红黑树与C实现算法 - RedBlackTree.c

红黑树与C实现算法

cheungmine

 

本文全部内容摘自互联网，作者根据需要做了修改和补充，最主要的是提供了对set的支持，并且给出完整的测试用例。

红黑树是一种自平衡二叉查找树，是在计算机科学中用到的一种数据结构，典型的用途是实现关联数组。它是在1972年由Rudolf Bayer发明的，他称之为"对称二叉B树"，它现代的名字是在 Leo J. Guibas 和 Robert Sedgewick 于1978年写的一篇论文中获得的。它是复杂的，但它的操作有着良好的最坏情况运行时间，并且在实践中是高效的: 它可以在O(log n)时间内做查找，插入和删除，这里的n 是树中元素的数目。

红黑树是一种很有意思的平衡检索树。它的统计性能要好于平衡二叉树(有些书籍根据作者姓名，Adelson-Velskii和Landis，将其称为AVL-树)，因此，红黑树在很多地方都有应用。在C++ STL中，很多部分(目前包括set, multiset, map, multimap)应用了红黑树的变体(SGI STL中的红黑树有一些变化，这些修改提供了更好的性能，以及对set操作的支持)。

 

 

红黑树的实现代码如下(red_black_tree.h,red_black_tree.c和测试文件rbtree_test.c)：

/****************************************************************************** * red_black_tree.h * * Download From: * * http://www.cs.tau.ac.il/~efif/courses/Software1_Summer_03/code/rbtree/ * * Last Edited by: * * cheungmine * * 2010-8 * * Container class for a red-black tree: A binary tree that satisfies the * * following properties: * * 1. Each node has a color, which is either red or black. * * 2. A red node cannot have a red parent. * * 3. The number of black nodes from every path from the tree root to a leaf * * is the same for all tree leaves (it is called the 'black depth' of the * * tree). * * Due to propeties 2-3, the depth of a red-black tree containing n nodes * * is bounded by 2*log_2(n). * * * * The red_black_tree_t template requires two template parmeters: * * - The contained TYPE class represents the objects stored in the tree. * * It has to support the copy constructor and the assignment operator * * (operator=). * * * * - pfcbRBTreeCompFunc is a functor used to define the order of objects of * * class TYPE: * * This class has to support an operator() that recieves two objects from * * the TYPE class and returns a negative, zero or a positive integer, * * depending on the comparison result. * ******************************************************************************/ #ifndef RED_BLACK_TREE_H #define RED_BLACK_TREE_H /*! * Define RBTREE_SUPPORTS_MULTI_OBJECTS for supporting mapset (multi-key-map) * if RBTREE_SUPPORTS_MULTI_OBJECTS defined, object must inherit from struct * rbtree_object_base. That means the first member of object must be a struct * pointer to next possible object if it has. * * #define RBTREE_SUPPORTS_MULTI_OBJECTS */ #define RBTREE_SUPPORTS_MULTI_OBJECTS #ifdef RBTREE_SUPPORTS_MULTI_OBJECTS typedef struct _rbtree_object_base { struct _rbtree_object_base *__next_object; }rbtree_object_base; #endif /*! Color enumeration for nodes of red-black tree */ typedef enum _red_black_color_enum { rbcRed, rbcBlack } red_black_color_enum; /*! Representation of a node in a red-black tree */ typedef struct _red_black_node_t { void * object; /* the stored object user defined */ red_black_color_enum color; /* the color of the node */ struct _red_black_node_t * parent; /* points to the parent node */ struct _red_black_node_t * right; /* points to the right child */ struct _red_black_node_t * left; /* points to the left child */ } red_black_node_t; /*! Callback function prototype for comparing objects */ typedef int (pfcbRBTreeCompFunc)(void *object1, void *object2); /*! Callback function prototype for traverse objects */ typedef void(pfcbRBTreeOperFunc)(void *object, void *param); /*! Construct of a red-black tree node * param object The object stored in the node * param color The color of the node */ extern red_black_node_t * rbnode_construct(void * object, red_black_color_enum color); /*! Recursive destructor for the entire sub-tree */ extern void rbnode_destruct(red_black_node_t * node); /*! Calculate the depth of the sub-tree spanned by the given node * param node The sub-tree root * return The sub-tree depth */ extern int rbnode_depth(red_black_node_t * node); /*! Get the leftmost node in the sub-tree spanned by the given node * param node The sub-tree root * return The sub-tree minimum */ extern red_black_node_t * rbnode_minimum(red_black_node_t * node); /*! Get the rightmost node in the sub-tree spanned by the given node * param node The sub-tree root * return The sub-tree maximum */ extern red_black_node_t * rbnode_maximum(red_black_node_t * node); /*! Replace the object */ extern void rbnode_replace(red_black_node_t * node, void * object); /*! Get the next node in the tree (according to the tree order) * param node The current node * return The successor node, or NULL if node is the tree maximum */ extern red_black_node_t * rbnode_successor(red_black_node_t * node); /*! Get the previous node in the tree (according to the tree order) * param node The current node * return The predecessor node, or NULL if node is the tree minimum */ extern red_black_node_t * rbnode_predecessor(red_black_node_t * node); /*! Duplicate the entire sub-tree rooted at the given node * param node The sub-tree root * return A pointer to the duplicated sub-tree root */ extern red_black_node_t * rbnode_duplicate(red_black_node_t * node); /*! Traverse a red-black sub-tree left first * param node The sub-tree root * param op The operation to perform