红黑树学习终极篇

至此，红黑树内容基本学习完了，不过代码实现是个什么样子呢，这里转载网上搜到一篇blog：http://blog.csdn.net/yukid2012/article/details/40660633

c代码实现，写的不错，之前看过，好像打印节点颜色有点问题，太晚了不仔细看了。。。

#include <stdlib.h>#include <stdio.h>typedef int EleType;typedef enum Color  //颜色属性：红、黑{RED = 0, BLACK = 1} Color;typedef struct Node{struct Node* left;struct Node* right;struct Node* parent;Color color;EleType key;} Node;//哨兵结点，表示空，黑色。红黑树中的所有指向空的指针均指向该结点Node tree_nil = { &tree_nil, &tree_nil, &tree_nil, BLACK, 0 };void rb_display( Node* root );Node* rb_search( Node* root, int key );Node* tree_maximum( Node* x );Node* tree_minimum( Node* x );Node* tree_successor( Node* x );Node* left_rotate( Node* root, Node* x );Node* right_rotate( Node* root, Node* x );Node* rb_insert( Node* root, int key );Node* rb_insertFixup(Node* root, Node* x );Node* rb_delete( Node* root, EleType key );Node* rb_deleteFixup( Node* root, Node* x );//中序遍历红黑树，输出所有结点及其颜色。递归实现void rb_display( Node* root ){if( root != &tree_nil ){rb_display( root->left );printf( "%d, color is %s\n", root->key, (root->color?"RED":"BLACK") );rb_display( root->right );} }//查找结点。给定关键字，返回其所在结点。若红黑树中不存在该结点，返回空。递归实现Node* rb_search( Node* root, int key ){if( (root == &tree_nil) || (root->key == key) )return root;if( key < root->key )return rb_search( root->left, key );elsereturn rb_search( root->right, key ); }//返回结点的最大子结点，递归实现Node* tree_maximum( Node* x ){if( x->right == &tree_nil )return x;elsereturn tree_maximum( x->right );}//返回结点的最小子结点，递归实现Node* tree_minimum( Node* x ){if( x->left == &tree_nil )return x;elsereturn tree_minimum( x->left );}//返回结点的后继（大于x.key的最小结点）Node* tree_successor( Node* x ){if( x->right != &tree_nil )return tree_minimum( x->right );Node* y = x->parent;while( (y != &tree_nil) && (x == y->right) ){x = y;y = y->parent;}return y;}//左旋Node* left_rotate( Node* root, Node* x ){Node* y;if( x->right == &tree_nil ) //左旋结点必须有右子结点{    printf( "have no right child,rotation cancel.\n" );    return root;}y = x->right;x->right = y->left; //β子树从y的左子树变成x的右子树if( y->left != &tree_nil )y->left->parent = x;y->parent = x->parent; //y的父结点从x变为x的父结点if( x->parent == &tree_nil )root = y;else if( x == x->parent->left )x->parent->left = y;elsex->parent->right = y;y->left = x;x->parent = y;return root;}//右旋Node* right_rotate( Node* root, Node* x ){Node* y;if( x->left == &tree_nil ) //右旋结点必须有左子结点{    printf( "have no left child,rotation cancel.\n" );    return root;}y = x->left;x->left = y->right;if( y->right != &tree_nil )y->right->parent = x;y->parent = x->parent;if( x->parent == &tree_nil )root = y;else if( x == x->parent->left )x->parent->left = y;elsex->parent->right = y;y->right = x;x->parent = y;return root;}Node* rb_insert( Node* root, int key ){Node* y = &tree_nil;Node* x = root;Node* z = (Node*) malloc( sizeof(Node) );z->key = key;while( x != &tree_nil ){y = x;if ( key < x->key )x = x->left;elsex = x->right;}z->parent = y;if ( y == &tree_nil )root = z;else if ( z->key < y->key )y->left = z;elsey->right = z;z->left = &tree_nil;z->right = &tree_nil;z->color = RED;return rb_insertFixup( root, z );}Node* rb_insertFixup( Node* root, Node* z ){while( z->parent->color == RED ){if( z->parent == z->parent->parent->left ){Node* y = z->parent->parent->right;if( y->color == RED ) //第一种情况：当前结点的叔结点是红色{z->parent->color = BLACK;y->color = BLACK;z->parent->parent->color = RED;z = z->parent->parent;}else{if( z == z->parent->right ) //第二种情况：当前结点是右孩子，且叔结点是黑色{z = z->parent;root = left_rotate( root, z );}z->parent->color = BLACK; //第三种情况：当前结点是左孩子，且叔结点是黑色z->parent->parent->color = RED;root = right_rotate( root, z->parent->parent );}}else{Node* y = z->parent->parent->left;if( y->color == RED ){z->parent->color = BLACK;y->color = BLACK;z->parent->parent->color = RED;z = z->parent->parent;}else{if( z == z->parent->left ){z = z->parent;root = right_rotate( root, z );}z->parent->color = BLACK;z->parent->parent->color = RED;root = left_rotate( root, z->parent->parent );}}}root->color = BLACK;return root;}Node* rb_delete( Node* root, EleType key ){Node* z;z = rb_search( root, key );if( z == &tree_nil ){printf("The element %d is not in the tree\n", key );return root;}else{Node *x, *y;if( (z->left == &tree_nil) || (z->right == &tree_nil) )y = z;elsey = tree_successor(z);if ( y->left != &tree_nil )x = y->left;elsex = y->right;x->parent = y->parent;if ( y->parent == &tree_nil )root = x;else if ( y == x->parent->left )y->parent->left = x;elsey->parent->right = x;if ( y != z )z->key = y->key;if ( y->color == BLACK )root = rb_deleteFixup( root, x );free(y);return root;}}Node* rb_deleteFixup( Node* root, Node* x ){Node* w;while ( (x != root) && (x->color == BLACK) ){if ( x == x->parent->left ){w = x->parent->right;if (w->color == RED) //情况1；待删结点的兄弟结点w是红色{w->color = BLACK;x->parent->color = RED;root = left_rotate( root, x->parent );w = x->parent->right;}if ( (w->left->color == BLACK) && (w->right->color == BLACK) ) //情况2；待删结点的兄弟结点w是黑色，且w的两个子结点都是黑色{w->color = RED;x = x->parent;}else{if ( w->right->color == BLACK ) //情况3；待删结点的兄弟结点w是黑色，且w左孩子红色，右孩子黑色{w->left->color = BLACK;w->color = RED;root = right_rotate( root, w );w = x->parent->right;}w->color = x->parent->color; //情况4；待删结点的兄弟结点w是黑色，且w的右孩子是红色x->parent->color = BLACK;w->right->color = BLACK;root = left_rotate( root, x->parent );x = root;}}else{w = x->parent->left;if ( w->color == RED ){w->color = BLACK;x->parent->color = RED;root = right_rotate( root, x->parent );w = x->parent->right;}if ( (w->right->color == BLACK) && (w->left->color == BLACK) ){w->color = RED;x = x->parent;}else{if ( w->left->color == BLACK ){w->right->color = BLACK;w->color = RED;root = left_rotate( root, w );w = x->parent->left;}w->color = x->parent->color;x->parent->color = BLACK;w->left->color = BLACK;root = right_rotate( root, x->parent );x = root;}}}x->color = BLACK;return root;}int main(){Node* root;root = &tree_nil;root->parent = &tree_nil;root = rb_insert( root, 11 );root = rb_insert( root, 1 );root = rb_insert( root, 9 );root = rb_insert( root, 2 );root = rb_insert( root, 10 );rb_display( root );root = rb_delete( root, 2 );rb_display( root );root = rb_delete( root, -10 );rb_display( root );return 0;}