红黑树实现（Java语言）

最近在看红黑树，也想自己写程序实现一下，因为红黑树的删除还没有看，所以程序中并没有包含删除操作，等看完了再补上，呵呵。。。

至于红黑树的原理我就不多说了，我是参考<算法导论>中的伪代码写的程序。

代码实现如下：

package com.datastructure.tree;

public class MyRbTree {

RbTreeNode root=null;
RbTreeNode nilNode=null;

public RbTreeNode getRoot() {
return root;
}

public MyRbTree()
{
this.nilNode=new RbTreeNode(-1);
this.nilNode.color=TreeNodeColor.Black;
this.nilNode.left=null;
this.nilNode.right=null;
this.nilNode.parent=null;
this.root=this.nilNode;
}

/**
* @param args
*/
public static void main(String[] args) {
// TODO Auto-generated method stub
MyRbTree mytree=new MyRbTree();
int[] array={2,5,3,4,1,0};
for(int i=0;i<array.length;i++)
{
mytree.insert(array[i]);
mytree.preorder(mytree.getRoot());
System.out.println();

}

}

private void leftRotate(MyRbTree tree,RbTreeNode x)
{
RbTreeNode y=x.right;
x.right=y.left;
y.left.parent=x;
y.parent=x.parent;
if(x.parent==this.nilNode)
{
tree.root=y;
}else
{
if(x==x.parent.left)
x.parent.left=y;
else
x.parent.right=y;
}
y.left=x;
x.parent=y;
}

private void rightRotate(MyRbTree tree,RbTreeNode y)
{
RbTreeNode x=y.left;
y.left=x.right;
x.right.parent=y;
x.parent=y.parent;
if(y.parent==this.nilNode)
{
tree.root=x;
}else
{
if(y==y.parent.left)
y.parent.left=x;
else
y.parent.right=x;
}
x.right=y;
y.parent=x;
}

private void insert(MyRbTree tree,int value)
{
RbTreeNode y=this.nilNode;
RbTreeNode x=tree.root;
RbTreeNode z=new RbTreeNode(value);

while(x!=this.nilNode)
{
y=x;
if(value<x.key)
x=x.left;
else
x=x.right;
}
z.parent=y;
if(y==this.nilNode)
{
tree.root=z;
}else
{
if(value<y.key)
{
y.left=z;
}
else
{
y.right=z;
}
}
z.left=this.nilNode;
z.right=this.nilNode;

insertFixUp(tree,z);

}

public void insert(int value)
{
insert(this,value);
}

private void insertFixUp(MyRbTree tree,RbTreeNode z)
{
while(z.parent.color==TreeNodeColor.Red)
{
if(z.parent==z.parent.parent.left)
{
RbTreeNode uncle=z.parent.parent.right;
if(uncle.color==TreeNodeColor.Red)
{
z.parent.color=TreeNodeColor.Black;
uncle.color=TreeNodeColor.Black;
z.parent.parent.color=TreeNodeColor.Red;
z=z.parent.parent;
}else
{
if(z==z.parent.right)
{
z=z.parent;
leftRotate(tree,z);
}
z.parent.color=TreeNodeColor.Black;
z.parent.parent.color=TreeNodeColor.Red;
rightRotate(tree,z.parent.parent);
}
}else if(z.parent==z.parent.parent.right)
{
RbTreeNode uncle=z.parent.parent.left;
if(uncle.color==TreeNodeColor.Red)
{
z.parent.color=TreeNodeColor.Black;
uncle.color=TreeNodeColor.Black;
z.parent.parent.color=TreeNodeColor.Red;
z=z.parent.parent;
}else
{
if(z==z.parent.left)
{
z=z.parent;
rightRotate(tree,z);
}
z.parent.color=TreeNodeColor.Black;
z.parent.parent.color=TreeNodeColor.Red;
leftRotate(tree,z.parent.parent);
}

}
}
tree.root.color=TreeNodeColor.Black;

}

public void preorder(RbTreeNode root)
{
if(root!=null)
{
preorder(root.left);
getNodeInfo(root);
preorder(root.right);
}
}

public void getNodeInfo(RbTreeNode node)
{
if(node!=this.nilNode)
{
System.out.println(node.key+" "+node.color.toString());
}
}

