看动画学算法之:排序-快速排序

{"type":"doc","content":[{"type":"heading","attrs":{"align":null,"level":1},"content":[{"type":"text","text":"简介"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"快速排序也采用的是分而制之的思想。那么快速排序和归并排序的区别在什么地方呢？"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"归并排序是将所有的元素拆分成一个个排好序的数组，然后将这些数组再进行合并。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"而快速排序虽然也是拆分，但是拆分之后的操作是从数组中选出一个中间节点，然后将数组分成两部分。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"左边的部分小于中间节点，右边的部分大于中间节点。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"然后再分别处理左边的数组合右边的数组。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"heading","attrs":{"align":null,"level":1},"content":[{"type":"text","text":"快速排序的例子"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"假如我们有一个数组：29,10,14,37,20,25,44,15，怎么对它进行快速排序呢？"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"先看一个动画："}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/16/16cee42670c0457ac833d6205ec4824f.gif","alt":"","title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们再分析一下快速排序的步骤。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们选择的是最左边的元素29作为中间点元素，然后将数组分成三部分：[0, 14, 15, 20, 25],[29],[44, 37]。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"中间节点29已经排好序了，不需要处理。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"接下来我们再对左右分别进行快速排序。最后就得到了一个所有元素都排序的数组。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"heading","attrs":{"align":null,"level":1},"content":[{"type":"text","text":"快速排序的java代码实现"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们先来看最核心的部分partition，如何将数组以中间节点为界，分成左右两部分呢？"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们的最终结果，是要将array分割成为三部分。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"首先我们选择最左侧的元素作为中间节点的值。然后遍历数组中的其他元素。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"假如m=middleIndex，k=要遍历的元素index"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"考虑两种情况，第一种情况是数组中的元素比中间节点的值要大。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/4e/4e061e7201da99386d669bac6c087eed.png","alt":"","title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这种情况下，m不需要移动，k+1继续遍历即可。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"第二种情况下，数组中的元素比中间节点的值要小。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/36/36bdd008130321a5a3591743d72f5f03.png","alt":"","title":null,"style":null,"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"因为m左边的元素都要比中间节点的值要小，所以这种情况下m需要+1，即右移一位。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"现在m+1位置的元素要么还没有进行比较，要么就是比中间节点的值要大，我们可以巧妙的将m+1位置的元素和k位置的元素互换位置，这样仍然能够保证m左侧的元素要比中间节点的值要小。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"将上面的分析总结成java代码如下："}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"codeblock","attrs":{"lang":null},"content":[{"type":"text","text":" private int partition(int[] array, int i, int j) {\n //选择最左侧的元素作为中心点,middleValue就是中心点的值\n int middleValue = array[i];\n int middleIndex = i;\n //从i+1遍历整个数组\n for (int k = i+1; k <= j; k++) {\n //如果数组元素小于middleValue，表示middleIndex需要右移一位\n //右移之后，我们需要将小于middleValue的array[k]移动到middleIndex的左边，\n // 最简单的办法就是交换k和middleIndex的值\n if (array[k] < middleValue) {\n middleIndex++;\n //交换数组的两个元素\n swap(array, k , middleIndex);\n } //如果数组元素大于等于middleValue,则继续向后遍历,middleIndex值不变\n }\n // 最后将中心点放入middleIndex位置\n swap(array, i, middleIndex);\n return middleIndex;\n }\n"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"最后我们需要将最左侧的元素和中间节点应该在的index的元素互换下位置，这样就将中间节点移动到了中间位置，并返回中间位置。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"再来看下divide的代码："}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"codeblock","attrs":{"lang":null},"content":[{"type":"text","text":" public void doQuickSort(int[] array, int low, int high) {\n //递归的结束条件\n if (low < high) {\n //找出中心节点的值\n int middleIndex = partition(array, low, high);\n //数组分成了三部分：\n // a[low..high] ~> a[low..m–1], pivot, a[m+1..high]\n //递归遍历左侧部分\n doQuickSort(array, low, middleIndex-1);\n // a[m] 是中心节点，已经排好序了，不需要继续遍历\n //递归遍历右侧部分\n doQuickSort(array, middleIndex+1, high);\n log.info(\"QuickSort之后的数组:{}\",array);\n }\n }\n"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"divide的代码就很简单了，找到中间节点的位置之后，我们再分别遍历数组的左右两边即可。最后得到排好序的数组。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"heading","attrs":{"align":null,"level":1},"content":[{"type":"text","text":"随机快速排序的java实现"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面的例子中，我们的中间节点的选择是数组的最左元素，为了保证排序的效率，我们可以从数组中随机选择一个元素来作为中间节点。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"codeblock","attrs":{"lang":null},"content":[{"type":"text","text":" private int partition(int[] array, int i, int j) {\n //随机选择一个元素作为中心点,middleValue就是中心点的值\n int randomIndex=i+new Random().nextInt(j-i);\n log.info(\"randomIndex:{}\",randomIndex);\n //首先将randomIndex的值和i互换位置,就可以复用QuickSort的逻辑\n swap(array, i , randomIndex);\n int middleValue = array[i];\n int middleIndex = i;\n //从i遍历整个数组\n for (int k = i+1; k <= j; k++) {\n //如果数组元素小于middleValue，表示middleIndex需要右移一位\n //右移之后，我们需要将小于middleValue的array[k]移动到middleIndex的左边，\n // 最简单的办法就是交换k和middleIndex的值\n if (array[k] < middleValue) {\n middleIndex++;\n //交换数组的两个元素\n swap(array, k , middleIndex);\n } //如果数组元素大于等于middleValue,则继续向后遍历,middleIndex值不变\n }\n // 最后将中心点放入middleIndex位置\n swap(array, i, middleIndex);\n return middleIndex;\n }\n"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"上面的代码，我们在分区的时候，先选择出一个随机的节点，然后将这个随机的节点和最左侧的元素交换位置，后面的代码就可以重用上面的QuickSort的代码逻辑了。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"heading","attrs":{"align":null,"level":1},"content":[{"type":"text","text":"快速排序的时间复杂度"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"从上面的分析我们可以看出，每次分区的时间复杂度应该是O(N)，而divide又近似二分法，所以总的时间复杂度是O(N logN)。"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"本文的代码地址："}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"link","attrs":{"href":"https://github.com/ddean2009/learn-algorithm/tree/master/sorting","title":null},"content":[{"type":"text","text":"learn-algorithm"}]}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"blockquote","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"italic"}],"text":"本文作者：flydean程序那些事"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"italic"}],"text":"本文链接："},{"type":"link","attrs":{"href":"http://www.flydean.com/algorithm-quick-sort/","title":null},"content":[{"type":"text","text":"http://www.flydean.com/algorithm-quick-sort/"}],"marks":[{"type":"italic"}]}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"italic"}],"text":"本文来源：flydean的博客"}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","marks":[{"type":"italic"}],"text":"欢迎关注我的公众号:程序那些事，更多精彩等着您！"}]}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}}]}