河内塔是一个数学难题。它由三个杆子和许多不同大小的圆盘组成，可以滑到任何杆子上。拼图从一个圆盘开始，在一个极中按照尺寸升序排列整齐，最小的在顶部，从而形成一个圆锥形状。拼图的目标是在第三个极点(例如辅助极点)的帮助下将所有圆盘从一个极点(例如“源极点”)移动到另一个极点(例如“目的极点”)。
拼图有以下两条规则：
1. 不能将较大的磁盘放在较小的磁盘上
2. 一次只能移动一个磁盘
我们已经讨论了河内塔的递归解决方案。我们还看到，对于 n 个磁盘，总共需要 2 n – 1 次移动。
迭代算法：
1. Calculate the total number of moves required i.e. "pow(2, n)
- 1" here n is number of disks.
2. If number of disks (i.e. n) is even then interchange destination
pole and auxiliary pole.
3. for i = 1 to total number of moves:
if i%3 == 1:
legal movement of top disk between source pole and
destination pole
if i%3 == 2:
legal movement top disk between source pole and
auxiliary pole
if i%3 == 0:
legal movement top disk between auxiliary pole
and destination pole 例子：
Let us understand with a simple example with 3 disks:
So, total number of moves required = 7
S A D
When i= 1, (i % 3 == 1) legal movement between‘S’ and ‘D’ 
When i = 2, (i % 3 == 2) legal movement between ‘S’ and ‘A’ 
When i = 3, (i % 3 == 0) legal movement between ‘A’ and ‘D’ ’
When i = 4, (i % 3 == 1) legal movement between ‘S’ and ‘D’ 
When i = 5, (i % 3 == 2) legal movement between ‘S’ and ‘A’
When i = 6, (i % 3 == 0) legal movement between ‘A’ and ‘D’ 
When i = 7, (i % 3 == 1) legal movement between ‘S’ and ‘D’ 
所以，毕竟这些目标极点包含所有的大小顺序。
观察上面的迭代，我们可以认为移动了最小磁盘以外的磁盘后，下一个要移动的磁盘一定是最小的磁盘，因为它是搁在备用杆上的顶部磁盘，没有其他选择移动一个磁盘。
C++
// C Program for Iterative Tower of Hanoi
#include
#include
#include
#include
// A structure to represent a stack
struct Stack
{
unsigned capacity;
int top;
int *array;
};
// function to create a stack of given capacity.
struct Stack* createStack(unsigned capacity)
{
struct Stack* stack =
(struct Stack*) malloc(sizeof(struct Stack));
stack -> capacity = capacity;
stack -> top = -1;
stack -> array =
(int*) malloc(stack -> capacity * sizeof(int));
return stack;
}
// Stack is full when top is equal to the last index
int isFull(struct Stack* stack)
{
return (stack->top == stack->capacity - 1);
}
// Stack is empty when top is equal to -1
int isEmpty(struct Stack* stack)
{
return (stack->top == -1);
}
// Function to add an item to stack. It increases
// top by 1
void push(struct Stack *stack, int item)
{
if (isFull(stack))
return;
stack -> array[++stack -> top] = item;
}
// Function to remove an item from stack. It
// decreases top by 1
int pop(struct Stack* stack)
{
if (isEmpty(stack))
return INT_MIN;
return stack -> array[stack -> top--];
}
//Function to show the movement of disks
void moveDisk(char fromPeg, char toPeg, int disk)
{
printf("Move the disk %d from \'%c\' to \'%c\'\n",
disk, fromPeg, toPeg);
}
// Function to implement legal movement between
// two poles
void moveDisksBetweenTwoPoles(struct Stack *src,
struct Stack *dest, char s, char d)
{
int pole1TopDisk = pop(src);
int pole2TopDisk = pop(dest);
// When pole 1 is empty
if (pole1TopDisk == INT_MIN)
{
push(src, pole2TopDisk);
moveDisk(d, s, pole2TopDisk);
}
// When pole2 pole is empty
else if (pole2TopDisk == INT_MIN)
{
push(dest, pole1TopDisk);
moveDisk(s, d, pole1TopDisk);
}
// When top disk of pole1 > top disk of pole2
else if (pole1TopDisk > pole2TopDisk)
{
push(src, pole1TopDisk);
push(src, pole2TopDisk);
moveDisk(d, s, pole2TopDisk);
}
// When top disk of pole1 < top disk of pole2
else
{
push(dest, pole2TopDisk);
push(dest, pole1TopDisk);
moveDisk(s, d, pole1TopDisk);
}
}
//Function to implement TOH puzzle
void tohIterative(int num_of_disks, struct Stack
*src, struct Stack *aux,
struct Stack *dest)
{
int i, total_num_of_moves;
char s = 'S', d = 'D', a = 'A';
//If number of disks is even, then interchange
//destination pole and auxiliary pole
if (num_of_disks % 2 == 0)
{
char temp = d;
d = a;
a = temp;
}
total_num_of_moves = pow(2, num_of_disks) - 1;
//Larger disks will be pushed first
for (i = num_of_disks; i >= 1; i--)
push(src, i);