}

class RbTreeNode{
TreeNodeColor color=TreeNodeColor.Red;
int key=-1;
RbTreeNode left=null;
RbTreeNode right=null;
RbTreeNode parent=null;

public RbTreeNode(int value)
{
this.key=value;
}
}

运行结果如下所示：

2 Black

2 Black
5 Red

2 Red
3 Black
5 Red

2 Black
3 Black
4 Red
5 Black

1 Red
2 Black
3 Black
4 Red
5 Black

0 Red
1 Black
2 Red
3 Black
4 Red
5 Black

从运行结果可以看出程序是没有问题的。有改进的地方大家可以提啊，谢谢！

今天看了看算法导论中关于红黑树删除的有关知识，自己实现了一下，现添加到上面的程序中，程序代码和运行结果如下所示，我是严格按照算法导论的伪代码写的，相信大家可以看得很清楚。

package com.datastructure.tree;

public class MyRbTree {

RbTreeNode root=null;
RbTreeNode nilNode=null;

public RbTreeNode getRoot() {
return root;
}

public MyRbTree()
{
this.nilNode=new RbTreeNode(-1);
this.nilNode.color=TreeNodeColor.Black;
this.nilNode.left=null;
this.nilNode.right=null;
this.nilNode.parent=null;
this.root=this.nilNode;
}

/**
* @param args
*/
public static void main(String[] args) {
// TODO Auto-generated method stub
MyRbTree mytree=new MyRbTree();
int[] array={41,38,31,12,19,8};
for(int i=0;i<array.length;i++)
{
System.out.println("插入"+array[i]);
mytree.insert(array[i]);
mytree.preorder(mytree.getRoot());
System.out.println();
}
for(int i=5;i>=0;i--)
{
System.out.println("删除"+array[i]);
mytree.delete(array[i]);
mytree.preorder(mytree.getRoot());
System.out.println();
}

}

private void leftRotate(MyRbTree tree,RbTreeNode x)
{
RbTreeNode y=x.right;
x.right=y.left;
y.left.parent=x;
y.parent=x.parent;
if(x.parent==this.nilNode)
{
tree.root=y;
}else
{
if(x==x.parent.left)
x.parent.left=y;
else
x.parent.right=y;
}
y.left=x;
x.parent=y;
}

private void rightRotate(MyRbTree tree,RbTreeNode y)
{
RbTreeNode x=y.left;
y.left=x.right;
x.right.parent=y;
x.parent=y.parent;
if(y.parent==this.nilNode)
{
tree.root=x;
}else
{
if(y==y.parent.left)
y.parent.left=x;
else
y.parent.right=x;
}
x.right=y;
y.parent=x;
}

private void insert(MyRbTree tree,int value)
{
RbTreeNode y=this.nilNode;
RbTreeNode x=tree.root;
RbTreeNode z=new RbTreeNode(value);

while(x!=this.nilNode)
{
y=x;
if(value<x.key)
x=x.left;
else
x=x.right;
}
z.parent=y;
if(y==this.nilNode)
{
tree.root=z;
}else
{
if(value<y.key)
{
y.left=z;
}
else
{
y.right=z;
}
}
z.left=this.nilNode;
z.right=this.nilNode;

insertFixUp(tree,z);

}

public void insert(int value)
{
insert(this,value);
}

private RbTreeNode search(MyRbTree tree,int value)
{
RbTreeNode node=tree.root;
while((node!=tree.nilNode)&&(node.key!=value))
{
if(value<node.key)
{
node=node.left;
}else
{
node=node.right;
}
}
return node;
}

public boolean search(int value)
{
if(search(this,value)!=this.nilNode)
return true;
else
return false;
}

public RbTreeNode minimum(RbTreeNode x)
{
while(x.left!=this.nilNode)
{
x=x.left;
}
return x;
}

public RbTreeNode successor(RbTreeNode x)
{
if(x.right!=this.nilNode)
{
return minimum(x.right);
}
RbTreeNode y=x.parent;
while(y!=this.nilNode&&x==y.right)
{
x=y;
y=y.parent;
}
return y;
}

private boolean delete(MyRbTree tree,int value)
{
RbTreeNode z=search(tree,value);
if(z==tree.nilNode)
{
return false;
}
RbTreeNode y=null;
if(z.left==tree.nilNode||z.right==tree.nilNode)
{
y=z;
}else
{
y=successor(z);
}
RbTreeNode x=null;
if(y.left!=tree.nilNode)
{
x=y.left;
}else
{
x=y.right;
}
x.parent=y.parent;
if(y.parent==tree.nilNode)
{
this.root=x;
}else
{
if(y==y.parent.left)
{
y.parent.left=x;
}else
{
y.parent.right=x;
}
}
if(y!=z)
{
z.key=y.key;
}
if(y.color==TreeNodeColor.Black)
{
deleteFixUp(tree,x);
}
return true;
}

