汉诺塔的变种

1. 有三根柱子，在一根柱子上从下往上按大小顺序摞着n片圆盘。要求把圆盘从下面开始按大小顺序重新摆放在另一根柱子上。并且规定，在小圆盘上不能放大圆盘，在三根柱子之间一次只能移动一个圆盘。

package hanoi;

/**
 * formulas:
 * T0 = 0
 * Tn = Tn-1 + 1
 * 
 * closed form:
 * Tn = 2(n) -1
 * 
 * @author yaoh
 *
 */
public class SimpleHanoi {

    public static int count = 0;

    public static void hanoi(String a, String b, String c, int n) {
        if(n <= 0)  System.out.println("No move needed.");
        
        if(n == 1) {
            System.out.println("Step "+ ++count+": move "+n+" from "+a+" to "+c);
        } else {
            hanoi(a, c, b, n - 1);
            
            System.out.println("Step "+ ++count+ ": move "+n+" from "+a+" to "+c);
            
            hanoi(b, a, c, n - 1);
        }
    }
    
    public static void main(String[] args) {
        hanoi("a", "b", "c", 5);
        
        System.out.println("Overall steps: " + count);
    }
}

2. 有四根柱子，在一根柱子上从下往上按大小顺序摞着n片圆盘。要求把圆盘从下面开始按大小顺序重新摆放在另一根柱子上。并且规定，在小圆盘上不能放大圆盘，在四根柱子之间一次只能移动一个圆盘。

package hanoi;

/**
 * formula
 * T1 = 1
 * T2 = 3
 * Tn = 2T(n-2) + 3
 * 
 * closed form:
 * 
 * 
 * @author yaoh
 *
 */
public class FourHanoi {
	
	public static int count = 0;
	
	public static void hanoi(String a, String b, String c, String d, int n) {
		if(n == 1) {
			System.out.println("Step " + ++count + ": move " + n + " from " + a + " to " + d);
		}else if(n == 2) {
			System.out.println("Step " + ++count + ": move " + (n - 1) + " from " + a + " to " + b);
			System.out.println("Step " + ++count + ": move " + n + " from " + a + " to " + d);
			System.out.println("Step " + ++count + ": move " + (n - 1) + " from " + b + " to " + d);
		}
		else {
			hanoi(a, b, d, c, n - 2);
			
			System.out.println("Step " + ++count + ": move " + (n - 1) + " from " + a + " to " + b);
			System.out.println("Step " + ++count + ": move " + n + " from " + a + " to " + d);
			System.out.println("Step " + ++count + ": move " + (n - 1) + " from " + b + " to " + d);
			
			hanoi(c, a, b, d, n - 2);
		}
	}
	
	public static void main(String[] args) {
		hanoi("a", "b", "c", "d", 6);
		
		System.out.println("Overall steps: " + count);
	}
}

3. 有三根柱子，在一根柱子上从下往上按大小顺序摞着m片圆盘， 另一根柱子上从下往上按大小顺序摞着n片圆盘，要求把圆盘从下面开始按大小顺序重新摆放在最后一根柱子上。并且规定，在小圆盘上不能放大圆盘，在三根柱子之间一次只能移动一个圆盘。

4. 有三根柱子，在三根柱子上从下往上按大小顺序分别摞着m，n，l片圆盘， 要求把圆盘从下面开始按大小顺序重新摆放在最后一根柱子上。并且规定，在小圆盘上不能放大圆盘，在三根柱子之间一次只能移动一个圆盘。

最后两道题两个并做一个写，太jb复杂了，回头看看别人有没什么好办法

/*Problem Statement
     	There are three stacks of crates - two of them outside of the warehouse, and one inside the warehouse. 
     	We have a crane that can move one crate at a time, and we would like to move all of the crates to the stack inside the warehouse. 
     	A heavier crate can never be stacked on top of a lighter crate, and all three initial stacks obey that rule.
     	Create a class CraneWork that contains a method moves that is given int[]s stack1, stack2, and warehouse containing the initial three stacks, 
     	and returns the minimum number of moves required to move all the crates into the warehouse stack. 
     	The elements of stack1, stack2, and warehouse represent the weights of the crates and are given from top to bottom 
     	(and thus in non-decreasing order of weight).
     	
