Java十大经典排序算法的实现图解
297
2022-07-29
目录1.汉诺塔介绍2.解塔步骤3.C++实现(递归结果及显示步骤)(1)递归结果(2)显示步骤4.java实现(递归结果及显示http://步骤)(1)递归结果(2)显示步骤
1.汉诺塔介绍
汉诺塔规则
1.有三根杆子A,B,C。A杆上有若干碟子
2.每次移动一块碟子,小的只能叠在大的上面
3.把所有碟子从A杆全部移到C杆上
经过研究发现,汉诺塔的破解很简单,就是按照移动规则向一个方向移动金片: 如3阶汉诺塔的移动:A→C,A→B,C→B,A→C,B→A,B→C,A→C
2.解塔步骤
圆盘:12345 柱子:ABC
1→C,2→B,1→B,3→C,1→A,2→C,1→C,4→B; 1→B,2→A,1→A,3→B,1→C,2→B,1→B,5→C; 1→A,2→C,1→C,4→A,1→B,2→A,1→A,4→C; 1→C,2→B,1→B,3→C,1→A,2→C,1→C,完成!
3.C++实现(递归结果及显示步骤)
(1)递归结果
#include
using namespace std;
int H_tower(int num);
int main()
{
int num;
cout<<"请输入需要移动的盘子数"<
cin>>num;
cout<
}
int H_tower(int num)
{
if(num<1)
{
cout<<"请输入大于等于一的数"<
exit(-1); //输入不合法,退出程序
}
if(num==1)
{
return 1;
}
return (2*H_tower(num-1)+1);//规律递归
}
(2)显示步骤
#include
using namespace std;
void hannuo(int num);
void Move(int &sum,int num,char A,char B,char C);
int main()
{
int num;
cout<<"请输入需要移动的盘子数"<
cin>>num;
hannuo(3);
}
void hannuo(int num)
{
if(num<1)
{
cout<<"请输入大于等于一的数"<
exit(-1); //输入不合法,退出程序
}
int sum=0;
Move(sum,num,'A','B','C');
}
void Move(int &sum,int num,char A,char B,char C)
{
if(num==1)
{
sum++;
//圆盘只有一个时,只需将其从A塔移到C塔
cout << "第 "<
}
else
{
Move(sum,num - 1, A, C, B);//递归,把A塔上编号1~n-1的圆盘移到B上,以C为辅助塔
sum++;
cout << "第 "<
Move(sum,num - 1, B, A, C);//递归,把B塔上编号1~n-1的圆盘移到C上,以A为辅助塔
}
}
4.Java实现(递归结果及显示步骤)
(1)递归结果
hannuo.java
import java.util.Scanner;
public class hannuo {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int num;
System.out.println("请输入需要移动的盘子数");
num= sc.nextInt();
tower t=new tower();
System.out.println("需要移动的次数 = "+t.H_tower(num));
}
}
tower.java
public class tower {
public int H_tower(int num) {
if (num < 1) {
System.out.println("请输入大于等于一的数" );
}
if (num == 1) {
return 1;
}
return (2 * H_tower(num - 1) + 1);//规律递归
}
}
(2)显示步骤
hannuo.java
import java.util.Scanner;
public class hannuo {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int num;
System.out.println("请输入需要移动的盘子数");
num= sc.nextInt();
tower t=new tower();
t.hannuo(num);
}
}
tower.java
public class tower {
public void hannuo(int num)
{
if(num<1)
{
System.out.println("请输入大于等于一的数");
}
int sum[]={0};
Move(num,'A','B','C');
}
public void Move(int num,char A,char B,char C)
{
if(num==1)
{
//圆盘只有一个时,只需将其从A塔移到C塔
System.out.println(" move " + num + " from " + A + " to " + C );
}
else
{
Move(num - 1, A, C, B);//递归,把A塔上编号1~n-1的圆盘移到B上,以C为辅助塔
System.out.println(" move " + num + " from " + A + " to " + C );//把A塔上编号为n的圆盘移到C上
Move(num - 1, B, A, C);//递归,把B塔上编号1~n-1的圆盘移到C上,以A为辅助塔
}
}
}
cin>>num;
cout<
}
int H_tower(int num)
{
if(num<1)
{
cout<<"请输入大于等于一的数"<
exit(-1); //输入不合法,退出程序
}
if(num==1)
{
return 1;
}
return (2*H_tower(num-1)+1);//规律递归
}
(2)显示步骤
#include
using namespace std;
void hannuo(int num);
void Move(int &sum,int num,char A,char B,char C);
int main()
{
int num;
cout<<"请输入需要移动的盘子数"<
