javascript 排序(Sorting)算法与说明

排序的介绍

排序是算法最常用的一种运算之一，数据记录到数据库，都需要经过排序输出到客户端上。不然乱输出不规整的数据，是难以阅读的。

本文章介绍几种最常用见的排序方法：冒泡排序，选择排序，插入排序，归并排序和快速排序。

冒泡排序

冒泡排序是从运行时间的角度上来看，最差的一个。因为冒泡排序回比较任何两周相邻的项，如果第一个比第二个大，则交换它们。

选择排序

选择排序的思路是找到数据结构中的最小值并将其放置在第一位，接着找到第二小的值放在第二位，以此类推。

插入排序

插入排序每次排一个数组项，以此方式构建最后的排序数组。假定第一项已经排序了，接着，它和第二项进行比较，第二项是应该待在原位还是插到第一项之前呢？这样，头两就已正常排序，接着和第三项比较（它是该插入到第一、第二还是第三位置呢？）以此类推。

归并排序

归并排序是第一个可以被实际使用的排序算法。而javascript中的array类的sort在firefox浏览器上 就是用这种排序的。归并排序是一种分治算法。其思想是将原始数组切分成较小的数组，知道每个小数组只有一个位置，接着将小数组归并成较大的数组，直到最后只有一个排序完毕的大数组。

快速排序

快速排序也许是最常用的排序算法。和归并排序一样，快速排序也使用分治的方法，将原始数组分位较小的数组（但它没有像归并排序那样将它们分割开）。这个重点说下过程。

首先，从数组中选择中间一项作为主元。

创建两个指针，左边一个指向数组第一个项，右边一个指向数组最后一个项。移动左指针直到我们找到一个比主元大的元素，接着，移动右指针直到找到一个比主元小的元素，然后交换它们，重复这个过程，直到左指针超过了右指针。这个过程将使得比主元小的值都排在主元之前，而比主元大的值都排在主元之后。这一步叫作划分操作。

接着，算法对划分后的小数组（较主元小的值组成的子数组，以及较主元大的值组成的子数组）重复之前的两个步骤，直至数组已完全排序。

排序的算法实例

function createNonSortedArray(size){
var array = new ArrayList();

for (var i = size; i> 0; i--){
array.insert(i);
}

return array;
}

function createRandomNonSortedArray(){
var array = new ArrayList();

array.insert(3);
array.insert(5);
array.insert(1);
array.insert(6);
array.insert(4);
array.insert(7);
array.insert(2);

return array;
}

function printArray(array){
console.log(array.toString());
}

function createNonSortedArrayAndPrint(size){
var array = createNonSortedArray(size);
printArray(array);

return array;
}

var array = createNonSortedArrayAndPrint(5);
array.bubbleSort();//5,4,3,2,1

array = createNonSortedArrayAndPrint(5);
array.modifiedBubbleSort();//5,4,3,2,1

array = createNonSortedArrayAndPrint(5);
array.selectionSort();//5,4,3,2,1

array = createNonSortedArrayAndPrint(5);
array.insertionSort();//5,4,3,2,1

array = createNonSortedArrayAndPrint(8);
array.mergeSort();//8,7,6,5,4,3,2,1

array = createRandomNonSortedArray();
array.quickSort();//1,2,3,4,5,6,7

ES6排序完整实现代码：

let ArrayList = (function() {
class ArrayList {
constructor() {
this.array = [];
}

insert(item) {
this.array.push(item);
}

swap(array, index1, index2) {
var aux = this.array[index1];
this.array[index1] = this.array[index2];
this.array[index2] = aux;
}

toString() {
return this.array.join();
}

array() {
return this.array;
}

bubbleSort() {
var length = this.array.length;

for(var i = 0; i < length; i++) {
console.log('--- ');
for(var j = 0; j < length - 1; j++) {
console.log('compare ' + this.array[j] + ' with ' + this.array[j + 1]);
if(this.array[j] > this.array[j + 1]) {
console.log('swap ' + this.array[j] + ' with ' + this.array[j + 1]);
this.swap(this.array, j, j + 1);
}
}
}
};

modifiedBubbleSort() {
var length = this.array.length;

for(var i = 0; i < length; i++) {
console.log('--- ');
for(var j = 0; j < length - 1 - i; j++) {
console.log('compare ' + this.array[j] + ' with ' + this.array[j + 1]);
if(this.array[j] > this.array[j + 1]) {
console.log('swap ' + this.array[j] + ' with ' + this.array[j + 1]);
this.swap(j, j + 1);
}
}
}

