: 3px; margin-right: 3px;">奇怪的數(shù) </h3>
<h4 id="h-15" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; font-size: 1.2em;">問題</h4>
給定一個(gè)非空數(shù)組，其中除了一個(gè)元素只出現(xiàn)一次外，其他元素都出現(xiàn)了兩次，求這個(gè)只出現(xiàn)一次的元素
<h4 id="h-16" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; font-size: 1.2em;">解答</h4>
這里的一個(gè)關(guān)鍵運(yùn)算符是^ 異或運(yùn)算符，主要是利用到了異或運(yùn)算a^b滿足的如下規(guī)律：
<ul style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; padding-left: 32px; list-style-type: disc;">
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">a^b=ba 交換律</li>
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">a^bc=a^(bc)結(jié)合律</li>
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">a^{a=0,同時(shí)0}0=0</li>
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">0^a=a</li>
</ul>
<pre style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px;"><code class="hljs dart" style="overflow-wrap: break-word; margin: 0px 2px; line-height: 18px; font-size: 14px; font-weight: normal; word-spacing: 0px; letter-spacing: 0px; font-family: Consolas, Inconsolata, Courier, monospace; border-radius: 0px; overflow-x: auto; padding: 0.5em; color: rgb(51, 51, 51); background: rgb(248, 248, 248); white-space: pre !important; word-wrap: normal !important; word-break: normal !important; overflow: auto !important; display: -webkit-box !important;"><span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">1int?loseNumber(int[]?num)?{
<span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">2????????<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">return?Arrays.stream(num).reduce(0,?(n1,?n2)?->?n1?^?n2);
<span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">3????}
</code></pre>
<h3 id="h-17" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; border-bottom: 2px solid rgb(239, 112, 96); font-size: 1.3em;"><span style="font-size: inherit; line-height: inherit; margin: 0px; display: inline-block; font-weight: normal; background: rgb(239, 112, 96); color: rgb(255, 255, 255); padding: 3px 10px 1px; border-top-right-radius: 3px; border-top-left-radius: 3px; margin-right: 3px;">約瑟夫環(huán)問題 </h3>
<h4 id="h-18" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; font-size: 1.2em;">問題</h4>
編號(hào)為1-n的n個(gè)戰(zhàn)士圍成一圈，從編號(hào)1的戰(zhàn)士開始依次報(bào)數(shù)，數(shù)到m的戰(zhàn)士會(huì)淘汰，以后的戰(zhàn)士再重新報(bào)數(shù)，直到剩下一個(gè)士兵，求這個(gè)士兵的編號(hào)
<h4 id="h-19" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; font-size: 1.2em;">解答</h4>
<table style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; display: table; width: 100%; text-align: left;">
<thead style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px;">
<tr style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; border-width: 1px 0px 0px; border-right-style: initial; border-bottom-style: initial; border-left-style: initial; border-right-color: initial; border-bottom-color: initial; border-left-color: initial; border-image: initial; border-top-style: solid; border-top-color: rgb(204, 204, 204); background-color: white;">
<th style="color: inherit; line-height: inherit; margin: 0px; font-size: 1em; border: 1px solid rgb(204, 204, 204); padding: 0.5em 1em; text-align: left; font-weight: bold; background-color: rgb(240, 240, 240);">刪除前（old）</th>
<th style="color: inherit; line-height: inherit; margin: 0px; font-size: 1em; border: 1px solid rgb(204, 204, 204); padding: 0.5em 1em; text-align: left; font-weight: bold; background-color: rgb(240, 240, 240);">刪除后（new）</th>
</tr>
</thead>
<tbody style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; border: 0px;">
<tr style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; border-width: 1px 0px 0px; border-right-style: initial; border-bottom-style: initial; border-left-style: initial; border-right-color: initial; border-bottom-color: initial; border-left-color: initial; border-image: initial; border-top-style: solid; border-top-color: rgb(204, 204, 204); background-color: white;">
<td style="color: inherit; line-height: inherit; margin: 0px; font-size: 1em; border: 1px solid rgb(204, 204, 204); padding: 0.5em 1em; text-align: left;">m-2</td>
<td style="color: inherit; line-height: inherit; margin: 0px; font-size: 1em; border: 1px solid rgb(204, 204, 204); padding: 0.5em 1em; text-align: left;">n-2</td>
</tr>
<tr style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; border-width: 1px 0px 0px; border-right-style: initial; border-bottom-style: initial; border-left-style: initial; border-right-color: initial; border-bottom-color: initial; border-left-color: initial; border-image: initial; border-top-style: solid; border-top-color: rgb(204, 204, 204); background-color: rgb(248, 248, 248);">
<td style="color: inherit; line-height: inherit; margin: 0px; font-size: 1em; border: 1px solid rgb(204, 204, 204); padding: 0.5em 1em; text-align: left;">m-1</td>
<td style="color: inherit; line-height: inherit; margin: 0px; font-size: 1em; border: 1px solid rgb(204, 204, 204); padding: 0.5em 1em; text-align: left;">n-1</td>
</tr>
<tr style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; border-width: 1px 0px 0px; border-right-style: initial; border-bottom-style: initial; border-left-style: initial; border-right-color: initial; border-bottom-color: initial; border-left-color: initial; border-image: initial; border-top-style: solid; border-top-color: rgb(204, 204, 204); background-color: white;">
<td style="color: inherit; line-height: inherit; margin: 0px; font-size: 1em; border: 1px solid rgb(204, 204, 204); padding: 0.5em 1em; text-align: left;">m</td>
<td style="color: inherit; line-height: inherit; margin: 0px; font-size: 1em; border: 1px solid rgb(204, 204, 204); padding: 0.5em 1em; text-align: left;">無</td>
