优先队列之堆排序

Posted 2020-08-13

1、最大堆

 

import java.util.Scanner ;

public class MaxPQ<Key extends Comparable<Key>>{
	private int N = 0 ;
	private Key[] pq ; 
	
	public MaxPQ(int max){
		pq = (Key[])new Comparable[max+1] ;
	}
	
	public MaxPQ(Key[] a){
		pq = (Key[])new Comparable[a.length+1] ;
		for (int i=0;i<a.length;i++) {
			insert(a[i]) ;
		}
	}
	
	public void insert(Key v){
		N++ ;
		pq[N] = v ;
		swim(N) ;
	}
	private void swim(int k){
		if(k>1){
			if(less(k/2,k)){
				exch(k,k/2) ;
				swim(k/2) ;
			}else{
				return ;
			}
		}else{
			return ;
		}
	}
	private boolean less(int i,int j){
		return pq[i].compareTo(pq[j])<0 ;
	}
	private void exch(int i, int j){
		Key t = pq[i] ;
		pq[i] = pq[j] ;
		pq[j] = t ;
	}

	public Key max(){
		return pq[1] ;
	}
	
	public Key delMax(){
		Key max = pq[1] ;
		pq[1] = pq[N] ;
		N-- ;
		pq[N+1] = null ;
		sink(1) ;
		return max ;
	}
	private void sink(int k){
		if(2*k<=N){
			int t = k ;
			if(less(t,2*k)) {
				t = 2*k ;
			}
			if(2*k+1<=N && less(t,2*k+1)){
				t = 2*k+1 ;
			}
			if(t!=k){
				exch(t,k) ;
				sink(t) ;
			}else{
				return ;
			}
		}else{
			return ;
		}
	}
	
	public boolean isEmpty(){
		return N == 0 ;
	}
	
	public int size(){
		return N ;
	}

	public static void main(String[] args) {
		System.out.println("please input the lenghth of heap: ") ;
		Scanner sc = new Scanner(System.in) ;
		int len = sc.nextInt() ;
		MaxPQ<Integer> pq = new MaxPQ<Integer>(len) ;
		System.out.println("please input the items:") ;

		for(int i=0;i<len;i++){
			pq.insert(sc.nextInt()) ;
		}

		for (int i=0;i<len;i++) {
		 	System.out.print(pq.delMax() + " ") ;	
		} 	
	} 
}

　　

2、最小堆

 

import java.util.Scanner ;

public class MinPQ<Key extends Comparable<Key>>{
	private int N = 0 ;
	private Key[] pq ; 
	
	public MinPQ(int max){
		pq = (Key[])new Comparable[max+1] ;
	}
	
	public MinPQ(Key[] a){
		pq = (Key[])new Comparable[a.length+1] ;
		for (int i=0;i<a.length;i++) {
			insert(a[i]) ;	
		}
	}
	
	public void insert(Key v){
		N++ ;
		pq[N] = v ;
		swim(N) ;
	}
	private void swim(int k){
		if(k>1){
			if(less(k,k/2)){
				exch(k,k/2) ;
				swim(k/2) ;
			}else{
				return ;
			}
		}else{
			return ;
		}
	}
	private boolean less(int i,int j){
		return pq[i].compareTo(pq[j])<0 ;
	}
	private void exch(int i, int j){
		Key t = pq[i] ;
		pq[i] = pq[j] ;
		pq[j] = t ;
	}

	public Key min(){
		return pq[1] ;
	}
	
	public Key delMin(){
		Key max = pq[1] ;
		pq[1] = pq[N] ;
		N-- ;
		pq[N+1] = null ;
		sink(1) ;
		return max ;
	}
	private void sink(int k){
		if(2*k<=N){
			int t = k ;
			if(less(2*k,t)) {
				t = 2*k ;
			}
			if(2*k+1<=N && less(2*k+1,t)){
				t = 2*k+1 ;
			}
			if(t!=k){
				exch(t,k) ;
				sink(t) ;
			}else{
				return ;
			}
		}else{
			return ;
		}
	}
	
	public boolean isEmpty(){
		return N == 0 ;
	}
	
	public int size(){
		return N ;
	}

	public static void main(String[] args) {
		//System.out.println("please input the lenghth of heap: ") ;
		//Scanner sc = new Scanner(System.in) ;
		//int len = sc.nextInt() ;
		//MinPQ<Integer> pq = new MinPQ<Integer>(len) ;
		//System.out.println("please input the items:") ;
		//int len = sc.nextInt() ;

		//for(int i=0;i<len;i++){
		//	pq.insert(sc.nextInt()) ;
		//}

		Integer[] a = {10,9,8,7,6,5,4,3,2,1} ; 
		MinPQ<Integer> pq = new MinPQ<Integer>(a) ;
		for (int i=0;i<a.length;i++) {
		 	System.out.print(pq.delMin() + " ") ;	
		} 	
	} 
}

　　

3、堆排序

import java.util.Scanner ;

public class HeapSort{
	public static void heapSort(Comparable[] a){
		int N = a.length-1 ;
		for(int i=N/2;i>=1;i--){     //for循环构造了最大堆；
			sink(a,i,N) ;
		}

		while(N>1){                  //while循环完成了从小到大排序
			exch(a,1,N) ;
			N-- ;
			sink(a,1,N) ;
		}
	}

	private static void sink(Comparable[] a, int i, int j){
		if(2*i<=j){
			int t = i ;
			if(less(a[t],a[2*i])){
				t = 2*i ;
			}
			if(2*i+1<=j && less(a[t],a[2*i+1])){
				t = 2*i+1 ;
			}
			if(t!=i){
				exch(a,t,i) ;
				sink(a,t,j) ;
			}else{
				return ;
			}
		}else{
			return ;
		}
	}

	private static boolean less(Comparable v, Comparable w){
		return v.compareTo(w)<0 ;
	}

	private static void exch(Comparable[] a, int i, int j){
		Comparable temp = a[i] ;
		a[i] = a[j] ;
		a[j] = temp ;
	}

	private static void show(Comparable[] a){
		for(int i=0;i<a.length;i++){
			System.out.print(a[i] + " ") ;
		}
		System.out.println() ;
	}

	public static boolean isSorted(Comparable[] a){
		for(int i=2;i<a.length;i++){
			if(less(a[i],a[i-1])){
				return false ;
			}
		}
		return true ;
	}

	public static void main(String[] args){
		
		System.out.println("please input the length of array:") ;
		
		Scanner sc = new Scanner(System.in) ;
		int len = sc.nextInt() ;
		Integer[] a = new Integer[len] ;

		System.out.println("please input the numbers of array:") ;
		for (int i=0;i<len;i++) {
			a[i] = sc.nextInt() ;
		}
		
		if (!isSorted(a)) {
			heapSort(a) ;
		}

		show(a) ;
	} 
}