on each object in the sub-tree */ extern void rbnode_traverse(red_black_node_t *node, pfcbRBTreeOperFunc *opFunc, void *param); /*! Traverse a red-black sub-tree right first */ extern void rbnode_traverse_right(red_black_node_t *node, pfcbRBTreeOperFunc *opFunc, void*param); /*! Representation of a red-black tree */ typedef struct _red_black_tree_t { red_black_node_t * root; /* pointer to the tree root */ int iSize; /* number of objects stored */ pfcbRBTreeCompFunc * comp; /* compare function */ } red_black_tree_t; /*! Initialize a red-black tree with a comparision function * param tree The tree * param comp The comparision function */ void rbtree_init(red_black_tree_t * tree, pfcbRBTreeCompFunc * comp); /*! Construct a red-black tree with a comparison object * param comp A pointer to the comparison object to be used by the tree * return The newly constructed tree */ red_black_tree_t * rbtree_construct(pfcbRBTreeCompFunc * comp); /*! Clean a red-black tree [takes O(n) operations] * param tree The tree */ extern void rbtree_clean(red_black_tree_t * tree); /*! Destruct a red-black tree * param tree The tree */ extern void rbtree_destruct(red_black_tree_t * tree); /*! Get the size of the tree [takes O(1) operations] * param tree The tree * return The number of objects stored in the tree */ extern int rbtree_size(red_black_tree_t * tree); /*! Get the depth of the tree [takes O(n) operations] * param tree The tree * return The length of the longest path from the root to a leaf node */ extern int rbtree_depth(red_black_tree_t * tree); /*! Check whether the tree contains an object [takes O(log n) operations] * param tree The tree * param object The query object * return (true) if an equal object is found in the tree, otherwise (false) */ extern int rbtree_contains(red_black_tree_t * tree, void * object); /*! Insert an object to the tree [takes O(log n) operations] * param tree The tree * param object The object to be inserted * return the inserted object node */ extern red_black_node_t * rbtree_insert(red_black_tree_t * tree, void * object); /*! Insert an unique object to the tree */ extern red_black_node_t * rbtree_insert_unique(red_black_tree_t * tree, void * object); /*! Insert a new object to the tree as the a successor of a given node * param tree The tree * return The new node */ extern red_black_node_t * insert_successor_at(red_black_tree_t * tree, red_black_node_t * at_node, void * object); /*! Insert a new object to the tree as the a predecessor of a given node * param tree The tree * return The new node */ extern red_black_node_t * insert_predecessor_at(red_black_tree_t * tree, red_black_node_t * at_node, void * object); /*! Remove an object from the tree [takes O(log n) operations] * param tree The tree * param object The object to be removed * pre The object should be contained in the tree */ extern void rbtree_remove(red_black_tree_t * tree, void * object); /*! Get a handle to the tree minimum [takes O(log n) operations] * param tree The tree * return the minimal object in the tree, or a NULL if the tree is empty */ extern red_black_node_t * rbtree_minimum(red_black_tree_t * tree); /*! Get a handle to the tree maximum [takes O(log n) operations] * param tree The tree * return the maximal object in the tree, or a NULL if the tree is empty */ extern red_black_node_t * rbtree_maximum(red_black_tree_t * tree); /*! Get the next node in the tree (according to the tree order) * [takes O(log n) operations at worst-case, but only O(1) amortized] * param tree The tree * param node The current object * return The successor node, or a NULL, if we are at the tree maximum */ extern red_black_node_t * rbtree_successor(red_black_tree_t * tree, red_black_node_t * node); /*! Get the previous node in the tree (according to the tree order) * [takes O(log n) operations at worst-case, but only O(1) amortized] * param tree The tree * param node The current object * return The predecessor node, or a NULL, if we are at the tree minimum */ extern red_black_node_t * rbtree_predecessor(red_black_tree_t * tree, red_black_node_t * node); /*! Find a node that contains the given object * param tree The tree * param object The desired object * return A node that contains the given object, or NULL if no such object * is found in the tree */ extern red_black_node_t * rbtree_find(red_black_tree_t * tree, void * object); /*! Remove the object stored in the given tree node * param tree The tree * param node The node storing the object to be removed from the tree */ extern void rbtree_remove_at(red_black_tree_t * tree, red_black_node_t * node); /*! Left-rotate the sub-tree spanned by the given node * param tree The tree * param node The sub-tree root */ extern void rbtree_rotate_left(red_black_tree_t * tree, red_black_node_t * node); /*! Right-rotate the sub-tree spanned by the given node * param tree The tree * param node The sub-tree root */ extern void rbtree_rotate_right(red_black_tree_t * tree, red_black_node_t * node); /*! * Fix-up the red-black tree properties