cin>>num;
hannuo(3);
}
void hannuo(int num)
{
if(num<1)
{
cout<<"请输入大于等于一的数"<
exit(-1); //输入不合法,退出程序
}
int sum=0;
Move(sum,num,'A','B','C');
}
void Move(int &sum,int num,char A,char B,char C)
{
if(num==1)
{
sum++;
//圆盘只有一个时,只需将其从A塔移到C塔
cout << "第 "<
}
else
{
Move(sum,num - 1, A, C, B);//递归,把A塔上编号1~n-1的圆盘移到B上,以C为辅助塔
sum++;
cout << "第 "<
Move(sum,num - 1, B, A, C);//递归,把B塔上编号1~n-1的圆盘移到C上,以A为辅助塔
}
}
4.Java实现(递归结果及显示步骤)
(1)递归结果
hannuo.java
import java.util.Scanner;
public class hannuo {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int num;
System.out.println("请输入需要移动的盘子数");
num= sc.nextInt();
tower t=new tower();
System.out.println("需要移动的次数 = "+t.H_tower(num));
}
}
tower.java
public class tower {
public int H_tower(int num) {
if (num < 1) {
System.out.println("请输入大于等于一的数" );
}
if (num == 1) {
return 1;
}
return (2 * H_tower(num - 1) + 1);//规律递归
}
}
(2)显示步骤
hannuo.java
import java.util.Scanner;
public class hannuo {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int num;
System.out.println("请输入需要移动的盘子数");
num= sc.nextInt();
tower t=new tower();
t.hannuo(num);
}
}
tower.java
public class tower {
public void hannuo(int num)
{
if(num<1)
{
System.out.println("请输入大于等于一的数");
}
int sum[]={0};
Move(num,'A','B','C');
}
public void Move(int num,char A,char B,char C)
{
if(num==1)
{
//圆盘只有一个时,只需将其从A塔移到C塔
System.out.println(" move " + num + " from " + A + " to " + C );
}
else
{
Move(num - 1, A, C, B);//递归,把A塔上编号1~n-1的圆盘移到B上,以C为辅助塔
System.out.println(" move " + num + " from " + A + " to " + C );//把A塔上编号为n的圆盘移到C上
Move(num - 1, B, A, C);//递归,把B塔上编号1~n-1的圆盘移到C上,以A为辅助塔
}
}
}
}
int H_tower(int num)
{
if(num<1)
{
cout<<"请输入大于等于一的数"<
exit(-1); //输入不合法,退出程序
}
if(num==1)
{
return 1;
}
return (2*H_tower(num-1)+1);//规律递归
}
(2)显示步骤
#include
using namespace std;
void hannuo(int num);
void Move(int &sum,int num,char A,char B,char C);
int main()
{
int num;
cout<<"请输入需要移动的盘子数"<
cin>>num;
hannuo(3);
}
void hannuo(int num)
{
if(num<1)
{
cout<<"请输入大于等于一的数"<
exit(-1); //输入不合法,退出程序
}
int sum=0;
Move(sum,num,'A','B','C');
}
void Move(int &sum,int num,char A,char B,char C)
{
if(num==1)
{
sum++;
//圆盘只有一个时,只需将其从A塔移到C塔
cout << "第 "<
}
else
{
Move(sum,num - 1, A, C, B);//递归,把A塔上编号1~n-1的圆盘移到B上,以C为辅助塔
sum++;
cout << "第 "<
Move(sum,num - 1, B, A, C);//递归,把B塔上编号1~n-1的圆盘移到C上,以A为辅助塔
}
}
4.Java实现(递归结果及显示步骤)
(1)递归结果
hannuo.java
import java.util.Scanner;
public class hannuo {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int num;
System.out.println("请输入需要移动的盘子数");
num= sc.nextInt();
tower t=new tower();
System.out.println("需要移动的次数 = "+t.H_tower(num));
}
}
tower.java
public class tower {
public int H_tower(int num) {
if (num < 1) {
System.out.println("请输入大于等于一的数" );
}
if (num == 1) {
return 1;
}
return (2 * H_tower(num - 1) + 1);//规律递归
}
}
(2)显示步骤
hannuo.java
