forked from xuos/xiuos
rbtree
This commit is contained in:
lmh
parent
7754a149a9
commit
a95841c277
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@ -240,5 +240,9 @@ menu "test app"
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bool "Config test soft timer"
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default n
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menuconfig USER_TEST_RBTREE
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bool "Config test red black tree"
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default n
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endif
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endmenu
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@ -99,6 +99,10 @@ ifeq ($(CONFIG_ADD_XIZI_FETURES),y)
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ifeq ($(CONFIG_USER_TEST_TIMER),y)
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SRC_FILES += test_timer.c
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endif
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ifeq ($(CONFIG_USER_TEST_RBTREE),y)
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SRC_FILES += test_rbtree/test_rbtree.c
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endif
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include $(KERNEL_ROOT)/compiler.mk
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@ -0,0 +1,69 @@
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# 基于cortex-m4-emulator实现红黑树并测试验证
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## 1. 简介
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红黑树是一种自平衡的二叉查找树，具有良好的插入、删除和查找性能，本次提交结果为红黑树数据结构的简单实现。test_rbtree.h中定义了红黑树的数据结构和声明插入、删除、查找相关操作函数;test_rbtree.c中为操作函数的定义，并提供了测试函数TestRBTree用于验证红黑树的正确性。
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## 2. 数据结构设计说明
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**RBNodeType 结构体**
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用来存储一个红黑树结点的相关信息
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- key：节点的键值
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- left_child：指向左子节点的指针
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- right_child：指向右子节点的指针
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- parent：指向父节点的指针
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- is_red：表示节点的颜色，true表示红色，false表示黑色
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**RBTreeType 结构体**
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用来存储一个红黑树的相关信息
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- root：指向红黑树的根节点的指针
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- leaf：红黑树的叶节点，由于叶节点并不需要存储数据，故每棵树只分配一个叶节点
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**RBTreeTraversal 函数**
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该函数用于遍历红黑树并打印节点的键值。采用中序遍历的方式，递归地遍历左子树、当前节点和右子树。
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**RBTreeLeftRotate 函数**
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该函数实现红黑树的左旋转操作。接受一个当前节点指针作为参数，并按照左旋转的规则调整节点和子树的位置。
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**RBTreeRightRotate 函数**
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该函数实现红黑树的右旋转操作。接受一个当前节点指针作为参数，并按照右旋转的规则调整节点和子树的位置。
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**InsertFixup 函数**
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该函数用于插入节点后修复红黑树的平衡性。接受一个当前节点指针作为参数，并根据红黑树的性质进行旋转和着色操作，以恢复平衡。
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**RBTreeInsert 函数**
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该函数用于向红黑树中插入一个新节点。接受一个新节点指针作为参数，并根据新节点的键值插入到适当的位置，然后调用 InsertFixup 进行修复。
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**DeleteFixup 函数**
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该函数用于删除节点后修复红黑树的平衡性。接受一个当前节点指针作为参数，并根据红黑树的性质进行旋转和着色操作，以恢复平衡。
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**RBTreeDelete 函数**
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该函数用于从红黑树中删除指定节点。接受一个目标节点指针作为参数，并根据不同的情况进行节点的替换和删除操作，然后调用 DeleteFixup 进行修复。
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**FindSuccessor 函数**
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该函数用于查找给定节点的后继节点。接受一个当前节点指针作为参数，并在红黑树中找到当前节点的后继节点。
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**RBTreeSearch 函数**
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该函数用于在红黑树中查找指定键值的节点。接受一个键值作为参数，并在红黑树中进行查找，返回找到的节点指针。
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## 3. 测试程序说明
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TestRBTree用于验证红黑树的功能和正确性,下面是该程序的使用步骤和说明:
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- 函数中定义一个默认关键字数组，其中包含了20个整数关键字，运行时自动遍历数组构建红黑树，构建完成后中序遍历输出结果，可以根据输出结果验证红黑树的节点顺序以及颜色是否符合预期。
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- 对关键字数组中的每个关键字，在红黑树中进行搜索，并输出找到节点的父节点、左子节点和右子节点的关键字，随后删除该节点。
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- 在每次删除操作后，程序会询问是否显示当前的红黑树。如果输入 "Y" 或 "y"，将再次进行中序遍历，并输出当前红黑树中的结点，可以根据输出结果查看结点是否符合预期。当树空时结束程序。
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## 4. 运行结果（##需结合运行测试截图按步骤说明##）
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根据默认关键字数组构建红黑树
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根据键值查找结点，输出相关信息并删除，可以输入'Y'或'y'展示删除后的红黑树
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到达空树，退出程序
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@ -0,0 +1,341 @@
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/*
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* Copyright (c) 2023 AIIT XUOS Lab
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* XiUOS is licensed under Mulan PSL v2.