Definition
	Class: 	CraneWork
	Method: 	moves
	Parameters: 	int[], int[], int[]
	Returns: 	int
	Method signature: 	int moves(int[] stack1, int[] stack2, int[] warehouse)
	(be sure your method is public)

Constraints
 	stack1, stack2, and warehouse will each contain between 0 and 20 elements, inclusive.
 	The total number of elements in the three stacks will be between 1 and 20, inclusive.
 	Each element in the three stacks will be between 1 and 200, inclusive.
 	stack1, stack2, and warehouse will each be in non-decreasing order.

Examples

	0){3,50}   {}     {1,2,50,50,50}
	Returns: 12
	Move 3 to stack2, 1 to stack1, 
		2 to stack2, 1 to stack2, 
		50 to warehouse, 1 to warehouse, 
		2 to stack1, 1 to stack1, 
		3 to warehouse, 1 to stack2, 
		2 to warehouse, 1 to warehouse.

	1){50}    {50}    {10,20,30}
	Returns: 17
	Start by moving 50 from stack2 to stack1. 
	It then takes 7 moves to transfer the 10,20,30 
	to stack 2, 2 moves to transfer the 2 50's to the warehouse, 
	and 7 more to transfer the 10,20,30 to the warehouse.

	2){}      {}      {2,5,6,7}
	Returns: 0
	All the crates are already in the warehouse.

	3){1,2,3}  {}     {}
	Returns: 7
	Move 1 from stack1 to warehouse, 2 from stack1 to stack2, 
	1 from warehouse to stack2, 3 from stack1 to warehouse, 
	1 from stack2 to stack1, 2 from stack2 to warehouse, 1 from stack1 to warehouse.

	This problem statement is the exclusive and proprietary property of TopCoder, Inc. 
	Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. 
	is strictly prohibited. (c)2003, TopCoder, Inc. All rights reserved. */

package cranework_2;

public class CraneWork {
	
  	public static void moves(int[] stack_1, int[] stack_2, int[] ware_house) throws Exception{
  		CrateStack stack1 = new CrateStack(stack_1);
  		CrateStack stack2 = new CrateStack(stack_2);
  		CrateStack warehouse = new CrateStack(ware_house);
  		
  		show(stack1, stack2, warehouse);
  		moves(stack1, 0, stack2, 0, warehouse, 0);  		
	}
  	
  	/**
  	 * @param stack1
  	 * @param cursor1
  	 * @param stack2
  	 * @param cursor2
  	 * @param stack3
  	 * @param cursor3
  	 * @throws Exception
  	 */
  	public static void moves(CrateStack stack1, int cursor1, CrateStack stack2, int cursor2, CrateStack stack3, int cursor3) throws Exception{
  		
  		if(cursor1 == stack1.root && cursor2 == stack2.root) return;
  		
  		if(cursor1 == stack1.root) {
  	  		if(cursor3 == stack3.root) {
  	  			moves(stack2, cursor2 + 1, stack3, stack3.root, stack1, stack1.root);
  	  			
  	  			stack3.pushCrate(stack2.popCrate());
  	  				
  	  			show(stack1, stack2, stack3);
  	  			
  	  			moves(stack1, cursor1, stack2, stack2.root, stack3, stack3.root);
  	  		} else if (stack2.getValue(cursor2) > stack3.getValue(cursor3)) {
				moves(stack2, cursor2 + 1, stack3, cursor3, stack1, stack1.root);

				stack3.pushCrate(stack2.popCrate());

				show(stack1, stack2, stack3);

				moves(stack1, cursor1, stack2, stack2.root, stack3, stack3.root);
  			}else {
  				cursor3 = stack3.find(stack2.getValue(cursor2));
  				
  				moves(stack2, cursor2 + 1, stack3, cursor3, stack1, stack1.root);
  				
  				stack3.pushCrate(stack2.popCrate());
  				
  				show(stack1, stack2, stack3);
				
  				moves(stack1, cursor1, stack2, stack2.root, stack3, stack3.root);
  			}
  		} else if(cursor2 == stack2.root) {	
  			if(cursor3 == stack3.root) {
  	  			moves(stack1, cursor1 + 1, stack3, stack3.root, stack2, stack2.root);
  	  				
  	  			stack3.pushCrate(stack1.popCrate());
  	  				
  	  			show(stack1, stack2, stack3);
  	  				
  	  			moves(stack2, cursor2, stack1, stack1.root, stack3, stack3.root);
  	  		} else if (stack1.getValue(cursor1) > stack3.getValue(cursor3)) {
  				moves(stack1, cursor1 + 1, stack3, cursor3, stack2, stack2.root);
  				
  				stack3.pushCrate(stack1.popCrate());
  				