import java.util.Scanner;
public class hannuo {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int num;
System.out.println("请输入需要移动的盘子数");
num= sc.nextInt();
tower t=new tower();
t.hannuo(num);
}
}
tower.java
public class tower {
public void hannuo(int num)
{
if(num<1)
{
System.out.println("请输入大于等于一的数");
}
int sum[]={0};
Move(num,'A','B','C');
}
public void Move(int num,char A,char B,char C)
{
if(num==1)
{
//圆盘只有一个时,只需将其从A塔移到C塔
System.out.println(" move " + num + " from " + A + " to " + C );
}
else
{
Move(num - 1, A, C, B);//递归,把A塔上编号1~n-1的圆盘移到B上,以C为辅助塔
System.out.println(" move " + num + " from " + A + " to " + C );//把A塔上编号为n的圆盘移到C上
Move(num - 1, B, A, C);//递归,把B塔上编号1~n-1的圆盘移到C上,以A为辅助塔
}
}
}
exit(-1); //输入不合法,退出程序
}
if(num==1)
{
return 1;
}
return (2*H_tower(num-1)+1);//规律递归
}
(2)显示步骤
#include
using namespace std;
void hannuo(int num);
void Move(int &sum,int num,char A,char B,char C);
int main()
{
int num;
cout<<"请输入需要移动的盘子数"<
cin>>num;
hannuo(3);
}
void hannuo(int num)
{
if(num<1)
{
cout<<"请输入大于等于一的数"<
exit(-1); //输入不合法,退出程序
}
int sum=0;
Move(sum,num,'A','B','C');
}
void Move(int &sum,int num,char A,char B,char C)
{
if(num==1)
{
sum++;
//圆盘只有一个时,只需将其从A塔移到C塔
cout << "第 "<
}
else
{
Move(sum,num - 1, A, C, B);//递归,把A塔上编号1~n-1的圆盘移到B上,以C为辅助塔
sum++;
cout << "第 "<
Move(sum,num - 1, B, A, C);//递归,把B塔上编号1~n-1的圆盘移到C上,以A为辅助塔
}
}
4.Java实现(递归结果及显示步骤)
(1)递归结果
hannuo.java
import java.util.Scanner;
public class hannuo {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int num;
System.out.println("请输入需要移动的盘子数");
num= sc.nextInt();
tower t=new tower();
System.out.println("需要移动的次数 = "+t.H_tower(num));
}
}
tower.java
public class tower {
public int H_tower(int num) {
if (num < 1) {
System.out.println("请输入大于等于一的数" );
}
if (num == 1) {
return 1;
}
return (2 * H_tower(num - 1) + 1);//规律递归
}
}
(2)显示步骤
hannuo.java
import java.util.Scanner;
public class hannuo {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int num;
System.out.println("请输入需要移动的盘子数");
num= sc.nextInt();
tower t=new tower();
t.hannuo(num);
}
}
tower.java
public class tower {
public void hannuo(int num)
{
if(num<1)
{
System.out.println("请输入大于等于一的数");
}
int sum[]={0};
Move(num,'A','B','C');
}
public void Move(int num,char A,char B,char C)
{
if(num==1)
{
//圆盘只有一个时,只需将其从A塔移到C塔
System.out.println(" move " + num + " from " + A + " to " + C );
}
else
{
Move(num - 1, A, C, B);//递归,把A塔上编号1~n-1的圆盘移到B上,以C为辅助塔
System.out.println(" move " + num + " from " + A + " to " + C );//把A塔上编号为n的圆盘移到C上
Move(num - 1, B, A, C);//递归,把B塔上编号1~n-1的圆盘移到C上,以A为辅助塔
}
}
}
cin>>num;
hannuo(3);
}
void hannuo(int num)
{
if(num<1)
{
cout<<"请输入大于等于一的数"<
exit(-1); //输入不合法,退出程序
}
int sum=0;
Move(sum,num,'A','B','C');
}
void Move(int &sum,int num,char A,char B,char C)
{
if(num==1)
{
sum++;
