> For the complete documentation index, see [llms.txt](https://xyy94813.gitbook.io/x-note/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://xyy94813.gitbook.io/x-note/ji-chu-suan-fa/quick-sort.md).

# 快速排序

\*\*快速排序（Quick Sort）**又称为**划分交换排序（partition-exchange sort）\*\*是一种有效率的排序算法。

* 平均时间复杂度：$$O({n}\log\_{2}{n})$$
* 最好时间复杂度：$$O({n}\log\_{2}{n})$$
* 最坏时间复杂度：$$O(n^2)$$
* 空间复杂度：根据实现方式不同为 $$O(n)$$ 或 $$O(\log\_{2}{n})$$
* 稳定性：不稳定
* 排序方式：原地（In-place）

步骤：

1. 从序列中挑出一个元素作为**基准（Pivot）**，一般选取序列中的第一个；
2. 从后向前遍历剩余元素，找到第一个比基准小的元素的索引；
3. 从前向后遍历剩余元素，找到第一个比基准数大的元素的索引；
4. 交换两个元素；
5. 重复 2\~4，直到从后向前的游标和从前向后的游标重叠；
6. 交换基准与当前两个游标重叠的位置的元素，此时，所有比基准值小的元素放在基准前面，所有比基准大的放在基准后面（相同的可放在前面或后面）；
7. 划分结束后，以基准所在位置划分左右两个分区；
8. 对新划分的分区执行 1\~5，直到无法划分分区。

可以简单理解为，从每个的分区中，取一个基准值，然后找到这个基准值所在的位置。

![](https://upload.wikimedia.org/wikipedia/commons/6/6a/Sorting_quicksort_anim.gif)

递归实现：

```js
function swap(arr, i, j) {
  let tmp = arr[i];
  arr[i] = arr[j];
  arr[j] = tmp;
}

function quickSort(arr, left, right) {
  const len = arr.length;
  if (left > right) {
    return arr;
  }
  let pivot = arr[left];
  let i = left;
  let j = right;
  while (i != j) {
    while (arr[j] >= pivot && i < j) {
      j--;
    }
    while (arr[i] <= pivot && i < j) {
      i++;
    }
    if (i < j && arr[i] !== arr[j]) {
      swap(arr, i, j);
    }
  }

  if (left !== i && arr[left] !== arr[i]) {
    swap(arr, left, i);
  }

  quickSort(arr, left, i - 1);
  quickSort(arr, i + 1, right);

  return arr;
}

let arr = [3, 7, 8, 5, 2, 1, 9, 5, 4];
quickSort(arr, 0, arr.length - 1); // [1, 2, 3, 4, 5, 5, 7, 8, 9]
```

非递归实现：

```js
function swap(arr, i, j) {
  let tmp = arr[i];
  arr[i] = arr[j];
  arr[j] = tmp;
}
const quickSort = (arr) => {
  const stack = [0, arr.length - 1];

  while (stack.length > 0) {
    const left = stack.pop();
    const right = stack.pop();

    if (left >= right) {
      continue;
    }

    let i = left;
    let j = right;
    let p = arr[left];
    while (i < j) {
      while (i < j && arr[j] >= p) {
        j--;
      }
      while (i < j && arr[i] <= p) {
        i++;
      }
      if (i !== j && arr[i] !== arr[j]) {
        swap(arr, i, j);
      }
    }
    stack.push(left, i - 1);
    stack.push(i + 1, right);
  }
  return arr;
};

let arr = [3, 7, 8, 5, 2, 1, 9, 5, 4];
quickSort(arr, 0, arr.length - 1); // [1, 2, 3, 4, 5, 5, 7, 8, 9]
```


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