介绍

桶排序（Bucket sort）或所谓的箱排序，是一个排序算法，工作的原理是将数组分到有限数量的桶里。每个桶再个别排序（有可能再使用别的排序算法或是以递归方式继续使用桶排序进行排序）。桶排序是 鸽巢排序 的一种归纳结果。当要被排序的数组内的数值是均匀分配的时候，桶排序使用线性时间（${\Theta (n)}$）。但桶排序并不是比较排序，他不受到${O(n\log n)}$ 下限的影响。

原理

桶排序以下列程序进行：

• 设置一个定量的数组当作空桶。
• 寻访序列，并且把项目一个一个放到对应的桶子去。

• 对每个不是空的桶子进行排序。
• 从非空的桶里把项目再放回原来的序列中。

伪代码

function bucket-sort(array, n) is
  buckets ← new array of n empty lists
  for i = 0 to (length(array)-1) do
    insert array[i] into buckets[msbits(array[i], k)]
  for i = 0 to n - 1 do
    next-sort(buckets[i])
  return the concatenation of buckets[0], ..., buckets[n-1]

动画

实现

JavaScript

/**
 * BucketSort implementation.
 *
 * Wikipedia says: Bucket sort, or bin sort, is a sorting algorithm that works by distributing the elements of an array
 * into a number of buckets. Each bucket is then sorted individually, either using a different sorting algorithm, or by
 * recursively applying the bucket sorting algorithm. It is a distribution sort, and is a cousin of radix sort in the
 * most to least significant digit flavour. Bucket sort is a generalization of pigeonhole sort. Bucket sort can be
 * implemented with comparisons and therefore can also be considered a comparison sort algorithm. The computational
 * complexity estimates involve the number of buckets.
 *
 * @see https://en.wikipedia.org/wiki/Bucket_sort#:~:text=Bucket%20sort%2C%20or%20bin%20sort,applying%20the%20bucket%20sorting%20algorithm.&text=Sort%20each%20non%2Dempty%20bucket.
 *
 * Time Complexity of Solution:
 * Best Case O(n); Average Case O(n); Worst Case O(n)
 *
 * @param {number[]} list The array of numbers to be sorted.
 * @param {number} size The size of the buckets used. If not provided, size will be 5.
 * @return {number[]} An array of numbers sorted in increasing order.
 */
export function bucketSort (list, size) {
  if (undefined === size) {
    size = 5
  }
  if (list.length === 0) {
    return list
  }
  let min = list[0]
  let max = list[0]
  // find min and max
  for (let iList = 0; iList < list.length; iList++) {
    if (list[iList] < min) {
      min = list[iList]
    } else if (list[iList] > max) {
      max = list[iList]
    }
  }
  // how many buckets we need
  const count = Math.floor((max - min) / size) + 1

  // create buckets
  const buckets = []
  for (let iCount = 0; iCount < count; iCount++) {
    buckets.push([])
  }

  // bucket fill
  for (let iBucket = 0; iBucket < list.length; iBucket++) {
    const key = Math.floor((list[iBucket] - min) / size)
    buckets[key].push(list[iBucket])
  }
  const sorted = []
  // now sort every bucket and merge it to the sorted list
  for (let iBucket = 0; iBucket < buckets.length; iBucket++) {
    const arr = buckets[iBucket].sort((a, b) => a - b)
    for (let iSorted = 0; iSorted < arr.length; iSorted++) {
      sorted.push(arr[iSorted])
    }
  }
  return sorted
}

参考

• 桶排序 - 维基百科，自由的百科全书 (opens new window)