//圆盘只有一个时,只需将其从A塔移到C塔
cout << "第 "<
}
else
{
Move(sum,num - 1, A, C, B);//递归,把A塔上编号1~n-1的圆盘移到B上,以C为辅助塔
sum++;
cout << "第 "<
Move(sum,num - 1, B, A, C);//递归,把B塔上编号1~n-1的圆盘移到C上,以A为辅助塔
}
}
4.Java实现(递归结果及显示步骤)
(1)递归结果
hannuo.java
import java.util.Scanner;
public class hannuo {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int num;
System.out.println("请输入需要移动的盘子数");
num= sc.nextInt();
tower t=new tower();
System.out.println("需要移动的次数 = "+t.H_tower(num));
}
}
tower.java
public class tower {
public int H_tower(int num) {
if (num < 1) {
System.out.println("请输入大于等于一的数" );
}
if (num == 1) {
return 1;
}
return (2 * H_tower(num - 1) + 1);//规律递归
}
}
(2)显示步骤
hannuo.java
import java.util.Scanner;
public class hannuo {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int num;
System.out.println("请输入需要移动的盘子数");
num= sc.nextInt();
tower t=new tower();
t.hannuo(num);
}
}
tower.java
public class tower {
public void hannuo(int num)
{
if(num<1)
{
System.out.println("请输入大于等于一的数");
}
int sum[]={0};
Move(num,'A','B','C');
}
public void Move(int num,char A,char B,char C)
{
if(num==1)
{
//圆盘只有一个时,只需将其从A塔移到C塔
System.out.println(" move " + num + " from " + A + " to " + C );
}
else
{
Move(num - 1, A, C, B);//递归,把A塔上编号1~n-1的圆盘移到B上,以C为辅助塔
System.out.println(" move " + num + " from " + A + " to " + C );//把A塔上编号为n的圆盘移到C上
Move(num - 1, B, A, C);//递归,把B塔上编号1~n-1的圆盘移到C上,以A为辅助塔
}
}
}
exit(-1); //输入不合法,退出程序
}
int sum=0;
Move(sum,num,'A','B','C');
}
void Move(int &sum,int num,char A,char B,char C)
{
if(num==1)
{
sum++;
//圆盘只有一个时,只需将其从A塔移到C塔
cout << "第 "<
}
else
{
Move(sum,num - 1, A, C, B);//递归,把A塔上编号1~n-1的圆盘移到B上,以C为辅助塔
sum++;
cout << "第 "<
Move(sum,num - 1, B, A, C);//递归,把B塔上编号1~n-1的圆盘移到C上,以A为辅助塔
}
}
4.Java实现(递归结果及显示步骤)
(1)递归结果
hannuo.java
import java.util.Scanner;
public class hannuo {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int num;
System.out.println("请输入需要移动的盘子数");
num= sc.nextInt();
tower t=new tower();
System.out.println("需要移动的次数 = "+t.H_tower(num));
}
}
tower.java
public class tower {
public int H_tower(int num) {
if (num < 1) {
System.out.println("请输入大于等于一的数" );
}
if (num == 1) {
return 1;
}
return (2 * H_tower(num - 1) + 1);//规律递归
}
}
(2)显示步骤
hannuo.java
import java.util.Scanner;
public class hannuo {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int num;
System.out.println("请输入需要移动的盘子数");
num= sc.nextInt();
tower t=new tower();
t.hannuo(num);
}
}
tower.java
public class tower {
public void hannuo(int num)
{
if(num<1)
{
System.out.println("请输入大于等于一的数");
}
int sum[]={0};
Move(num,'A','B','C');
}
public void Move(int num,char A,char B,char C)
{
if(num==1)
{
//圆盘只有一个时,只需将其从A塔移到C塔
System.out.println(" move " + num + " from " + A + " to " + C );
}
else
{
Move(num - 1, A, C, B);//递归,把A塔上编号1~n-1的圆盘移到B上,以C为辅助塔