};

selectionSort() {
var length = this.array.length,
indexMin;

for(var i = 0; i < length - 1; i++) {
indexMin = i;
console.log('index ' + this.array[i]);
for(var j = i; j < length; j++) {
if(this.array[indexMin] > this.array[j]) {
console.log('new index min ' + this.array[j]);
indexMin = j;
}
}
if(i !== indexMin) {
console.log('swap ' + this.array[i] + ' with ' + this.array[indexMin]);
this.swap(i, indexMin);
}
}
};

insertionSort() {
var length = this.array.length,
j, temp;
for(var i = 1; i < this.length; i++) {
j = i;
temp = this.array[i];
console.log('to be inserted ' + temp);
while(j > 0 && this.array[j - 1] > temp) {
console.log('shift ' + this.array[j - 1]);
this.array[j] = this.array[j - 1];
j--;
}
console.log('insert ' + temp);
this.array[j] = temp;
}
};

insertionSort_(array) {
var length = array.length,
j, temp;
for(var i = 1; i < length; i++) {
j = i;
temp = array[i];
while(j > 0 && array[j - 1] > temp) {
array[j] = array[j - 1];
j--;
}
this.array[j] = temp;
}
};

mergeSort() {
this.array = this.mergeSortRec(this.array);
};

mergeSortRec(array) {

var length = array.length;

if(length === 1) {
console.log(array);
return array;
}

var mid = Math.floor(length / 2),
left = array.slice(0, mid),
right = array.slice(mid, length);

return this.merge(this.mergeSortRec(left), this.mergeSortRec(right));
};

merge(left, right) {
var result = [],
il = 0,
ir = 0;

while(il < left.length && ir < right.length) {

if(left[il] < right[ir]) {
result.push(left[il++]);
} else {
result.push(right[ir++]);
}
}

while(il < left.length) {
result.push(left[il++]);
}

while(ir < right.length) {
result.push(right[ir++]);
}

console.log(result);

return result;
};

quickSort() {
this.quick(this.array, 0, this.array.length - 1);
};

partition(array, left, right) {

var pivot = array[Math.floor((right + left) / 2)],
i = left,
j = right;

console.log('pivot is ' + pivot + '; left is ' + left + '; right is ' + right);

while(i <= j) {
while(array[i] < pivot) {
i++;
console.log('i = ' + i);
}

while(array[j] > pivot) {
j--;
console.log('j = ' + j);
}

if(i <= j) {
console.log('swap ' + array[i] + ' with ' + array[j]);
this.swap(array, i, j);
i++;
j--;
}
}

return i;
};

quick(array, left, right) {

var index;

if(array.length > 1) {

index = this.partition(array, left, right);

if(left < index - 1) {
this.quick(array, left, index - 1);
}

if(index < right) {
this.quick(array, index, right);
}
}
return array;
};

heapSort() {
var heapSize = this.array.length;

this.buildHeap(array);

while(heapSize > 1) {
heapSize--;
console.log('swap (' + +array[0] + ',' + array[heapSize] + ')');
this.swap(array, 0, heapSize);
console.log('heapify ' + this.array.join());
this.heapify(array, heapSize, 0);
}
};

buildHeap(array) {
console.log('building heap');
var heapSize = array.length;
for(var i = Math.floor(array.length / 2); i >= 0; i--) {
this.heapify(array, heapSize, i);
}
console.log('heap created: ' + this.array.join());
};

heapify(array, heapSize, i) {
var left = i * 2 + 1,
right = i * 2 + 2,
largest = i;

if(left < heapSize && array[left] > array[largest]) {
largest = left;
}

if(right < heapSize && array[right] > array[largest]) {
largest = right;
}

console.log('Heapify Index = ' + i + ' and Heap Size = ' + heapSize);

