堆的定義如下:具有n個(gè)元素的序列(h1,h2,...,hn),當(dāng)且僅當(dāng)滿足(hi>=h2i,hi>=2i+1)或(hi<=h2i,hi<=2i+1)(i=1,2,...,n/2)時(shí)稱之為堆。在這里只討論滿足前者條件的堆。由堆的定義可以看出,堆頂元素(即第一個(gè)元素)必為最大項(xiàng)(大頂堆)。完全二叉樹可以很直觀地表示堆的結(jié)構(gòu)。堆頂為根,其它為左子樹、右子樹。初始時(shí)把要排序的數(shù)的序列看作是一棵順序存儲(chǔ)的二叉樹,調(diào)整它們的存儲(chǔ)序,使之成為一個(gè)堆,這時(shí)堆的根節(jié)點(diǎn)的數(shù)最大。然后將根節(jié)點(diǎn)與堆的最后一個(gè)節(jié)點(diǎn)交換。然后對(duì)前面(n-1)個(gè)數(shù)重新調(diào)整使之成為堆。依此類推,直到只有兩個(gè)節(jié)點(diǎn)的堆,并對(duì)它們作交換,最后得到有n個(gè)節(jié)點(diǎn)的有序序列。從算法描述來看,堆排序需要兩個(gè)過程,一是建立堆,二是堆頂與堆的最后一個(gè)元素交換位置。所以堆排序有兩個(gè)函數(shù)組成。一是建堆的滲透函數(shù),二是反復(fù)調(diào)用滲透函數(shù)實(shí)現(xiàn)排序的函數(shù)。(2)實(shí)例:
初始序列:46,79,56,38,40,84 建堆:
交換,從堆中踢出最大數(shù)
依次類推:最后堆中剩余的最后兩個(gè)結(jié)點(diǎn)交換,踢出一個(gè),排序完成。(3)用java實(shí)現(xiàn)
1.2.3.4.import java.util.Arrays;
public class HeapSort { int
a[]={49,38,65,97,76,13,27,49,78,34,12,64,5,4,62,99,98,54,56,17,18,23,34,15,35,25,53,51};5.6.7.public HeapSort(){ heapSort(a);} 8.9.10.11.12.13.14.15.16.17.18.19.20.21.22.23.24.25.26.27.28.29.30.31.32.33.34.35.36.37.38.39.40.41.42.43.44.45.46.47.48.49.50.public void heapSort(int[] a){ System.out.println(“開始排序”);
int arrayLength=a.length;
//循環(huán)建堆
for(int i=0;i//建堆
buildMaxHeap(a,arrayLength-1-i);
//交換堆頂和最后一個(gè)元素
swap(a,0,arrayLength-1-i);
System.out.println(Arrays.toString(a));} }
private void swap(int[] data, int i, int j){
// TODO Auto-generated method stub
int tmp=data[i];data[i]=data[j];data[j]=tmp;}
//對(duì)data數(shù)組從0到lastIndex建大頂堆
private void buildMaxHeap(int[] data, int lastIndex){
// TODO Auto-generated method stub
//從lastIndex處節(jié)點(diǎn)(最后一個(gè)節(jié)點(diǎn))的父節(jié)點(diǎn)開始
for(int i=(lastIndex-1)/2;i>=0;i--){
//k保存正在判斷的節(jié)點(diǎn)
int k=i;
//如果當(dāng)前k節(jié)點(diǎn)的子節(jié)點(diǎn)存在while(k*2+1<=lastIndex){
//k節(jié)點(diǎn)的左子節(jié)點(diǎn)的索引
int biggerIndex=2*k+1;
//如果biggerIndex小于lastIndex,即biggerIndex+1代表的k節(jié) if(biggerIndex//若果右子節(jié)點(diǎn)的值較大
if(data[biggerIndex]//biggerIndex總是記錄較大子節(jié)點(diǎn)的索引
biggerIndex++;} }
//如果k節(jié)點(diǎn)的值小于其較大的子節(jié)點(diǎn)的值
if(data[k]//交換他們
swap(data,k,biggerIndex);點(diǎn)的右子節(jié)點(diǎn)存在 51.52.53.54.55.56.//將biggerIndex賦予k,開始while循環(huán)的下一次循環(huán),重新保 k=biggerIndex;}else{
break;}
}
}
align=“l(fā)eft”>??? }
}
5.冒泡排序
(1)基本思想:在要排序的一組數(shù)中,對(duì)當(dāng)前還未排好序的范圍內(nèi)的全部數(shù),自上而下對(duì)相鄰的兩個(gè)數(shù)依次進(jìn)行比較和調(diào)整,讓較大的數(shù)往下沉,較小的往上冒。即:每當(dāng)兩相鄰的數(shù)比較后發(fā)現(xiàn)它們的排序與排序要求相反時(shí),就將它們互換。(2)實(shí)例:
(3)用java實(shí)現(xiàn)
1.2.3.public class bubbleSort { public bubbleSort(){ int
a[]={49,38,65,97,76,13,27,49,78,34,12,64,5,4,62,99,98,54,56,17,18,23,34,15,35,25,53,51};4.5.6.7.8.9.int temp=0;
for(int i=0;ifor(int j=0;jif(a[j]>a[j+1]){ temp=a[j];a[j]=a[j+1];10.11.12.13.14.15.16.17.18.a[j+1]=temp;} } }
for(int i=0;i6.快速排序
(1)基本思想:選擇一個(gè)基準(zhǔn)元素,通常選擇第一個(gè)元素或者最后一個(gè)元素,通過一趟掃描,將待排序列分成兩部分,一部分比基準(zhǔn)元素小,一部分大于等于基準(zhǔn)元素,此時(shí)基準(zhǔn)元素在其排好序后的正確位置,然后再用同樣的方法遞歸地排序劃分的兩部分。(2)實(shí)例:
(3)用java實(shí)現(xiàn)
1.public class quickSort { 2.int
a[]={49,38,65,97,76,13,27,49,78,34,12,64,5,4,62,99,98,54,56,17,18,23,34,15,35,25,53,51};