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* You can use this software according to the terms and conditions of the Mulan PSL v2.
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* You may obtain a copy of Mulan PSL v2 at:
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* http://license.coscl.org.cn/MulanPSL2
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* THIS SOFTWARE IS PROVIDED ON AN "AS IS" BASIS, WITHOUT WARRANTIES OF ANY KIND,
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* EITHER EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO NON-INFRINGEMENT,
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* MERCHANTABILITY OR FIT FOR A PARTICULAR PURPOSE.
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* See the Mulan PSL v2 for more details.
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*/
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/**
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* @file: test_rbtree.c
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* @brief: a application of red-black tree function
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* @version: 1.0
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* @author: AIIT XUOS Lab
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* @date: 2023/6/23
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*/
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#include<string.h>
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#include <transform.h>
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#include"test_rbtree.h"
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#ifdef ADD_XIZI_FETURES
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void RBTreeTraversal(RBTreeType *tree, RBNodeType *node)
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{
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if (node != tree->leaf) {
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RBTreeTraversal(tree, node->left_child);
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printf("key:%d, color:%s\n", node->key, (node->is_red ? "Red" : "Black"));
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RBTreeTraversal(tree, node->right_child);
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}
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}
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RBNodeType* RBTreeSearch(RBTreeType *tree, int key)
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{
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RBNodeType* current_node = tree->root;
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while (current_node != tree->leaf){
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if (key < current_node->key)
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current_node = current_node->left_child;
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else if (key > current_node->key)
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current_node = current_node->right_child;
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else
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return current_node;
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}
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return tree->leaf;
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}
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void RBTreeLeftRotate(RBTreeType *tree, RBNodeType *current_node)
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{
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RBNodeType* child_node = current_node->right_child;
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current_node->right_child = child_node->left_child;
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if (child_node->left_child != tree->leaf)
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child_node->left_child->parent = current_node;
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child_node->parent = current_node->parent;
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if (current_node->parent == tree->leaf)
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tree->root = child_node;
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else if (current_node == current_node->parent->left_child)
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current_node->parent->left_child = child_node;
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else
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current_node->parent->right_child = child_node;
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child_node->left_child = current_node;
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current_node->parent = child_node;
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}
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void RBTreeRightRotate(RBTreeType *tree, RBNodeType* current_node)
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{
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RBNodeType* child_node = current_node->left_child;
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current_node->left_child = child_node->right_child;
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if (child_node->right_child != tree->leaf)
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child_node->right_child->parent = current_node;
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child_node->parent = current_node->parent;
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if (current_node->parent == tree->leaf)
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tree->root = child_node;
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else if (current_node == current_node->parent->right_child)
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current_node->parent->right_child = child_node;
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else
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current_node->parent->left_child = child_node;
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child_node->right_child = current_node;
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current_node->parent = child_node;
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}
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void InsertFixup(RBTreeType *tree, RBNodeType* current_node)
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{