  				show(stack1, stack2, stack3);
				
  				moves(stack2, cursor2, stack1, stack1.root, stack3, stack3.root);
  			}else {
  				cursor3 = stack3.find(stack1.getValue(cursor1));
  				
  				moves(stack1, cursor1 + 1, stack3, cursor3, stack2, stack2.root);
  				
  				stack3.pushCrate(stack1.popCrate());
  				
  				show(stack1, stack2, stack3);
				
  				moves(stack2, cursor2, stack1, stack1.root, stack3, stack3.root);
  			}
  		} else if(cursor3 == stack3.root) {
  			if (stack1.getValue(cursor1) > stack2.getValue(cursor2)) {
  				moves(stack1, cursor1 + 1, stack3, stack3.root, stack2, cursor2);
  				
  				stack3.pushCrate(stack1.popCrate());
  				
  				show(stack1, stack2, stack3);
  				
  				moves(stack2, cursor2, stack1, stack1.root, stack3, stack3.root);
  			} else {
  				moves(stack2, cursor2 + 1, stack3, stack3.root, stack1, cursor1);
  				
  				stack3.pushCrate(stack2.popCrate());
  				
  				show(stack1, stack2, stack3);
  				
  				moves(stack1, cursor1, stack2, stack2.root, stack3, stack3.root);
  			}
  		} else if (stack3.getValue(cursor3) > stack2.getValue(cursor2) && stack3.getValue(cursor3) > stack1.getValue(cursor1)) {
			if (stack1.getValue(cursor1) > stack2.getValue(cursor2)) {
				
				cursor3 = stack3.find(stack1.getValue(cursor1));
				
				moves(stack1, cursor1 + 1, stack3, cursor3, stack2, cursor2);
				
				stack3.pushCrate(stack1.popCrate());
				
				show(stack1, stack2, stack3);
				
				moves(stack2, cursor2, stack1, stack1.root, stack3, stack3.root);
			} else {
				cursor3 = stack3.find(stack2.getValue(cursor2));
				
				moves(stack2, cursor2 + 1, stack3, cursor3, stack1, cursor1);

				stack3.pushCrate(stack2.popCrate());

				show(stack1, stack2, stack3);
				
				moves(stack1, cursor1, stack2, stack2.root, stack3, stack3.root);
			}
		} else {
			if (stack1.getValue(cursor1) > stack2.getValue(cursor2)) {
				moves(stack1, cursor1 + 1, stack3, cursor3, stack2, cursor2);
				
				stack3.pushCrate(stack1.popCrate());
				
				show(stack1, stack2, stack3);
				
				moves(stack2, cursor2, stack1, stack1.root, stack3, stack3.root);
			}
			else {
				moves(stack2, cursor2 + 1, stack3, cursor3, stack1, cursor1);

				stack3.pushCrate(stack2.popCrate());

				show(stack1, stack2, stack3);

				moves(stack1, cursor1, stack2, stack2.root, stack3, stack3.root);
			}
		}
	}
  	
	public static void show(CrateStack stack1, CrateStack stack2, CrateStack stack3){
		System.out.println("Round:");
		stack1.showStack();
		stack2.showStack();
		stack3.showStack();
		//System.out.print("\n " + cursor1.weight + "   " + cursor2.weight + "   " +  cursor3.weight);
		System.out.println("\n");
	}
}

class CrateStack {
	
	private int[] stack = new int[20];
	
	public int root = 0;

	public CrateStack(int weight) {
		stack[0] = weight;
		root++;
	}
	
	public CrateStack(int[] array) {
		for(int i = 0; i < array.length; i++) {
			stack[i] = array[i];
		}
		root = array.length;
	}
	
	//Push a Value into Stack
	public void pushCrate(int value) {
		stack[root] = value;
		root++;
	}
	
	//Pop a Value into Stack
	public int popCrate() throws Exception{
		if(root != 0) {
			root--;
			int result = stack[root];
			stack[root] = 0;
			return result;
		}
		throw new NullPointerException();
	}
	
	
	public boolean isTop(int cursor) {
		if(cursor == root - 1) return true;
		return false;
	}
	
	public void showStack() {
		try {
			if (root == 0) {
				System.out.print("{}");
			} else {
				int temp = root - 1;
				System.out.print("{");
				while (temp >= 0) {
					System.out.print(stack[temp] + ",");
					temp--;
				}
				System.out.print("}");
			}
		} catch (Exception e) {
			//
		}
	}
	