after an insertion operation * param tree The tree * param node The node that has just been inserted to the tree * pre The color of node must be red */ extern void rbtree_insert_fixup(red_black_tree_t * tree, red_black_node_t * node); /*! Fix-up the red-black tree properties after a removal operation * param tree The tree * param node The child of the node that has just been removed from the tree */ extern void rbtree_remove_fixup(red_black_tree_t * tree, red_black_node_t * node); /*! Traverse a red-black tree left first * param tree The tree * param op The operation to perform on every object of the tree (according to * the tree order) */ extern void rbtree_traverse(red_black_tree_t * tree, pfcbRBTreeOperFunc * op, void *param); #define rbtree_traverse_left rbtree_traverse /*! Traverse a red-black tree right first */ extern void rbtree_traverse_right(red_black_tree_t * tree, pfcbRBTreeOperFunc * op, void *param); #endif /* RED_BLACK_TREE_H */

/****************************************************************************** * red_black_tree.c * * Download From: * * http://www.cs.tau.ac.il/~efif/courses/Software1_Summer_03/code/rbtree/ * * Last Edited by: cheungmine * ******************************************************************************/ #include <stdio.h> #include <stdlib.h> #include <assert.h> #include "red_black_tree.h" /*! * Operations on red_black_node_t struct */ /* Construct a red-black tree node */ red_black_node_t * rbnode_construct(void * object, red_black_color_enum color) { red_black_node_t * node = (red_black_node_t *) malloc(sizeof(red_black_node_t)); if (!node) { fprintf(stderr, "Not enough memory!/n"); return NULL; } node->object = object; node->color = color; node->parent = node->right = node->left = NULL; return node; } /* Destructor of a red-black tree node */ void rbnode_destruct(red_black_node_t * node) { if (!node) return; rbnode_destruct(node->right); rbnode_destruct(node->left); free(node); } /* Calculate the depth of the subtree spanned by a given node */ int rbnode_depth(red_black_node_t * node) { /* Recursively calculate the depth of the left and right sub-trees */ int iRightDepth = (node->right) ? rbnode_depth(node->right) : 0; int iLeftDepth = (node->left) ? rbnode_depth(node->left) : 0; /* Return the maximal child depth + 1 (the current node) */ return ((iRightDepth > iLeftDepth) ? (iRightDepth + 1) : (iLeftDepth + 1)); } /* Return the leftmost leaf in the tree */ red_black_node_t * rbnode_minimum(red_black_node_t * node) { while (node->left) node = node->left; return node; } /* Return the rightmost leaf in the tree */ red_black_node_t * rbnode_maximum(red_black_node_t * node) { while (node->right) node = node->right; return node; } /* Replace the object */ void rbnode_replace(red_black_node_t * node, void * object) { /* Make sure the replacement does not violate the tree order */ /* Replace the object at node */ node->object = object; } /* Get the next node in the tree (according to the tree order) */ red_black_node_t * rbnode_successor(red_black_node_t * node) { red_black_node_t * succ_node; if (node->right) { /* If there is a right child, the successor is the minimal object in * the sub-tree spanned by this child. */ succ_node = node->right; while (succ_node->left) succ_node = succ_node->left; } else { /* Otherwise, go up the tree until reaching the parent from the left * direction. */ red_black_node_t * prev_node = node; succ_node = node->parent; while (succ_node && prev_node == succ_node->right) { prev_node = succ_node; succ_node = succ_node->parent; } } return (succ_node); } /* Get the previous node in the tree (according to the tree order) */ red_black_node_t * rbnode_predecessor(red_black_node_t * node) { red_black_node_t * pred_node; if (node->left) { /* If there is a left child, the predecessor is the maximal object in * the sub-tree spanned by this child. */ pred_node = node->left; while (pred_node->right) pred_node = pred_node->right; } else { /* Otherwise, go up the tree until reaching the parent from the right * direction. */ red_black_node_t * prev_node = node; pred_node = node->parent; while (pred_node && prev_node == pred_node->left) { prev_node = pred_node; pred_node = pred_node->parent; } } return (pred_node); } /* Return a pointer to a duplication of the given node */ red_black_node_t * rbnode_duplicate(red_black_node_t * node) { /* Create a node of the same color, containing the same object */ red_black_node_t * dup_node = rbnode_construct(node->object, node->color); if (!dup_node) return NULL; /* Duplicate the children recursively */ if (node->right) { dup_node->right = rbnode_duplicate (node->right); dup_node->right->parent = dup_node; } else { dup_node->right = NULL; } if (node->left) { dup_node->left = rbnode_duplicate(node->left); dup_node->left->parent = dup_node; } else { dup_node->left = NULL; } return dup_node; /* Return the duplicated node */ } /* Traverse a red-black subtree */ void rbnode_traverse(red_black_node_t * node, pfcbRBTreeOperFunc * opFunc, void* param) { if (!node) return; rbnode_traverse(node->left, opFunc, param); opFunc(node->object, param); rbnode_traverse(node->right, opFunc, param); } /* Right-first traverse a red-black subtree */ void rbnode_traverse_right(red_black_node_t * node, pfcbRBTreeOperFunc * opFunc, void* param) { if (!node) return; rbnode_traverse_right(node->right, opFunc, param); opFunc(node->object, param); rbnode_traverse_right(node->left, opFunc, param); } /* * Operations on red_black_tree_t struct */ /* Intialize a tree */ void rbtree_init(red_black_tree_t * tree, pfcbRBTreeCompFunc * comp) { tree->comp = comp; tree->iSize = 0; tree->root = NULL; } /* Construct a tree given a comparison function */ red_black_tree_t * rbtree_construct(pfcbRBTreeCompFunc * comp) { red_black_tree_t * tree = (red_black_tree_t *) malloc(sizeof(red_black_tree_t)); if (!tree) { fprintf(stderr, "Not enough memory!/n"); return NULL; } rbtree_init(tree, comp); return tree; } /* Remove all objects from a black-red tree */ void rbtree_clean(red_black_tree_t * tree) { if (tree->root) rbnode_destruct(tree->root); tree->root = NULL; tree->iSize = 0; } /* Destruct a red-black tree */ void rbtree_destruct(red_black_tree_t * tree) { rbtree_clean(tree); free(tree); } /* Returns the size of the tree */ int rbtree_size(red_black_tree_t * tree) { return tree->iSize; } /* Returns the depth of the tree */ int rbtree_depth(red_black_tree_t * tree) { if (!(tree->root)) return 0; return rbnode_depth(tree->root); } /* Check whether the tree contains an object */ int rbtree_contains(red_black_tree_t * tree, void * object) { return (rbtree_find(tree, object) != NULL); } /* Insert an object to the tree */ red_black_node_t * rbtree_insert(red_black_tree_t * tree, void * object) { int cmp; red_black_node_t * cur_node; red_black_node_t * new_node = NULL; if (!(tree->root)) { /* Assign a new root node. Notice that the root is always black */ new_node = rbnode_construct(object, rbcBlack); if (!new_node) return NULL; tree->root = new_node; tree->iSize = 1; return new_node; } /* Find a place for the new object, and insert it as a red leaf */ cur_node = tree->root; while (cur_node) { cmp = (*(tree->comp))(object, cur_node->object); #ifdef RBTREE_SUPPORTS_MULTI_OBJECTS if (cmp==0) { if (cur_node->object != object) ((rbtree_object_base*)cur_node->object)->__next_object = (rbtree_object_base*)object; return cur_node; } #endif /* Compare inserted object with the object stored in the current node */ if (cmp > 0) { if (!(cur_node->left)) { /* Insert the new leaf as the left child of the current node */ new_node = rbnode_construct(object, rbcRed); if (!new_node) return NULL; cur_node->left = new_node; new_node->parent = cur_node; cur_node = NULL; /* terminate the while loop */ } else { cur_node = cur_node->left; /* Go to the left sub-tree */ } } else { if (!(cur_node->right)) { /* Insert the new leaf as the right child of the current node */ new_node = rbnode_construct(object, rbcRed); if (!new_node) return NULL; cur_node->right = new_node; new_node->parent = cur_node; cur_node = NULL; /* terminate the while loop */ } else { cur_node = cur_node->right; /* Go to the right sub-tree */ } } } /* Mark that a new node was added */ tree->iSize++; /* Fix up the tree properties */ rbtree_insert_fixup(tree, new_node); return new_node; } /* Insert an unique object to the tree */ red_black_node_t * rbtree_insert_unique(red_black_tree_t * tree, void * object) { int cmp; red_black_node_t * cur_node; red_black_node_t * new_node = NULL; if (!(tree->root)) { /* Assign a new root node. Notice that the root is always black */ new_node = rbnode_construct(object, rbcBlack); if (!new_node) return NULL; tree->root = new_node; tree->iSize = 1; return new_node; } /* Find a place for the new object, and insert it as a red leaf */ cur_node = tree->root; while (cur_node) { cmp = (*(tree->comp))(object, cur_node->object); if (cmp==0) { /* there already has an object with the same id as object to be inserted */ return cur_node; } /* Compare inserted object with the object stored in the current node */ if (cmp > 0) { if (!(cur_node->left)) { /* Insert the new leaf as the left child of the current node */ new_node = rbnode_construct(object, rbcRed); if (!new_node) return NULL; cur_node->left = new_node; new_node->parent = cur_node; cur_node = NULL; /* terminate the while loop */ } else { cur_node = cur_node->left; /* Go to the left sub-tree */ } } else { if (!(cur_node->right)) { /* Insert the new leaf as the right child of the current node */ new_node = rbnode_construct(object, rbcRed); if (!new_node) return NULL; cur_node->right = new_node; new_node->parent = cur_node; cur_node = NULL; /* terminate the while loop */ } else { cur_node = cur_node->right; /* Go to the right sub-tree */ } } } /* Mark that a new node was added */ tree->iSize++; /* Fix up the tree properties */ rbtree_insert_fixup(tree, new_node); return new_node; } /* Insert a new object to the tree as the a successor of a given node */ red_black_node_t * insert_successor_at(red_black_tree_t * tree, red_black_node_t * at_node, void * object) { red_black_node_t * parent; red_black_node_t * new_node; if (!