if(largest !== i) {
console.log('swap index ' + i + ' with ' + largest + ' (' + +array[i] + ',' + array[largest] + ')');
this.swap(array, i, largest);
console.log('heapify ' + array.join());
this.heapify(array, heapSize, largest);
}
};

countingSort() {

var i,
maxValue = this.findMaxValue(),
sortedIndex = 0,
counts = new Array(maxValue + 1);

for(i = 0; i < array.length; i++) {
if(!counts[array[i]]) {
counts[array[i]] = 0;
}
counts[array[i]]++;
}

console.log('Frequencies: ' + counts.join());

for(i = 0; i < counts.length; i++) {
while(counts[i] > 0) {
array[sortedIndex++] = i;
counts[i]--;
}
}
};

bucketSort(bucketSize) {

var i,
minValue = this.findMinValue(),
maxValue = this.findMaxValue(),
BUCKET_SIZE = 5;

console.log('minValue ' + minValue);
console.log('maxValue ' + maxValue);

bucketSize = bucketSize || BUCKET_SIZE;
var bucketCount = Math.floor((maxValue - minValue) / bucketSize) + 1;
var buckets = new Array(bucketCount);
console.log('bucketSize = ' + bucketCount);
for(i = 0; i < buckets.length; i++) {
buckets[i] = [];
}

for(i = 0; i < this.array.length; i++) {
buckets[Math.floor((this.array[i] - minValue) / bucketSize)].push(this.array[i]);
console.log('pushing item ' + this.array[i] + ' to bucket index ' + Math.floor((this.array[i] - minValue) / bucketSize));
}

this.array = [];
for(i = 0; i < buckets.length; i++) {
this.insertionSort_(buckets[i]);

console.log('bucket sorted ' + i + ': ' + buckets[i].join());

for(var j = 0; j < buckets[i].length; j++) {
this.array.push(buckets[i][j]);
}
}
};

radixSort(radixBase) {

var i,
minValue = this.findMinValue(),
maxValue = this.findMaxValue(),
radixBase = radixBase || 10;

// Perform counting sort for each significant digit), starting at 1
var significantDigit = 1;
while(((maxValue - minValue) / significantDigit) >= 1) {
console.log('radix sort for digit ' + significantDigit);
this.array = this.countingSortForRadix(this.array, radixBase, significantDigit, minValue);
console.log(this.array.join());
significantDigit *= radixBase;
}
};

countingSortForRadix(array, radixBase, significantDigit, minValue) {
var i, countsIndex,
counts = new Array(radixBase),
aux = new Array(radixBase);

for(i = 0; i < radixBase; i++) {
counts[i] = 0;
}

for(i = 0; i < array.length; i++) {
countsIndex = Math.floor(((array[i] - minValue) / significantDigit) % radixBase);
counts[countsIndex]++;
}

for(i = 1; i < radixBase; i++) {
counts[i] += counts[i - 1];
}

for(i = array.length - 1; i >= 0; i--) {
countsIndex = Math.floor(((array[i] - minValue) / significantDigit) % radixBase);
aux[--counts[countsIndex]] = array[i];
}

for(i = 0; i < array.length; i++) {
array[i] = aux[i];
}

return array;
};

sequentialSearch(item) {

for(var i = 0; i < this.array.length; i++) {
if(item === array[i]) {
return i;
}
}

return -1;
};

findMaxValue() {
var max = this.array[0];
for(var i = 1; i < this.array.length; i++) {
if(max < this.array[i]) {
max = this.array[i];
}
}

return max;
};

findMinValue() {
var min = this.array[0];
for(var i = 1; i < this.array.length; i++) {
if(min > this.array[i]) {
min = this.array[i];
}
}

return min;
};

binarySearch(item) {
this.quickSort();

var low = 0,
high = array.length - 1,
mid, element;

while(low <= high) {
mid = Math.floor((low + high) / 2);
element = this.array[mid];
console.log('mid element is ' + element);
if(element < item) {
low = mid + 1;
console.log('low is ' + low);
} else if(element > item) {
high = mid - 1;
console.log('high is ' + high);
} else {
console.log('found it');
return mid;
}
}
return -1;
};

}
return ArrayList;
})()