桶排序是計數(shù)排序的升級版。它利用了函數(shù)的映射關(guān)系,高效與否的關(guān)鍵就在于這個映射函數(shù)的確定。為了使桶排序更加高效,我們需要做到這兩點:
- 在額外空間充足的情況下,盡量增大桶的數(shù)量
- 使用的映射函數(shù)能夠?qū)⑤斎氲?N 個數(shù)據(jù)均勻的分配到 K 個桶中
同時,對于桶中元素的排序,選擇何種比較排序算法對于性能的影響至關(guān)重要。
1. 什么時候最快
當輸入的數(shù)據(jù)可以均勻的分配到每一個桶中。
2. 什么時候最慢
當輸入的數(shù)據(jù)被分配到了同一個桶中。
3. 示意圖
元素分布在桶中:
然后,元素在每個桶中排序:
代碼實現(xiàn)
JavaScript
實例
if (arr.length === 0) {
return arr;
}
var i;
var minValue = arr[0];
var maxValue = arr[0];
for (i = 1; i < arr.length; i++) {
if (arr[i] < minValue) {
minValue = arr[i]; // 輸入數(shù)據(jù)的最小值
} else if (arr[i] > maxValue) {
maxValue = arr[i]; // 輸入數(shù)據(jù)的最大值
}
}
//桶的初始化
var DEFAULT_BUCKET_SIZE = 5; // 設(shè)置桶的默認數(shù)量為5
bucketSize = bucketSize || DEFAULT_BUCKET_SIZE;
var bucketCount = Math.floor((maxValue – minValue) / bucketSize) + 1;
var buckets = new Array(bucketCount);
for (i = 0; i < buckets.length; i++) {
buckets[i] = [];
}
//利用映射函數(shù)將數(shù)據(jù)分配到各個桶中
for (i = 0; i < arr.length; i++) {
buckets[Math.floor((arr[i] – minValue) / bucketSize)].push(arr[i]);
}
arr.length = 0;
for (i = 0; i < buckets.length; i++) {
insertionSort(buckets[i]); // 對每個桶進行排序,這里使用了插入排序
for (var j = 0; j < buckets[i].length; j++) {
arr.push(buckets[i][j]);
}
}
return arr;
}
Java
實例
private static final InsertSort insertSort = new InsertSort();
@Override
public int[] sort(int[] sourceArray) throws Exception {
// 對 arr 進行拷貝,不改變參數(shù)內(nèi)容
int[] arr = Arrays.copyOf(sourceArray, sourceArray.length);
return bucketSort(arr, 5);
}
private int[] bucketSort(int[] arr, int bucketSize) throws Exception {
if (arr.length == 0) {
return arr;
}
int minValue = arr[0];
int maxValue = arr[0];
for (int value : arr) {
if (value < minValue) {
minValue = value;
} else if (value > maxValue) {
maxValue = value;
}
}
int bucketCount = (int) Math.floor((maxValue – minValue) / bucketSize) + 1;
int[][] buckets = new int[bucketCount][0];
// 利用映射函數(shù)將數(shù)據(jù)分配到各個桶中
for (int i = 0; i < arr.length; i++) {
int index = (int) Math.floor((arr[i] – minValue) / bucketSize);
buckets[index] = arrAppend(buckets[index], arr[i]);
}
int arrIndex = 0;
for (int[] bucket : buckets) {
if (bucket.length <= 0) {
continue;
}
// 對每個桶進行排序,這里使用了插入排序
bucket = insertSort.sort(bucket);
for (int value : bucket) {
arr[arrIndex++] = value;
}
}
return arr;
}
/**
* 自動擴容,并保存數(shù)據(jù)
*
* @param arr
* @param value
*/
private int[] arrAppend(int[] arr, int value) {
arr = Arrays.copyOf(arr, arr.length + 1);
arr[arr.length – 1] = value;
return arr;
}
}
PHP
實例
{
if (count($arr) === 0) {
return $arr;
}
$minValue = $arr[0];
$maxValue = $arr[0];
for ($i = 1; $i < count($arr); $i++) {
if ($arr[$i] < $minValue) {
$minValue = $arr[$i];
} else if ($arr[$i] > $maxValue) {
$maxValue = $arr[$i];
}
}
$bucketCount = floor(($maxValue – $minValue) / $bucketSize) + 1;
$buckets = array();
for ($i = 0; $i < count($buckets); $i++) {
$buckets[$i] = [];
}
for ($i = 0; $i < count($arr); $i++) {
$buckets[floor(($arr[$i] – $minValue) / $bucketSize)][] = $arr[$i];
}
$arr = array();
for ($i = 0; $i < count($buckets); $i++) {
$bucketTmp = $buckets[$i];
sort($bucketTmp);
for ($j = 0; $j < count($bucketTmp); $j++) {
$arr[] = $bucketTmp[$j];
}
}
return $arr;
}
C++
實例
#include<iostream>
#include<vector>
using namespace std;
const int BUCKET_NUM = 10;
struct ListNode{
explicit ListNode(int i=0):mData(i),mNext(NULL){}
ListNode* mNext;
int mData;
};
ListNode* insert(ListNode* head,int val){
ListNode dummyNode;
ListNode *newNode = new ListNode(val);
ListNode *pre,*curr;
dummyNode.mNext = head;
pre = &dummyNode;
curr = head;
while(NULL!=curr && curr–>mData<=val){
pre = curr;
curr = curr–>mNext;
}
newNode–>mNext = curr;
pre–>mNext = newNode;
return dummyNode.mNext;
}
ListNode* Merge(ListNode *head1,ListNode *head2){
ListNode dummyNode;
ListNode *dummy = &dummyNode;
while(NULL!=head1 && NULL!=head2){
if(head1–>mData <= head2–>mData){
dummy–>mNext = head1;
head1 = head1–>mNext;
}else{
dummy–>mNext = head2;
head2 = head2–>mNext;
}
dummy = dummy–>mNext;
}
if(NULL!=head1) dummy–>mNext = head1;
if(NULL!=head2) dummy–>mNext = head2;
return dummyNode.mNext;
}
void BucketSort(int n,int arr[]){
vector<ListNode*> buckets(BUCKET_NUM,(ListNode*)(0));
for(int i=0;i<n;++i){
int index = arr[i]/BUCKET_NUM;
ListNode *head = buckets.at(index);
buckets.at(index) = insert(head,arr[i]);
}
ListNode *head = buckets.at(0);
for(int i=1;i<BUCKET_NUM;++i){
head = Merge(head,buckets.at(i));
}
for(int i=0;i<n;++i){
arr[i] = head–>mData;
head = head–>mNext;
}
}
參考地址:
https://github.com/hustcc/JS-Sorting-Algorithm/blob/master/9.bucketSort.md
https://zh.wikipedia.org/wiki/%E6%A1%B6%E6%8E%92%E5%BA%8F