(tree->root)) { /* Assign a new root node. Notice that the root is always black */ new_node = rbnode_construct(object, rbcBlack); if (!new_node) return NULL; tree->root = new_node; tree->iSize = 1; return new_node; } /* Insert the new object as a red leaf, being the successor of node */ new_node = rbnode_construct(object, rbcRed); if (!new_node) return NULL; if (!at_node) { /* The new node should become the tree minimum: Place is as the left * child of the current minimal leaf. */ parent = rbnode_minimum(tree->root); parent->left = new_node; } else { /* Make sure the insertion does not violate the tree order */ /* In case given node has no right child, place the new node as its * right child. Otherwise, place it at the leftmost position at the * sub-tree rooted at its right side. */ if (!at_node->right) { parent = at_node; parent->right = new_node; } else { parent = rbnode_minimum(at_node->right); parent->left = new_node; } } new_node->parent = parent; /* Mark that a new node was added */ tree->iSize++; /* Fix up the tree properties */ rbtree_insert_fixup(tree, new_node); return new_node; } /* Insert a new object to the tree as the a predecessor of a given node */ red_black_node_t * insert_predecessor_at(red_black_tree_t * tree, red_black_node_t * at_node, void * object) { red_black_node_t * parent; red_black_node_t * new_node; if (!(tree->root)) { /* Assign a new root node. Notice that the root is always black */ new_node = rbnode_construct(object, rbcBlack); if (!new_node) return NULL; tree->root = new_node; tree->iSize = 1; return new_node; } /* Insert the new object as a red leaf, being the predecessor of at_node */ new_node = rbnode_construct(object, rbcRed); if (!new_node) return NULL; if (!at_node) { /* The new node should become the tree maximum: Place is as the right * child of the current maximal leaf. */ parent = rbnode_maximum(tree->root); parent->right = new_node; } else { /* Make sure the insertion does not violate the tree order */ /* In case given node has no left child, place the new node as its * left child. Otherwise, place it at the rightmost position at the * sub-tree rooted at its left side. */ if (!(at_node->left)) { parent = at_node; parent->left = new_node; } else { parent = rbnode_maximum (at_node->left); parent->right = new_node; } } new_node->parent = parent; /* Mark that a new node was added */ tree->iSize++; /* Fix up the tree properties */ rbtree_insert_fixup(tree, new_node); return new_node; } /* Remove an object from the tree */ void rbtree_remove(red_black_tree_t * tree, void * object) { red_black_node_t * node = rbtree_find(tree, object); /* find the node */ rbtree_remove_at(tree, node); /* remove the node */ } /* Remove the object pointed by the given node. */ void rbtree_remove_at(red_black_tree_t * tree, red_black_node_t * node) { red_black_node_t * child = NULL; /* In case of deleting the single object stored in the tree, free the root, * thus emptying the tree. */ if (tree->iSize == 1) { rbnode_destruct(tree->root); tree->root = NULL; tree->iSize = 0; return; } /* Remove the given node from the tree */ if (node->left && node->right) { /* If the node we want to remove has two children, find its successor, * which is the leftmost child in its right sub-tree and has at most * one child (it may have a right child). */ red_black_node_t * succ_node = rbnode_minimum(node->right); /* Now physically swap node and its successor. Notice this may temporarily * violate the tree properties, but we are going to remove node anyway. * This way we have moved node to a position were it is more convinient * to delete it. */ int immediate_succ = (node->right == succ_node); red_black_node_t * succ_parent = succ_node->parent; red_black_node_t * succ_left = succ_node->left; red_black_node_t * succ_right = succ_node->right; red_black_color_enum succ_color = succ_node->color; succ_node->parent = node->parent; succ_node->left = node->left; succ_node->right = immediate_succ ? node : node->right; succ_node->color = node->color; node->parent = immediate_succ ? succ_node : succ_parent; node->left = succ_left; node->right = succ_right; node->color = succ_color; if (!immediate_succ) { if (succ_node == node->parent->left) node->parent->left = node; else node->parent->right = node; } if (node->left) node->left->parent = node; if (node->right) node->right->parent = node; if (succ_node->parent) { if (node == succ_node->parent->left) succ_node->parent->left = succ_node; else succ_node->parent->right = succ_node; } else { tree->root = succ_node; } if (succ_node->left) succ_node->left->parent = succ_node; if (succ_node->right) succ_node->right->parent = succ_node; } /* At this stage, the node we are going to remove has at most one child */ child = (node->left) ? node->left : node->right; /* Splice out the node to be removed, by linking its parent straight to the * removed node's single child. */ if (child) child->parent = node->parent; if (!