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while (current_node->parent->is_red){
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/* The parent of current_node is the left subtree of the grandfather */
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if (current_node->parent == current_node->parent->parent->left_child){
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RBNodeType * uncle_node = current_node->parent->parent->right_child;
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if (uncle_node->is_red){ /* case1:red uncle and red parent, change color */
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uncle_node->is_red = false;
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current_node->parent->is_red = false;
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current_node->parent->parent->is_red = true;
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current_node = current_node->parent->parent;
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}else{ /* case2:black uncle and red parent, need rotation */
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if (current_node->parent->right_child == current_node){
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current_node = current_node->parent;
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RBTreeLeftRotate(tree, current_node);
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}
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current_node->parent->is_red = false;
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current_node->parent->parent->is_red = true;
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RBTreeRightRotate(tree, current_node->parent->parent);
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}
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/* The parent of current_node is the right subtree of the grandfather, same with left subtree */
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}else{
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RBNodeType * uncle_node = current_node->parent->parent->left_child;
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if (uncle_node->is_red){
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uncle_node->is_red = false;
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current_node->parent->is_red = false;
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current_node->parent->parent->is_red = true;
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current_node = current_node->parent->parent;
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}else{
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if (current_node->parent->left_child == current_node){
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current_node = current_node->parent;
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RBTreeRightRotate(tree, current_node);
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}
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current_node->parent->is_red = false;
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current_node->parent->parent->is_red = true;
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RBTreeLeftRotate(tree, current_node->parent->parent);
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}
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}
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}
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tree->root->is_red = false;
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}
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void RBTreeInsert(RBTreeType *tree, RBNodeType* new_node)
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{
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RBNodeType* previous_node = tree->root;
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RBNodeType* current_node = tree->root;
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while (current_node != tree->leaf){
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previous_node = current_node;
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if (new_node->key > current_node->key)
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current_node = current_node->right_child;
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else if (new_node->key < current_node->key)
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current_node = current_node->left_child;
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else
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return;
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}
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if (previous_node == tree->leaf){
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tree->root = new_node;
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tree->root->parent = tree->leaf;
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}else{
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new_node->parent = previous_node;
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if (previous_node->key > new_node->key)
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previous_node->left_child = new_node;
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else
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previous_node->right_child = new_node;
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}
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InsertFixup(tree, new_node);
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}
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RBNodeType* FindSuccessor(RBTreeType *tree, RBNodeType* current_node)
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{
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RBNodeType* parent_node = current_node->parent;
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if (current_node->right_child != tree->leaf){
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current_node = current_node->right_child;
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while (current_node->left_child != tree->leaf)
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current_node = current_node->left_child;
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return current_node;
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}
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while ((parent_node != tree->leaf) && (current_node == parent_node->right_child)){