private void deleteFixUp(MyRbTree tree,RbTreeNode x)
{
while(x!=tree.root&&x.color==TreeNodeColor.Black)
{
if(x==x.parent.left)
{
RbTreeNode w=x.parent.right;
if(w.color==TreeNodeColor.Red)
{
w.color=TreeNodeColor.Black;
x.color=TreeNodeColor.Red;
leftRotate(tree,x.parent);
w=x.parent.right;
}
if(w.left.color==TreeNodeColor.Black&&w.right.color==TreeNodeColor.Black)
{
w.color=TreeNodeColor.Red;
x=x.parent;
}else
{
if(w.right.color==TreeNodeColor.Black)
{
w.left.color=TreeNodeColor.Black;
w.color=TreeNodeColor.Red;
rightRotate(tree,w);
w=x.parent.right;
}
w.color=x.parent.color;
x.parent.color=TreeNodeColor.Black;
w.right.color=TreeNodeColor.Black;
leftRotate(tree,x.parent);
x=tree.root;
}
}else
{
RbTreeNode w=x.parent.left;
if(w.color==TreeNodeColor.Red)
{
w.color=TreeNodeColor.Black;
x.color=TreeNodeColor.Red;
rightRotate(tree,x.parent);
w=x.parent.left;
}
if(w.left.color==TreeNodeColor.Black&&w.right.color==TreeNodeColor.Black)
{
w.color=TreeNodeColor.Red;
x=x.parent;
}else
{
if(w.left.color==TreeNodeColor.Black)
{
w.right.color=TreeNodeColor.Black;
w.color=TreeNodeColor.Red;
leftRotate(tree,w);
w=x.parent.left;
}
w.color=x.parent.color;
x.parent.color=TreeNodeColor.Black;
w.left.color=TreeNodeColor.Black;
leftRotate(tree,x.parent);
x=tree.root;
}
}
}
x.color=TreeNodeColor.Black;
}

public boolean delete(int value)
{
return delete(this,value);
}

private void insertFixUp(MyRbTree tree,RbTreeNode z)
{
while(z.parent.color==TreeNodeColor.Red)
{
if(z.parent==z.parent.parent.left)
{
RbTreeNode uncle=z.parent.parent.right;
if(uncle.color==TreeNodeColor.Red)
{
z.parent.color=TreeNodeColor.Black;
uncle.color=TreeNodeColor.Black;
z.parent.parent.color=TreeNodeColor.Red;
z=z.parent.parent;
}else
{
if(z==z.parent.right)
{
z=z.parent;
leftRotate(tree,z);
}
z.parent.color=TreeNodeColor.Black;
z.parent.parent.color=TreeNodeColor.Red;
rightRotate(tree,z.parent.parent);
}
}else if(z.parent==z.parent.parent.right)
{
RbTreeNode uncle=z.parent.parent.left;
if(uncle.color==TreeNodeColor.Red)
{
z.parent.color=TreeNodeColor.Black;
uncle.color=TreeNodeColor.Black;
z.parent.parent.color=TreeNodeColor.Red;
z=z.parent.parent;
}else
{
if(z==z.parent.left)
{
z=z.parent;
rightRotate(tree,z);
}
z.parent.color=TreeNodeColor.Black;
z.parent.parent.color=TreeNodeColor.Red;
leftRotate(tree,z.parent.parent);
}

}
}
tree.root.color=TreeNodeColor.Black;

}

public void preorder(RbTreeNode root)
{
if(root!=null)
{
preorder(root.left);
getNodeInfo(root);
preorder(root.right);
}
}

public void getNodeInfo(RbTreeNode node)
{
if(node!=this.nilNode)
{
System.out.println(node.key+" "+node.color.toString());
}
}

}

class RbTreeNode{
TreeNodeColor color=TreeNodeColor.Red;
int key=-1;
RbTreeNode left=null;
RbTreeNode right=null;
RbTreeNode parent=null;

public RbTreeNode(int value)
{
this.key=value;
}
}

运行结果如下所示：

插入41
41 Black

插入38
38 Red
41 Black

插入31
31 Red
38 Black
41 Red

插入12
12 Red
31 Black
38 Black
41 Black

插入19
12 Red
19 Black
31 Red
38 Black
41 Black

插入8
8 Red
12 Black
19 Red
31 Black
38 Black
41 Black

删除8
12 Black
19 Red
31 Black
38 Black
41 Black

删除19
12 Red
31 Black
38 Black
41 Black

删除12
31 Black
38 Black
41 Black

删除31
38 Black
41 Red

删除38
41 Black

删除41

我自己用纸也画了下插入和删除的红黑树图，跟运行的结果中每个节点的颜色都是吻合的，个人觉得是没有什么问题的，如果有什么问题，欢迎讨论，谢谢....