数据结构中的7种排序算法

数据结构中的7种排序算法

排序是将一个记录的任意序列重新排列成一个按键值有序的序列。 

时间复杂度主要考虑元素的移动次数。 

结构如下： 

1.直接插入排序

1，定义：依次将待排序序列中的每一个记录插入到一个已经排好序的序列中，直到全部记录都排好序。 

2，时间复杂度：在最好情况下，待排序序列为正序，时间复杂度为O(n)；最坏情况下，待排序序列为逆序，时间复杂度为O(n^2);平均情况下，时间复杂度为O(n^2)。 

3，空间复杂度：O(1)。

<code class="hljs cs 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;">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;">insertSort</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span>[] nums){<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//直接插入排序</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> i=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;i<nums.length;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=i;j><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;j--){
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(nums[j]<nums[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;">int</span> temp=nums[j];
nums[j]=nums[j-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>];
nums[j-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>]=temp;
}

}

System.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">out</span>.print(i+<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">":"</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> a:nums)
System.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">out</span>.print(a+<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">" "</span>);
System.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">out</span>.println();
}

}</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; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li></ul>

示例数组：{12,5,9,20,6,31,24} 
结果：

2.希尔排序

1，希尔排序是对直接插入排序的改进。 

2，定义：先将整个待排序序列记录序列分割为若干个子序列，在子序列内分别进行直接插入排序，待整个序列中的记录基本有序时，再对全体记录进行一次直接插入排序。 

3，时间复杂度：O（nlogn）~O(n^2)。 

4，空间复杂度：O(1).

<code class="hljs cs 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;">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;">shellSort</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span>[] nums){<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//希尔排序</span>

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> d=nums.length/<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>;<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//增量大小</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">while</span>(d><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> k=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//控制量</span>
<span class="hljs-keyword" styl
17af5
e="color: rgb(0, 0, 136); box-sizing: border-box;">while</span>(k<d){

<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//进行直接插入排序</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> i=k;i<nums.length;i=i+d){
<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=i;j><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>&&j-d>=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;j=j-d){
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(nums[j]<nums[j-d]){
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> temp=nums[j];
nums[j]=nums[j-d];
nums[j-d]=temp;
}
}
}

k++;<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//控制量增加</span>

}<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//while</span>

System.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">out</span>.print(d+<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">":"</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> a:nums)
System.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">out</span>.print(a+<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">" "</span>);
System.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">out</span>.println();

d=d/<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>;

}<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//while</span>
}</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; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li></ul>

示例数组：{12,5,9,20,6,31,24} 
结果：

3.冒泡排序

1，定义：两两比较相邻记录的关键码，如果是反序则交换，直到没有反序的记录为止。 

2，时间复杂度:在最好情况下，待排序序列为正序。其时间复杂度为O(n);在最坏情况下，待排序序列为逆序，时间复杂度为O(n^2)，平均时间复杂度为O(n^2). 

3，空间复杂度：O(1)。

<code class="hljs cs 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;">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;">bubbleSort</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span>[] nums){<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//冒泡排序</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> i=nums.length-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;i><span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;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;">0</span>;j<i;j++){
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(nums[j]>nums[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;">int</span> temp=nums[j];
nums[j]=nums[j+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>];
nums[j+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>]=temp;
}
}
System.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">out</span>.print(nums.length-i+<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">":"</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> a:nums)
System.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">out</span>.print(a+<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">" "</span>);
System.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">out</span>.println();
}

}
</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; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li></ul>

示例数组：{12,5,9,20,6,31,24} 
结果：

4.快速排序

1，快速排序是对冒泡排序的改进。 

2，定义：首先选一个轴值，将待排序记录分割成独立的两部分，左侧记录的关键字均小于或者等于轴值，右边记录的关键字均大于或者等于轴值，然后分别对这两部分重复上述过程，直到整个序列有序。 

3，在最好情况下，每次划分轴值的左侧子序列与右侧子序列的长度相同，时间复杂度为O(nlogn),在最坏情况下，待排序序列为正序或逆序，时间复杂度为O(n^2)；平均情况下，时间复杂度为O(nlogn)。 

4,空间复杂度：O(logn)。

<code class="hljs cs 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;">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;">quickSort</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span>[] nums,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> low ,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> high){<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//快速排序</span>

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(low<high) {
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> dp=partition(nums,low,high);
quickSort(nums,low,dp-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>);
quickSort(nums,dp+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,high);

}<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</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;">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;">int</span> <span class="hljs-title" style="box-sizing: border-box;">partition</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span>[] nums,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> low ,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> high){

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> pivot=nums[low];
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">while</span>(low<high){

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">while</span>(low < high && nums[high]>=pivot)
high--;
nums[low]=nums[high];

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">while</span>(low < high && nums[low]<=pivot)
low++;

nums[high]=nums[low];

}
nums[low]=pivot;<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//此时low等于high，所以，也可以写成nums[high]=pivot;</span>

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> low; <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//此时low等于high，所以返回任意一个都是正确的 </span>
}</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; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li></ul>