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current_node = parent_node;
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parent_node = parent_node->parent;
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}
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return parent_node;
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}
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void DeleteFixup(RBTreeType *tree, RBNodeType* current_node)
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{
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while ((current_node != tree->root) && (current_node->is_red == false)){
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if (current_node == current_node->parent->left_child){
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RBNodeType* brother_node = current_node->parent->right_child;
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if (brother_node->is_red){
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brother_node->is_red = false;
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current_node->parent->is_red = true;
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RBTreeLeftRotate(tree, current_node->parent);
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brother_node = current_node->parent->right_child;
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}
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if ((brother_node->left_child->is_red == false) && (brother_node->right_child->is_red == false)){
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brother_node->is_red = true;
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current_node = current_node->parent;
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}else{
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if (brother_node->right_child->is_red == false){
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brother_node->left_child->is_red = false;
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brother_node->is_red = true;
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RBTreeRightRotate(tree, brother_node);
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brother_node = current_node->parent->right_child;
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}
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brother_node->is_red = current_node->parent->is_red;
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current_node->parent->is_red = false;
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brother_node->right_child->is_red = false;
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RBTreeLeftRotate(tree, current_node->parent);
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current_node = tree->root;
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}
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}else{
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RBNodeType* brother_node = current_node->parent->left_child;
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if (brother_node->is_red){
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brother_node->is_red = false;
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current_node->parent->is_red = true;
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RBTreeRightRotate(tree, current_node->parent);
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brother_node = current_node->parent->left_child;
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}
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if ((brother_node->left_child->is_red == false) && (brother_node->right_child->is_red == false)){
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brother_node->is_red = true;
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current_node = current_node->parent;
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}else{
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if (brother_node->left_child->is_red == false){
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brother_node->right_child->is_red = false;
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brother_node->is_red = true;
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RBTreeLeftRotate(tree, brother_node);
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brother_node = current_node->parent->left_child;
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}
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brother_node->is_red = current_node->parent->is_red;
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current_node->parent->is_red = false;
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brother_node->left_child->is_red = false;
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RBTreeRightRotate(tree, current_node->parent);
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current_node = tree->root;
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}
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}
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}
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current_node->is_red = false;
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}
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void RBTreeDelete(RBTreeType *tree, RBNodeType* target_node)
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{
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RBNodeType* delete_node = tree->leaf;
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RBNodeType* replace_node = tree->leaf;
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if ((target_node->left_child == tree->leaf) || (target_node->right_child == tree->leaf))
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delete_node = target_node;
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else
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delete_node = FindSuccessor(tree, target_node);
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if (delete_node->left_child != tree->leaf) /* successor still has subtree */
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replace_node = delete_node->left_child;
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else if (delete_node->right_child != tree->leaf)
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replace_node = delete_node->right_child;
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replace_node->parent = delete_node->parent;