System.out.println(" move " + num + " from " + A + " to " + C );//把A塔上编号为n的圆盘移到C上
Move(num - 1, B, A, C);//递归,把B塔上编号1~n-1的圆盘移到C上,以A为辅助塔
}
}
}
}
else
{
Move(sum,num - 1, A, C, B);//递归,把A塔上编号1~n-1的圆盘移到B上,以C为辅助塔
sum++;
cout << "第 "<
Move(sum,num - 1, B, A, C);//递归,把B塔上编号1~n-1的圆盘移到C上,以A为辅助塔
}
}
4.Java实现(递归结果及显示步骤)
(1)递归结果
hannuo.java
import java.util.Scanner;
public class hannuo {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int num;
System.out.println("请输入需要移动的盘子数");
num= sc.nextInt();
tower t=new tower();
System.out.println("需要移动的次数 = "+t.H_tower(num));
}
}
tower.java
public class tower {
public int H_tower(int num) {
if (num < 1) {
System.out.println("请输入大于等于一的数" );
}
if (num == 1) {
return 1;
}
return (2 * H_tower(num - 1) + 1);//规律递归
}
}
(2)显示步骤
hannuo.java
import java.util.Scanner;
public class hannuo {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int num;
System.out.println("请输入需要移动的盘子数");
num= sc.nextInt();
tower t=new tower();
t.hannuo(num);
}
}
tower.java
public class tower {
public void hannuo(int num)
{
if(num<1)
{
System.out.println("请输入大于等于一的数");
}
int sum[]={0};
Move(num,'A','B','C');
}
public void Move(int num,char A,char B,char C)
{
if(num==1)
{
//圆盘只有一个时,只需将其从A塔移到C塔
System.out.println(" move " + num + " from " + A + " to " + C );
}
else
{
Move(num - 1, A, C, B);//递归,把A塔上编号1~n-1的圆盘移到B上,以C为辅助塔
System.out.println(" move " + num + " from " + A + " to " + C );//把A塔上编号为n的圆盘移到C上
Move(num - 1, B, A, C);//递归,把B塔上编号1~n-1的圆盘移到C上,以A为辅助塔
}
}
}
Move(sum,num - 1, B, A, C);//递归,把B塔上编号1~n-1的圆盘移到C上,以A为辅助塔
}
}
4.Java实现(递归结果及显示步骤)
(1)递归结果
hannuo.java
import java.util.Scanner;
public class hannuo {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int num;
System.out.println("请输入需要移动的盘子数");
num= sc.nextInt();
tower t=new tower();
System.out.println("需要移动的次数 = "+t.H_tower(num));
}
}
tower.java
public class tower {
public int H_tower(int num) {
if (num < 1) {
System.out.println("请输入大于等于一的数" );
}
if (num == 1) {
return 1;
}
return (2 * H_tower(num - 1) + 1);//规律递归
}
}
(2)显示步骤
hannuo.java
import java.util.Scanner;
public class hannuo {
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int num;
System.out.println("请输入需要移动的盘子数");
num= sc.nextInt();
tower t=new tower();
t.hannuo(num);
}
}
tower.java
public class tower {
public void hannuo(int num)
{
if(num<1)
{
System.out.println("请输入大于等于一的数");
}
int sum[]={0};
Move(num,'A','B','C');
}
public void Move(int num,char A,char B,char C)
{
if(num==1)
{
//圆盘只有一个时,只需将其从A塔移到C塔
System.out.println(" move " + num + " from " + A + " to " + C );
}
else
{
Move(num - 1, A, C, B);//递归,把A塔上编号1~n-1的圆盘移到B上,以C为辅助塔
System.out.println(" move " + num + " from " + A + " to " + C );//把A塔上编号为n的圆盘移到C上
Move(num - 1, B, A, C);//递归,把B塔上编号1~n-1的圆盘移到C上,以A为辅助塔
}
}
}
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