示例数组：{12,5,9,20,6,31,24} 
结果：

5.简单选择排序

1，定义：第i趟通过n-i次关键码的比较，在n-i-1(1<=i<=n-1)个记录中选取关键码最小的记录，并和第i个记录交换作为有序序列的第i个记录。 

2，时间复杂度：最好，最坏，平均的时间复杂度都是O(n^2)。 

3，空间复杂度：O(1)。

<code class="hljs cs 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;">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;">selectSort</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span>[] nums){<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//简单选择排序</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> i=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;i<nums.length-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;i++){
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> sIndex=i;<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//最小数下标</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> sNum=nums[i];<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//最小数大小        </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=i+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;j<nums.length;j++){
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(nums[j]<sNum){
sIndex=j;
sNum=nums[j];
}

}
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//交换</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> temp=nums[i];
nums[i]=nums[sIndex];
nums[sIndex]=temp;

System.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">out</span>.print(i+<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>+<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">":"</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> a:nums)
System.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">out</span>.print(a+<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">" "</span>);
System.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">out</span>.println();

}
}
</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; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li></ul>

示例数组：{12,5,9,20,6,31,24} 
结果：

6.堆排序

1，堆排序是对简单选择排序的改进。 

2，首先将待排序的记录序列构造成一个堆，此时，选出了堆中所有记录的最大者即堆顶记录，然后将他从堆中移走，并将剩下的记录再调整成堆，这样又找出了次大的记录，以此类推，直到堆中只有一个记录为止。 

3，时间复杂度：最好，最坏，平均的时间复杂度都是O(nlogn)。 

4，空间复杂度：O(nlogn)。

<code class="hljs cs 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;">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;">heapSort</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span>[] nums) {<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//堆排序</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (nums == <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">null</span> || nums.length <= <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;">return</span>;
}

buildMaxHeap(nums);<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//调用建立堆的函数</span>

<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//将堆顶元素调整至数组最后，然后，将当前堆继续调整为大顶堆</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> i = nums.length - <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; i >= <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; i--) {

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> temp=nums[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>];
nums[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>]=nums[i];
nums[i]=temp;

maxHeap(nums, i, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);

System.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">out</span>.print(nums.length-i+<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">":"</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> a:nums)
System.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">out</span>.print(a+<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">" "</span>);
System.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">out</span>.println();
}
}

<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;">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;">buildMaxHeap</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span>[] nums) {<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//建立堆</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (nums == <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">null</span> || nums.length <= <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;">return</span>;
}

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> half = nums.length / <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</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> i = half; i >= <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>; i--) {
maxHeap(nums, nums.length, i);
}
}

<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;">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;">maxHeap</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span>[] nums, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> heapSize, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> index) {<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//递归调整为大顶堆</span>

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> left = index * <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span> + <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;">int</span> right = index * <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span> + <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>;

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>( left > heapSize && right > heapSize ){
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//没有这个return，也是正确的，好吧!我没有看懂~</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;">int</span> largest = index;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (left < heapSize && nums[left] > nums[index]) {
largest = left;
}

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (right < heapSize && nums[right] >nums[largest]) {
largest = right;
}

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (index != largest) {
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> temp=nums[index];
nums[index]=nums[largest];
nums[largest]=temp;

maxHeap(nums, heapSize, largest);
}

}</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; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li></ul>

示例数组：{12,5,9,20,6,31,24} 
结果：

 
代码参考链接

7.二路归并排序

1，定义：将若干个有序序列进行两两归并，直至所有待排记录都在一个有序序列为止。 

2，时间复杂度：最好，最坏，平均都是O(nlogn)。 

3，空间复杂度：O(n)。

<code class="hljs cs 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;">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;">mergeSort</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span>[] a, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> left, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> right) {

<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(left<right){

<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//int center = (left + right) >> 1;</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> center=(left+right)/<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">2</span>;
mergeSort(a, left, center);
mergeSort(a, center + <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>, right);
merge(a, left, center, right);
}<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</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;">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;">merge</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span>[] data, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> left, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> center, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> right) {
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span>[] tmpArr = <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>[right+<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;">int</span> mid = center + <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;">int</span> index = left; <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// index记录临时数组的索引</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> tmp = left;

<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 从两个数组中取出最小的放入中临时数组</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">while</span> (left <= center && mid <= right) {
tmpArr[index++] = (data[left] <= data[mid]) ? data[left++]: data[mid++];
}
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 剩余部分依次放入临时数组</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">while</span> (mid <= right) {
tmpArr[index++] = data[mid++];
}
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">while</span> (left <= center) {
tmpArr[index++] = data[left++];
}
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">// 将临时数组中的内容复制回原数组</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> i = tmp; i <= right; i++) {
data[i] = tmpArr[i];
}
System.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">out</span>.println(Arrays.toString(data));
}

<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) {
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span>[] arr={<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">12</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">5</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">9</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">20</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">6</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">31</span>,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">24</span>};
mergeSort(arr, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>, arr.length-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>);
}
</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; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li></ul>

示例数组：{12,5,9,20,6,31,24} 
结果：

 
代码参考链接