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if (delete_node->parent == tree->leaf) /* delete a root node */
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tree->root = replace_node;
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else if (delete_node == delete_node->parent->left_child)
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delete_node->parent->left_child = replace_node;
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else
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delete_node->parent->right_child = replace_node;
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if (delete_node != target_node)
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target_node->key = delete_node->key;
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if (delete_node->is_red == false)
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DeleteFixup(tree, replace_node);
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free(delete_node);
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}
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void TestRBTree(void)
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{
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int default_key[] = { 16, 25, 23, 5, 2, 6, 17, 37, 38, 98, 20, 19, 47, 49, 12, 21, 9, 18, 14, 15 };
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int array_size = sizeof(default_key) / sizeof(default_key[0]);
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printf("Test Red Black Tree\n");
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printf("default_key array: ");
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for (int i = 0; i < array_size; i++)
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printf("%d ", default_key[i]);
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printf("\n%d elements\n", array_size);
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RBTreeType *tree = (RBTreeType *)malloc(sizeof(RBTreeType));
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if (tree == NULL) {
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printf("malloc failed\n");
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return;
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}
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tree->leaf = (RBNodeType*)malloc(sizeof(RBNodeType));
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tree->leaf->left_child = NULL;
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tree->leaf->right_child = NULL;
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tree->leaf->parent = NULL;
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tree->leaf->is_red = false;
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tree->leaf->key = -1;
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tree->root = tree->leaf;
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RBNodeType *node = tree->leaf;
|
||||
|
||||
for (int i = 0; i < array_size; i++) {
|
||||
node = (RBNodeType*)malloc(sizeof(RBNodeType));
|
||||
node->left_child = tree->leaf;
|
||||
node->right_child = tree->leaf;
|
||||
node->parent = NULL;
|
||||
node->is_red = true;
|
||||
node->key = default_key[i];
|
||||
printf("insert key[%d]=%d\n",i,default_key[i]);
|
||||
RBTreeInsert(tree, node);
|
||||
}
|
||||
|
||||
printf("------------------Inorder Traversal------------------\n");
|
||||
RBTreeTraversal(tree, tree->root);
|
||||
|
||||
for (int i = 0; i < array_size; i++) {
|
||||
printf("search key = %d\n", default_key[i]);
|
||||
node = RBTreeSearch(tree, default_key[i]);
|
||||
printf("search succeeded, parent node: %d, left-child: %d, right-child: %d\n", node->parent->key, node->left_child->key, node->right_child->key);
|
||||
|
||||
printf("delete key = %d\n", node->key);
|
||||
RBTreeDelete(tree, node);
|
||||
|
||||
printf("Show current tree?Y/N \n");
|
||||
char ch;
|
||||
scanf("%c", &ch);
|
||||
if (ch == 'Y' || ch == 'y') {
|
||||
printf("------------------Inorder Traversal Tree After Deletion------------------\n");
|
||||
if (tree->root != tree->leaf)
|
||||
RBTreeTraversal(tree, tree->root);
|
||||
else
|
||||
printf("the tree is empty.\n");
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
PRIV_SHELL_CMD_FUNCTION(TestRBTree, a red-black tree test sample, PRIV_SHELL_CMD_MAIN_ATTR);
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,60 @@
|
|||
/*
|
||||
* Copyright (c) 2023 AIIT XUOS Lab
|
||||
* XiUOS is licensed under Mulan PSL v2.
|
||||
* You can use this software according to the terms and conditions of the Mulan PSL v2.
|
||||
* You may obtain a copy of Mulan PSL v2 at:
|
||||
* http://license.coscl.org.cn/MulanPSL2
|
||||
* THIS SOFTWARE IS PROVIDED ON AN "AS IS" BASIS, WITHOUT WARRANTIES OF ANY KIND,
|
||||
* EITHER EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO NON-INFRINGEMENT,
|
||||
* MERCHANTABILITY OR FIT FOR A PARTICULAR PURPOSE.
|
||||
* See the Mulan PSL v2 for more details.
|
||||
*/
|
||||
|
||||
/**
|
||||
* @file: test_rbtree.h
|
||||
* @brief: a head file of red-black tree structure
|
||||
* @version: 1.0
|
||||
* @author: AIIT XUOS Lab
|
||||
* @date: 2023/6/23
|
||||
*/
|
||||
#ifndef REDBLACKTREE_H_
|
||||
#define REDBLACKTREE_H_
|
||||
#include <stdbool.h>
|
||||
#include <stdio.h>
|
||||
|
||||
typedef struct RedBlackNode
|
||||
{
|
||||
int key;
|
||||
struct RedBlackNode *left_child;
|
||||
struct RedBlackNode *right_child;
|
||||
struct RedBlackNode *parent;
|
||||
bool is_red;
|
||||
} RBNodeType;
|
||||
|
||||
typedef struct RedBlackTree
|
||||
{
|
||||
RBNodeType *root;
|
||||
RBNodeType *leaf;
|
||||
} RBTreeType;
|
||||
|
||||
void TestRBTree(void);
|
||||
|
||||
void RBTreeTraversal(RBTreeType *tree, RBNodeType *node);
|
||||
|
||||
void RBTreeLeftRotate(RBTreeType *tree, RBNodeType *current_node);
|
||||
|
||||
void RBTreeRightRotate(RBTreeType *tree, RBNodeType* current_node);
|
||||
|
||||
void InsertFixup(RBTreeType *tree, RBNodeType* current_node);
|
||||
|
||||
void RBTreeInsert(RBTreeType *tree, RBNodeType* new_node);
|
||||
|
||||
void DeleteFixup(RBTreeType *tree, RBNodeType* current_node);
|
||||
|
||||
void RBTreeDelete(RBTreeType *tree, RBNodeType* target_node);
|
||||
|
||||
RBNodeType* FindSuccessor(RBTreeType *tree, RBNodeType* current_node);
|
||||
|
||||
RBNodeType* RBTreeSearch(RBTreeType *tree, int key);
|
||||
|
||||
#endif
|
||||
Loading…
Reference in New Issue