3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.20.21.22.23.24.25.26.27.28.29.30.31.32.33.34.35.36.public quickSort(){ quick(a);
for(int i=0;ipublic int getMiddle(int[] list, int low, int high){
int tmp = list[low];//數(shù)組的第一個(gè)作為中軸
while(low < high){
while(low < high && list[high] >= tmp){
high--;}
list[low] = list[high];//比中軸小的記錄移到低端
while(low < high && list[low] <= tmp){ low++;}
list[high] = list[low];//比中軸大的記錄移到高端
}
list[low] = tmp;//中軸記錄到尾
return low;//返回中軸的位置
}
public void _quickSort(int[] list, int low, int high){
if(low < high){
int middle = getMiddle(list, low, high);//將list數(shù)組進(jìn) _quickSort(list, low, middle1);} } } 行一分為二
歸排序
排序
7、歸并排序
(1)基本排序:歸并(Merge)排序法是將兩個(gè)(或兩個(gè)以上)有序表合并成一個(gè)新的有序表,即把待排序序列分為若干個(gè)子序列,每個(gè)子序列是有序的。然后再把有序子序列合并為整體有序序列。(2)實(shí)例:
(3)用java實(shí)現(xiàn)
1.2.3.4.import java.util.Arrays;
public class mergingSort { int
a[]={49,38,65,97,76,13,27,49,78,34,12,64,5,4,62,99,98,54,56,17,18,23,34,15,35,25,53,51};5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.20.21.22.23.24.25.26.27.28.public mergingSort(){ sort(a,0,a.length-1);
for(int i=0;ipublic void sort(int[] data, int left, int right){
// TODO Auto-generated method stub
if(left//找出中間索引
int center=(left+right)/2;
//對(duì)左邊數(shù)組進(jìn)行遞歸
sort(data,left,center);
//對(duì)右邊數(shù)組進(jìn)行遞歸
sort(data,center+1,right);
//合并
merge(data,left,center,right);} }
public void merge(int[] data, int left, int center, int right){
// TODO Auto-generated method stub
int [] tmpArr=new int[data.length];
int mid=center+1;
//third記錄中間數(shù)組的索引
29.30.31.32.33.34.35.36.37.38.39.40.41.42.43.44.45.46.47.48.49.50.51.52.53.54.int third=left;
int tmp=left;
while(left<=center&&mid<=right){
//從兩個(gè)數(shù)組中取出最小的放入中間數(shù)組
if(data[left]<=data[mid]){ tmpArr[third++]=data[left++];}else{
tmpArr[third++]=data[mid++];} }
//剩余部分依次放入中間數(shù)組
while(mid<=right){
tmpArr[third++]=data[mid++];}
while(left<=center){
tmpArr[third++]=data[left++];}
//將中間數(shù)組中的內(nèi)容復(fù)制回原數(shù)組
while(tmp<=right){
data[tmp]=tmpArr[tmp++];}
System.out.println(Arrays.toString(data));}
}
8、基數(shù)排序
(1)基本思想:將所有待比較數(shù)值(正整數(shù))統(tǒng)一為同樣的數(shù)位長(zhǎng)度,數(shù)位較短的數(shù)前面補(bǔ)零。然后,從最低位開始,依次進(jìn)行一次排序。這樣從最低位排序一直到最高位排序完成以后,數(shù)列就變成一個(gè)有序序列。(2)實(shí)例:
(3)用java實(shí)現(xiàn)
1.2.3.4.5.import java.util.ArrayList;import java.util.List;
public class radixSort {
int
a[]={49,38,65,97,76,13,27,49,78,34,12,64,5,4,62,99,98,54,101,56,17,18,23,34,15,35,25,53,51};6.7.8.9.10.11.12.13.14.15.16.public radixSort(){ sort(a);
for(int i=0;ipublic void sort(int[] array){
//首先確定排序的趟數(shù);
int max=array[0];
for(int i=1;iif(array[i]>max){ 17.18.19.20.21.22.23.24.25.26.27.28.29.30.31.32.33.34.35.36.37.38.39.40.41.42.43.44.45.46.47.48.49.50.51.52.53.54.55.56.57.58.59.max=array[i];} }
int time=0;
//判斷位數(shù);
while(max>0){ max/=10;time++;}
//建立10個(gè)隊(duì)列;
List queue=new ArrayList();
for(int i=0;i<10;i++){
ArrayList queue1=new ArrayList();queue.add(queue1);}
//進(jìn)行time次分配和收集;
for(int i=0;i