(node->parent)) { /* If we are deleting the root, make the child the new tree node */ tree->root = child; } else { /* Link the removed node parent to its child */ if (node == node->parent->left) { node->parent->left = child; } else { node->parent->right = child; } } /* Fix-up the red-black properties that may have been damaged: If we have * just removed a black node, the black-depth property is no longer valid. */ if (node->color == rbcBlack && child) rbtree_remove_fixup(tree, child); /* Delete the un-necessary node (we nullify both its children because the * node's destructor is recursive). */ node->left = NULL; node->right = NULL; free(node); /* Descrease the number of objects in the tree */ tree->iSize--; } /* Get the tree minimum */ red_black_node_t * rbtree_minimum(red_black_tree_t * tree) { if (!(tree->root)) return NULL; /* Return the leftmost leaf in the tree */ return rbnode_minimum(tree->root); } /* Get the tree maximum */ red_black_node_t * rbtree_maximum(red_black_tree_t * tree) { if (!(tree->root)) return NULL; /* Return the rightmost leaf in the tree */ return rbnode_maximum(tree->root); } /* Return a pointer to the node containing the given object */ red_black_node_t * rbtree_find(red_black_tree_t * tree, void * object) { red_black_node_t * cur_node = tree->root; int comp_result; while (cur_node) { /* In case of equality, we can return the current node. */ if ((comp_result = (*(tree->comp))(object, cur_node->object)) == 0) return cur_node; /* Go down to the left or right child. */ cur_node = (comp_result > 0) ? cur_node->left : cur_node->right; } /* If we reached here, the object is not found in the tree */ return NULL; } /* Left-rotate the sub-tree spanned by the given node: * * | RoateRight(y) | * y --------------> x * / / / / . * x T3 RoatateLeft(x) T1 y . * / / <-------------- / / . * T1 T2 T2 T3 */ void rbtree_rotate_left(red_black_tree_t * tree, red_black_node_t * x_node) { /* Get the right child of the node */ red_black_node_t * y_node = x_node->right; /* Change its left subtree (T2) to x's right subtree */ x_node->right = y_node->left; /* Link T2 to its new parent x */ if (y_node->left != NULL) y_node->left->parent = x_node; /* Assign x's parent to be y's parent */ y_node->parent = x_node->parent; if (!(x_node->parent)) { /* Make y the new tree root */ tree->root = y_node; } else { /* Assign a pointer to y from x's parent */ if (x_node == x_node->parent->left) { x_node->parent->left = y_node; } else { x_node->parent->right = y_node; } } /* Assign x to be y's left child */ y_node->left = x_node; x_node->parent = y_node; } /* Right-rotate the sub-tree spanned by the given node */ void rbtree_rotate_right(red_black_tree_t * tree, red_black_node_t * y_node) { /* Get the left child of the node */ red_black_node_t * x_node = y_node->left; /* Change its right subtree (T2) to y's left subtree */ y_node->left = x_node->right; /* Link T2 to its new parent y */ if (x_node->right != NULL) x_node->right->parent = y_node; /* Assign y's parent to be x's parent */ x_node->parent = y_node->parent; if (!(y_node->parent)) { /* Make x the new tree root */ tree->root = x_node; } else { /* Assign a pointer to x from y's parent */ if (y_node == y_node->parent->left) { y_node->parent->left = x_node; } else { y_node->parent->right = x_node; } } /* Assign y to be x's right child */ x_node->right = y_node; y_node->parent = x_node; } /* Fix-up the tree so it maintains the red-black properties after insertion */ void rbtree_insert_fixup(red_black_tree_t * tree, red_black_node_t * node) { /* Fix the red-black propreties: we may have inserted a red leaf as the * child of a red parent - so we have to fix the coloring of the parent * recursively. */ red_black_node_t * curr_node = node; red_black_node_t * grandparent; red_black_node_t *uncle; assert(node && node->color == rbcRed); while (curr_node != tree->root && curr_node->parent->color == rbcRed) { /* Get a pointer to the current node's grandparent (notice the root is * always black, so the red parent must have a parent). */ grandparent = curr_node->parent->parent; if (curr_node->parent == grandparent->left) { /* If the red parent is a left child, the uncle is the right child of * the grandparent. */ uncle = grandparent->right; if (uncle && uncle->color == rbcRed) { /* If both parent and uncle are red, color them black and color the * grandparent red. * In case of a NULL uncle, we treat it as a black node. */ curr_node->parent->color = rbcBlack; uncle->color = rbcBlack; grandparent->color = rbcRed; /* Move to the grandparent */ curr_node = grandparent; } else { /* Make sure the current node is a right child. If not, left-rotate * the parent's sub-tree so the parent becomes the right child of the * current node (see _rotate_left). */ if (curr_node == curr_node->parent->right) { curr_node = curr_node->parent; rbtree_rotate_left(tree, curr_node); } /* Color the parent black and the grandparent red */ curr_node->parent->color = rbcBlack; grandparent->color = rbcRed; /* Right-rotate