	public int find (int temp) {
		int cursor = 0;
		if (temp != 0) {
			while(cursor != root) {
				if (stack[cursor] < temp) return cursor;
				cursor++;
			}
		}
		
		return root;
	}
	
	public int getValue(int index) {
		return stack[index];
	}
	
}

最近做了些思路上的转变，并对汉诺塔有了新的理解，回想之前的复杂汉诺塔的程序，觉得还是可以改进很多的。

package hanoi;

import java.util.Stack;

public class MultiHanoi {

	public static int count = 0;
	

	public static HanoiStack Largest(HanoiStack stackA, int locA, HanoiStack stackB, int locB, HanoiStack stackC, int locC) {
		if(stackA.get(locA) > stackB.get(locB) && stackA.get(locA) > stackC.get(locC)) return stackA;
		else if (stackB.get(locB) > stackA.get(locA) && stackB.get(locB) > stackC.get(locC)) return stackB;
		
		return stackC;
	}
	
	public static void multiHanoi(HanoiStack stackA, int locA,HanoiStack stackB, int locB, HanoiStack stackC, int locC) {
		if((stackA.size() == 0 || stackA.size() <= locA) && (stackB.size() == 0 || stackB.size() <= locB)) {
			return;
		} else if(stackA.size() == 0 || stackA.size() <= locA) {
			hanoi(stackB, locB, stackA, stackC);
		} else if(stackB.size() == 0 || stackB.size() <= locB) {
			hanoi(stackA, locA, stackB, stackC);
		} else {
			if(Largest(stackA, locA, stackB, locB, stackC, locC).name.equals(stackA.name)) {
				multiHanoi(stackA, locA + 1, stackC, locC, stackB, locB);
				int value = stackA.pop();
				stackC.push(value);
				System.out.println("Step " + ++count + ": move " + value + " from " + stackA.name + " to " + stackC.name);
				hanoi(stackB, locB, stackA, stackC);
			} else if(Largest(stackA, locA, stackB, locB, stackC, locC).name.equals(stackB.name)) {
				multiHanoi(stackB, locB + 1, stackC, locC, stackA, locA);
				int value = stackB.pop();
				stackC.push(value);
				System.out.println("Step " + ++count + ": move " + value + " from " + stackB.name + " to " + stackC.name);
				hanoi(stackA, locA, stackB, stackC);
			} else if(Largest(stackA, locA, stackB, locB, stackC, locC).name.equals(stackC.name)) {
				locC++;
				multiHanoi(stackA,locA, stackB, locB, stackC, locC);
			}
			
		}
		
	}
	
	public static void hanoi(HanoiStack sA, int locA, HanoiStack sB, HanoiStack sC) {
		if(sA.size() == locA + 1) {
			int value = sA.pop();
			sC.push(value);
			System.out.println("Step "+ ++count+ ": move "+value+" from "+sA.name+" to "+sC.name);
		} else {
			int locB = sB.size();
			
			hanoi(sA, locA + 1, sC, sB);
			
			int value = sA.pop();
			sC.push(value);
			System.out.println("Step "+ ++count+ ": move "+value+" from "+sA.name+" to "+sC.name);
			
			hanoi(sB, locB, sA, sC);
		}
		
		
	}
	
	public static void main(String[] args) {
		HanoiStack stackA = new HanoiStack("A");
		HanoiStack stackB = new HanoiStack("B");
		HanoiStack stackC = new HanoiStack("C");
		
		stackA.push(10);
		stackA.push(7);
		stackA.push(6);
		stackA.push(5);
		stackA.push(1);

		stackB.push(9);
		stackB.push(8);
		stackB.push(4);
		stackB.push(3);
		stackB.push(2);
		
		multiHanoi(stackA, 0, stackB, 0, stackC, 0);
		
		System.out.println("Overall steps: " + count);
	}
}

class HanoiStack {
	
	public String name;
	
	private Stack<Integer> stack;
	
	
	public HanoiStack(String name) {
		stack = new Stack<Integer>();
		
		this.name = name;
	}
	
	public void push(int val) {
		stack.push(val);
	}
	
	public int pop() {
		if(stack.isEmpty()) return 0;
		
		return stack.pop();
	}
	
	public int size() {
		return stack.size();
	}
	
	public int get(int loc) {
		if(loc >= stack.size()) return Integer.MIN_VALUE;
		return stack.get(loc);
	}
}

现在看起来比上一个程序简单明了了许多，但是其实步数是一样的，性能并没有增加。

不过基本上这已经算是最优的解法了。