for (i = 1; i <= total_num_of_moves; i++)
{
if (i % 3 == 1)
moveDisksBetweenTwoPoles(src, dest, s, d);
else if (i % 3 == 2)
moveDisksBetweenTwoPoles(src, aux, s, a);
else if (i % 3 == 0)
moveDisksBetweenTwoPoles(aux, dest, a, d);
}
}
// Driver Program
int main()
{
// Input: number of disks
unsigned num_of_disks = 3;
struct Stack *src, *dest, *aux;
// Create three stacks of size 'num_of_disks'
// to hold the disks
src = createStack(num_of_disks);
aux = createStack(num_of_disks);
dest = createStack(num_of_disks);
tohIterative(num_of_disks, src, aux, dest);
return 0;
} Java
// Java program for iterative
// Tower of Hanoi
class TOH{
// A structure to represent a stack
class Stack
{
int capacity;
int top;
int array[];
}
// Function to create a stack of given capacity.
Stack createStack(int capacity)
{
Stack stack = new Stack();
stack.capacity = capacity;
stack.top = -1;
stack.array = new int[capacity];
return stack;
}
// Stack is full when the top is equal
// to the last index
boolean isFull(Stack stack)
{
return (stack.top == stack.capacity - 1);
}
// Stack is empty when top is equal to -1
boolean isEmpty(Stack stack)
{
return (stack.top == -1);
}
// Function to add an item to stack.It
// increases top by 1
void push(Stack stack, int item)
{
if (isFull(stack))
return;
stack.array[++stack.top] = item;
}
// Function to remove an item from stack.It
// decreases top by 1
int pop(Stack stack)
{
if (isEmpty(stack))
return Integer.MIN_VALUE;
return stack.array[stack.top--];
}
// Function to implement legal movement between
// two poles
void moveDisksBetweenTwoPoles(Stack src, Stack dest,
char s, char d)
{
int pole1TopDisk = pop(src);
int pole2TopDisk = pop(dest);
// When pole 1 is empty
if (pole1TopDisk == Integer.MIN_VALUE)
{
push(src, pole2TopDisk);
moveDisk(d, s, pole2TopDisk);
}
// When pole2 pole is empty
else if (pole2TopDisk == Integer.MIN_VALUE)
{
push(dest, pole1TopDisk);
moveDisk(s, d, pole1TopDisk);
}
// When top disk of pole1 > top disk of pole2
else if (pole1TopDisk > pole2TopDisk)
{
push(src, pole1TopDisk);
push(src, pole2TopDisk);
moveDisk(d, s, pole2TopDisk);
}
// When top disk of pole1 < top disk of pole2
else
{
push(dest, pole2TopDisk);
push(dest, pole1TopDisk);
moveDisk(s, d, pole1TopDisk);
}
}
// Function to show the movement of disks
void moveDisk(char fromPeg, char toPeg, int disk)
{
System.out.println("Move the disk " + disk +
" from " + fromPeg +
" to " + toPeg);
}
// Function to implement TOH puzzle
void tohIterative(int num_of_disks, Stack
src, Stack aux, Stack dest)
{
int i, total_num_of_moves;
char s = 'S', d = 'D', a = 'A';
// If number of disks is even, then
// interchange destination pole and
// auxiliary pole
if (num_of_disks % 2 == 0)
{
char temp = d;
d = a;
a = temp;
}
total_num_of_moves = (int)(Math.pow(
2, num_of_disks) - 1);
// Larger disks will be pushed first
for(i = num_of_disks; i >= 1; i--)
push(src, i);
for(i = 1; i <= total_num_of_moves; i++)
{
if (i % 3 == 1)
moveDisksBetweenTwoPoles(src, dest, s, d);
else if (i % 3 == 2)
moveDisksBetweenTwoPoles(src, aux, s, a);
else if (i % 3 == 0)
moveDisksBetweenTwoPoles(aux, dest, a, d);
}
}
// Driver code
public static void main(String[] args)
{
// Input: number of disks
int num_of_disks = 3;
TOH ob = new TOH();
Stack src, dest, aux;
// Create three stacks of size 'num_of_disks'
// to hold the disks
src = ob.createStack(num_of_disks);
dest = ob.createStack(num_of_disks);
aux = ob.createStack(num_of_disks);
ob.tohIterative(num_of_disks, src, aux, dest);
}
}
// This code is contibuted by Sumit GhoshC#
// C# program for iterative
// Tower of Hanoi
using System;
class GFG
{
// A structure to represent a stack
public class Stack
{
public int capacity;
public int top;
public int []array;
}
// function to create a stack of given capacity.
