华为上机 亮灯的个数 java

一条长廊里依次装有n(1 ≤ n ≤ 65535)盏电灯，从头到尾编号1、2、3、…n-1、n。每盏电灯由一个拉线开关控制。开始，电灯全部关着。
有n个学生从长廊穿过。第一个学生把号码凡是1的倍数的电灯的开关拉一下；接着第二个学生把号码凡是2的倍数的电灯的开关拉一下；接着第三个学生把号码凡是3的倍数的电灯的开关拉一下；如此继续下去，最后第n个学生把号码凡是n的倍数的电灯的开关拉一下。n个学生按此规定走完后，长廊里电灯有几盏亮着。
注：电灯数和学生数一致。

<code class="hljs java has-numbering" style="display: block; padding: 0px; background-color: transparent; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; word-wrap: normal; background-position: initial initial; background-repeat: initial initial;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> java.util.Scanner;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">public</span> <span class="hljs-class" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">class</span> <span class="hljs-title" style="box-sizing: border-box; color: rgb(102, 0, 102);">Main</span> {</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> n;<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">private</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">boolean</span>[] lights;    <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/**     * 输入     */</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">public</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">void</span> <span class="hljs-title" style="box-sizing: border-box;">input</span>() {        Scanner sc = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> Scanner(System.in);        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">try</span> {            n = sc.nextInt();        } <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">catch</span> (Exception e) {            n = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;        } <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">finally</span> {            sc.close();        }    }    <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/**     * 解法一：循环次数n^2,时间复杂度是O(n^2)     */</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">public</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">void</span> <span class="hljs-title" style="box-sizing: border-box;">turnOnOff</span>() {        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (n < <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span> || n > <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">65535</span>) {            <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span>;        }        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">long</span> time1 = System.currentTimeMillis();        lights = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">boolean</span>[n];        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> (<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> i = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; i <= n; i++) {            <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> (<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> j = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; j <= n; j++) {                <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (j % i == <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>) {                    lights[j - <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>] = lights[j - <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>] ? <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">false</span> : <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">true</span>;                }            }        }        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> count = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> (<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> j = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; j <= n; j++) {            <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (lights[j - <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>]) {                count++;            }        }        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">long</span> time2 = System.currentTimeMillis();        System.out.println(count + <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">" 用时："</span> + (time2 - time1));    }    <span class="hljs-javadoc" style="color: rgb(136, 0, 0); box-sizing: border-box;">/**     * 解法二：循环次数n(n+1)/2，虽然也是O(n^2)数量级，但是循环次数有所减少，效率得到提升     */</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">public</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">void</span> <span class="hljs-title" style="box-sizing: border-box;">turnOnOff2</span>() {        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (n < <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span> || n > <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">65535</span>) {            <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span>;        }        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">long</span> time1 = System.currentTimeMillis();        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> onNum = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span>[] lights = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span>[n];        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> (<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> i = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; i <= n; i++) {            <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> (<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> j = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; j <= i; j++) {                <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (i % j == <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>) {                    lights[i - <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>]++;                }            }            <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> ((lights[i - <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>] & <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>) == <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>) {                onNum++;            }        }        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">long</span> time2 = System.currentTimeMillis();        System.out.println(onNum + <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">" 用时："</span> + (time2 - time1));    }    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">public</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">static</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">void</span> <span class="hljs-title" style="box-sizing: border-box;">main</span>(String[] args) {        Main m = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">new</span> Main();        m.input();        m.turnOnOff();    }}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; background-color: rgb(238, 238, 238); top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right;"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; 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• 解法一的思路：

以学生为中心，将学生遍历一遍，每一遍都要判断这个学生会开关哪些灯，学生遍历完以后，灯的最终状态就确定了。

• 解法二思路：

以灯为中心，将灯遍历一遍，每一遍都判断这个灯会被开关几次。只要学生的编号能整除灯的编号，这个学生就会开关灯一次，所以只要判断这个灯的序号能被哪些数整除（包括1和自身），就能知道这个灯会被开关几次，如果开关的次数是奇数，则最终是亮着的，如果开关次数为偶数，则最终是熄灭的。