the grandparent's sub-tree */ rbtree_rotate_right(tree, grandparent); } } else { /* If the red parent is a right child, the uncle is the left child of * the grandparent. */ uncle = grandparent->left; if (uncle && uncle->color == rbcRed) { /* If both parent and uncle are red, color them black and color the * grandparent red. * In case of a NULL uncle, we treat it as a black node. */ curr_node->parent->color = rbcBlack; uncle->color = rbcBlack; grandparent->color = rbcRed; /* Move to the grandparent */ curr_node = grandparent; } else { /* Make sure the current node is a left child. If not, right-rotate * the parent's sub-tree so the parent becomes the left child of the * current node. */ if (curr_node == curr_node->parent->left) { curr_node = curr_node->parent; rbtree_rotate_right(tree, curr_node); } /* Color the parent black and the grandparent red */ curr_node->parent->color = rbcBlack; grandparent->color = rbcRed; /* Left-rotate the grandparent's sub-tree */ rbtree_rotate_left(tree, grandparent); } } } /* Make sure that the root is black */ tree->root->color = rbcBlack; } void rbtree_remove_fixup(red_black_tree_t * tree, red_black_node_t * node) { red_black_node_t * curr_node = node; red_black_node_t * sibling; while (curr_node != tree->root && curr_node->color == rbcBlack) { /* Get a pointer to the current node's sibling (notice that the node's * parent must exist, since the node is not the root). */ if (curr_node == curr_node->parent->left) { /* If the current node is a left child, its sibling is the right * child of the parent. */ sibling = curr_node->parent->right; /* Check the sibling's color. Notice that NULL nodes are treated * as if they are colored black. */ if (sibling && sibling->color == rbcRed) { /* In case the sibling is red, color it black and rotate. * Then color the parent red (and the grandparent is now black). */ sibling->color = rbcBlack; curr_node->parent->color = rbcRed; rbtree_rotate_left(tree, curr_node->parent); sibling = curr_node->parent->right; } if (sibling && (!(sibling->left) || sibling->left->color == rbcBlack) && (!(sibling->right) || sibling->right->color == rbcBlack)) { /* If the sibling has two black children, color it red */ sibling->color = rbcRed; if (curr_node->parent->color == rbcRed) { /* If the parent is red, we can safely color it black and terminate * the fix-up process. */ curr_node->parent->color = rbcBlack; curr_node = tree->root; /* In order to stop the while loop */ } else { /* The black depth of the entire sub-tree rooted at the parent is * now too small - fix it up recursively. */ curr_node = curr_node->parent; } } else { if (!sibling) { /* Take special care of the case of a NULL sibling */ if (curr_node->parent->color == rbcRed) { curr_node->parent->color = rbcBlack; curr_node = tree->root; /* In order to stop the while loop */ } else { curr_node = curr_node->parent; } } else { /* In this case, at least one of the sibling's children is red. * It is therfore obvious that the sibling itself is black. */ if (sibling->right && sibling->right->color == rbcRed) { /* If the right child of the sibling is red, color it black and * rotate around the current parent. */ sibling->right->color = rbcBlack; rbtree_rotate_left(tree, curr_node->parent); } else { /* If the left child of the sibling is red, rotate around the * sibling, then rotate around the new sibling of our current * node. */ rbtree_rotate_right(tree, sibling); sibling = curr_node->parent->right; rbtree_rotate_left(tree, sibling); } /* It is now safe to color the parent black and to terminate the * fix-up process. */ if (curr_node->parent->parent) curr_node->parent->parent->color = curr_node->parent->color; curr_node->parent->color = rbcBlack; curr_node = tree->root; /* In order to stop the while loop */ } } } else { /* If the current node is a right child, its sibling is the left * child of the parent. */ sibling = curr_node->parent->left; /* Check the sibling's color. Notice that NULL nodes are treated * as if they are colored black. */ if (sibling && sibling->color == rbcRed) { /* In case the sibling is red, color it black and rotate. * Then color the parent red (and the grandparent is now black). */ sibling->color = rbcBlack; curr_node->parent->color = rbcRed; rbtree_rotate_right(tree, curr_node->parent); sibling = curr_node->parent->left; } if (sibling && (!(sibling->left) || sibling->left->color == rbcBlack) && (!