Stack createStack(int capacity)
{
Stack stack = new Stack();
stack.capacity = capacity;
stack.top = -1;
stack.array = new int[capacity];
return stack;
}
// Stack is full when top is equal to the last index
Boolean isFull(Stack stack)
{
return (stack.top == stack.capacity - 1);
}
// Stack is empty when top is equal to -1
Boolean isEmpty(Stack stack)
{
return (stack.top == -1);
}
// Function to add an item to stack.
// It increases top by 1
void push(Stack stack,int item)
{
if(isFull(stack))
return;
stack.array[++stack.top] = item;
}
// Function to remove an item from stack.
// It decreases top by 1
int pop(Stack stack)
{
if(isEmpty(stack))
return int.MinValue;
return stack.array[stack.top--];
}
// Function to implement legal
// movement between two poles
void moveDisksBetweenTwoPoles(Stack src, Stack dest,
char s, char d)
{
int pole1TopDisk = pop(src);
int pole2TopDisk = pop(dest);
// When pole 1 is empty
if (pole1TopDisk == int.MinValue)
{
push(src, pole2TopDisk);
moveDisk(d, s, pole2TopDisk);
}
// When pole2 pole is empty
else if (pole2TopDisk == int.MinValue)
{
push(dest, pole1TopDisk);
moveDisk(s, d, pole1TopDisk);
}
// When top disk of pole1 > top disk of pole2
else if (pole1TopDisk > pole2TopDisk)
{
push(src, pole1TopDisk);
push(src, pole2TopDisk);
moveDisk(d, s, pole2TopDisk);
}
// When top disk of pole1 < top disk of pole2
else
{
push(dest, pole2TopDisk);
push(dest, pole1TopDisk);
moveDisk(s, d, pole1TopDisk);
}
}
// Function to show the movement of disks
void moveDisk(char fromPeg, char toPeg, int disk)
{
Console.WriteLine("Move the disk "+disk +
" from "+fromPeg+" to "+toPeg);
}
// Function to implement TOH puzzle
void tohIterative(int num_of_disks, Stack
src, Stack aux, Stack dest)
{
int i, total_num_of_moves;
char s = 'S', d = 'D', a = 'A';
// If number of disks is even, then interchange
// destination pole and auxiliary pole
if (num_of_disks % 2 == 0)
{
char temp = d;
d = a;
a = temp;
}
total_num_of_moves = (int) (Math.Pow(2, num_of_disks) - 1);
// Larger disks will be pushed first
for (i = num_of_disks; i >= 1; i--)
push(src, i);
for (i = 1; i <= total_num_of_moves; i++)
{
if (i % 3 == 1)
moveDisksBetweenTwoPoles(src, dest, s, d);
else if (i % 3 == 2)
moveDisksBetweenTwoPoles(src, aux, s, a);
else if (i % 3 == 0)
moveDisksBetweenTwoPoles(aux, dest, a, d);
}
}
// Driver code
public static void Main(String []args)
{
// Input: number of disks
int num_of_disks = 3;
GFG ob = new GFG();
Stack src, dest, aux;
// Create three stacks of size 'num_of_disks'
// to hold the disks
src = ob.createStack(num_of_disks);
dest = ob.createStack(num_of_disks);
aux = ob.createStack(num_of_disks);
ob.tohIterative(num_of_disks, src, aux, dest);
}
}
// This code is Contributed by Arnab Kundu输出：
Move the disk 1 from 'S' to 'D'
Move the disk 2 from 'S' to 'A'
Move the disk 1 from 'D' to 'A'
Move the disk 3 from 'S' to 'D'
Move the disk 1 from 'A' to 'S'
Move the disk 2 from 'A' to 'D'
Move the disk 1 from 'S' to 'D'相关文章
- 递归函数
- 尾递归
- 递归测验
如果您希望与专家一起参加现场课程，请参阅DSA 现场工作专业课程和学生竞争性编程现场课程。