</tr>
<tr style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; border-width: 1px 0px 0px; border-right-style: initial; border-bottom-style: initial; border-left-style: initial; border-right-color: initial; border-bottom-color: initial; border-left-color: initial; border-image: initial; border-top-style: solid; border-top-color: rgb(204, 204, 204); background-color: rgb(248, 248, 248);">
<td style="color: inherit; line-height: inherit; margin: 0px; font-size: 1em; border: 1px solid rgb(204, 204, 204); padding: 0.5em 1em; text-align: left;">m+1</td>
<td style="color: inherit; line-height: inherit; margin: 0px; font-size: 1em; border: 1px solid rgb(204, 204, 204); padding: 0.5em 1em; text-align: left;">1</td>
</tr>
<tr style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; border-width: 1px 0px 0px; border-right-style: initial; border-bottom-style: initial; border-left-style: initial; border-right-color: initial; border-bottom-color: initial; border-left-color: initial; border-image: initial; border-top-style: solid; border-top-color: rgb(204, 204, 204); background-color: white;">
<td style="color: inherit; line-height: inherit; margin: 0px; font-size: 1em; border: 1px solid rgb(204, 204, 204); padding: 0.5em 1em; text-align: left;">m+2</td>
<td style="color: inherit; line-height: inherit; margin: 0px; font-size: 1em; border: 1px solid rgb(204, 204, 204); padding: 0.5em 1em; text-align: left;">2</td>
</tr>
</tbody>
</table>
<ul style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; padding-left: 32px; list-style-type: disc;">
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">假設(shè)old為刪除前的節(jié)點(diǎn)編號(hào)，new為刪除后的節(jié)點(diǎn)編號(hào)</li>
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">- 關(guān)系：old=(new+m-1)%n+1</li>
</ul>
<blockquote style="line-height: inherit; display: block; padding: 15px 15px 15px 1rem; font-size: 0.9em; margin: 1em 0px; color: rgb(0, 0, 0); border-left: 5px solid rgb(239, 112, 96); background: rgb(239, 235, 233); overflow: auto; overflow-wrap: normal; word-break: normal;">
注意：并不是old=(new+m)%n，因?yàn)榫幪?hào)是從1開始的而不是從0 開始的，如果new+m==n的話，會(huì)導(dǎo)致最后的計(jì)算結(jié)果old=0.
</blockquote>
<pre style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px;"><code class="hljs cpp" style="overflow-wrap: break-word; margin: 0px 2px; line-height: 18px; font-size: 14px; font-weight: normal; word-spacing: 0px; letter-spacing: 0px; font-family: Consolas, Inconsolata, Courier, monospace; border-radius: 0px; overflow-x: auto; padding: 0.5em; color: rgb(51, 51, 51); background: rgb(248, 248, 248); white-space: pre !important; word-wrap: normal !important; word-break: normal !important; overflow: auto !important; display: -webkit-box !important;"><span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">1<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">int?f(<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">int?n,<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">int?m){
<span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">2????<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">if(n==1)?
<span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">3????????<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">return?n;
<span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">4????<span class="hljs-keyword" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(51, 51, 51); font-weight: bold; word-wrap: inherit !important; word-break: inherit !important;">return?(f(n-1,m)+m-1)%n+1;
<span class="linenum hljs-number" style="font-size: inherit; line-height: inherit; margin: 0px; padding: 0px; color: rgb(0, 128, 128); padding-right: 20px; word-spacing: 0px; word-wrap: inherit !important; word-break: inherit !important;">5}
</code></pre>
<h3 id="h-20" style="color: inherit; line-height: inherit; padding: 0px; margin: 1.6em 0px; font-weight: bold; border-bottom: 2px solid rgb(239, 112, 96); font-size: 1.3em;"><span style="font-size: inherit; line-height: inherit; margin: 0px; display: inline-block; font-weight: normal; background: rgb(239, 112, 96); color: rgb(255, 255, 255); padding: 3px 10px 1px; border-top-right-radius: 3px; border-top-left-radius: 3px; margin-right: 3px;">最后 </h3>
<ul style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; padding-left: 32px; list-style-type: disc;">
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">如果覺得看完有收獲，希望能關(guān)注一下，順便給我點(diǎn)個(gè)贊，這將會(huì)是我更新的最大動(dòng)力，感謝各位的支持</li>
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">歡迎各位關(guān)注我的公眾號(hào)【java冢狐】，專注于java和計(jì)算機(jī)基礎(chǔ)知識(shí)，保證讓你看完有所收獲，不信你打我</li>
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">求一鍵三連：點(diǎn)贊、轉(zhuǎn)發(fā)、在看。</li>
<li style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px; margin-bottom: 0.5em;">如果看完有不同的意見或者建議，歡迎多多評(píng)論一起交流。感謝各位的支持以及厚愛。</li>
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<figure style="font-size: inherit; color: inherit; line-height: inherit; margin: 0px; padding: 0px;"><img src="https://cdn.nlark.com/yuque/0/2020/jpeg/677480/1602294384027-9449b36e-c1e7-4dc4-9251-ba59be6e4157.jpeg" alt="image" title="image" style="font-size: inherit; color: inherit; line-height: inherit; padding: 0px; display: block; margin: 0px auto; max-width: 100%;"><figcaption style="line-height: inherit; margin: 0px; padding: 0px; margin-top: 10px; text-align: center; color: rgb(153, 153, 153); font-size: 0.7em;">image</figcaption></figure></div>

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思維私塾——一行代碼解決算法

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