(sibling->right) || sibling->right->color == rbcBlack)) { /* If the sibling has two black children, color it red */ sibling->color = rbcRed; if (curr_node->parent->color == rbcRed) { /* If the parent is red, we can safely color it black and terminate * the fix-up process. */ curr_node->parent->color = rbcBlack; curr_node = tree->root; /* In order to stop the while loop */ } else { /* The black depth of the entire sub-tree rooted at the parent is * now too small - fix it up recursively. */ curr_node = curr_node->parent; } } else { if (!sibling) { /* Take special care of the case of a NULL sibling */ if (curr_node->parent->color == rbcRed) { curr_node->parent->color = rbcBlack; curr_node = tree->root; /* In order to stop the while loop */ } else { curr_node = curr_node->parent; } } else { /* In this case, at least one of the sibling's children is red. * It is therfore obvious that the sibling itself is black. */ if (sibling->left && sibling->left->color == rbcRed) { /* If the left child of the sibling is red, color it black and * rotate around the current parent */ sibling->left->color = rbcBlack; rbtree_rotate_right(tree, curr_node->parent); } else { /* If the right child of the sibling is red, rotate around the * sibling, then rotate around the new sibling of our current * node */ rbtree_rotate_left(tree, sibling); sibling = curr_node->parent->left; rbtree_rotate_right(tree, sibling); } /* It is now safe to color the parent black and to terminate the * fix-up process. */ if (curr_node->parent->parent) curr_node->parent->parent->color = curr_node->parent->color; curr_node->parent->color = rbcBlack; curr_node = tree->root; /* In order to stop the while loop */ } } } } /* The root can always be colored black */ curr_node->color = rbcBlack; } /* Traverse a red-black tree */ void rbtree_traverse(red_black_tree_t * tree, pfcbRBTreeOperFunc * op, void *param) { rbnode_traverse(tree->root, op, param); } /* Right-first traverse a red-black tree */ void rbtree_traverse_right(red_black_tree_t * tree, pfcbRBTreeOperFunc * op, void *param) { rbnode_traverse_right(tree->root, op, param); }

// // rbtree_test.c // by cheungmine // #include <stdio.h> #include <stdlib.h> #include <assert.h> // RBTREE_SUPPORTS_MULTI_OBJECTS 在下面的文件中被定义，如果不想支持多图，注释掉它 #include "red_black_tree.h" /*! */ int cmp_int(int a, int b) { return (a > b) ? -1 : ((a == b) ? 0 : 1); } /*! */ void my_print(int value) { printf("%d ", value); } #if !defined(RBTREE_SUPPORTS_MULTI_OBJECTS) void test_rbtree_insert_repeat() { int i, n; red_black_tree_t tree; red_black_node_t *node, *node2; n = 20; rbtree_init(&tree, (pfcbRBTreeCompFunc*) cmp_int); for (i=0; i<n; i++){ rbtree_insert(&tree, (void*) i); } node = rbtree_find(&tree, (void*) 5); assert(node); node2 = rbtree_insert(&tree, (void*) 5); assert(node2); assert(node!=node2); node = rbtree_find(&tree, (void*) 10); assert(node); node2 = rbtree_insert(&tree, (void*) 10); assert(node2); assert(node!=node2); printf("n = %d, d = %d/n", n, rbtree_depth(&tree)); rbtree_traverse(&tree, (pfcbRBTreeOperFunc*) my_print); printf("/n"); rbtree_traverse_right(&tree, (pfcbRBTreeOperFunc*) my_print); printf("/n"); rbtree_clean(&tree); } #endif void test_rbtree_insert_unique() { int i, n; red_black_tree_t tree; red_black_node_t *node, *node2; n = 20; rbtree_init(&tree, (pfcbRBTreeCompFunc*) cmp_int); for (i=0; i<n; i++){ rbtree_insert_unique(&tree, (void*) i); } node = rbtree_find(&tree, (void*) 5); assert(node); node2 = rbtree_insert_unique(&tree, (void*) 5); assert(node2); assert(node==node2); node = rbtree_find(&tree, (void*) 10); assert(node); node2 = rbtree_insert_unique(&tree, (void*) 10); assert(node2); assert(node==node2); printf("n = %d, d = %d/n", n, rbtree_depth(&tree)); rbtree_traverse(&tree, (pfcbRBTreeOperFunc*) my_print, 0); printf("/n"); rbtree_traverse_right(&tree, (pfcbRBTreeOperFunc*) my_print, 0); printf("/n"); rbtree_clean(&tree); } #ifdef RBTREE_SUPPORTS_MULTI_OBJECTS typedef struct _MYOBJECT { struct _MYOBJECT *__next_object; int data; }MYOBJECT; int cmp_int_multimap(MYOBJECT *a, MYOBJECT *b) { return (a->data > b->data) ? -1 : ((a->data == b->data) ? 0 : 1); } /*! */ void my_print_multimap(MYOBJECT *obj) { while (obj) { printf("%d ", obj->data); obj = obj->__next_object; } } void test_rbtree_insert_multimap() { int i, n; MYOBJECT *obj; MYOBJECT **objects; red_black_tree_t tree; red_black_node_t *node; n = 20; rbtree_init(&tree, (pfcbRBTreeCompFunc*) cmp_int_multimap); objects = (MYOBJECT**) calloc(n, sizeof(MYOBJECT*)); for (i=0; i<n; i++){ obj = (MYOBJECT*) malloc(sizeof(MYOBJECT)); objects[i] = obj; obj->__next_object = 0; // MUST be NULL obj->data = i; rbtree_insert(&tree, (void*) obj); } rbtree_insert(&tree, (void*) objects[5]); obj = (MYOBJECT*) malloc(sizeof(MYOBJECT)); obj->__next_object = 0; // MUST be NULL obj->data = 5; rbtree_insert(&tree, (void*) obj); printf("n = %d, d = %d/n", n, rbtree_depth(&tree)); printf("("); node = rbtree_find(&tree, (void*) objects[5]); if (node){ MYOBJECT *obj = node->object; while (obj) { printf("%d ", obj->data); obj = obj->__next_object; } } printf(")/n"); rbtree_traverse(&tree, (pfcbRBTreeOperFunc*) my_print_multimap, 0); printf("/n"); rbtree_traverse_right(&tree, (pfcbRBTreeOperFunc*) my_print_multimap, 0); printf("/n"); rbtree_clean(&tree); for (i=0; i<n; i++){ free(objects[i]); } free(objects); free(obj); } #endif // RBTREE_SUPPORTS_MULTI_OBJECTS int main(int argc, char * argv[]) { #if !defined(RBTREE_SUPPORTS_MULTI_OBJECTS) test_rbtree_insert_repeat(); #endif test_rbtree_insert_unique(); test_rbtree_insert_multimap(); return 0; }

 

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