一步一步写算法（之排序二叉树删除-3）-优快云博客

本文详细阐述了树结构中节点删除的四种情况，并提供了相应的代码实现。包括节点无子树、有左子树无右子树、有右子树无左子树、左右子树均存在的情况，以及左右子树均存在的特殊处理方式。

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3 普通节点的删除

3.1 删除的节点没有左子树，也没有右子树

测试用例1：删除节点6

/* * * 10 ======> 10 * / \ \ * 6 15 15 * */ static void test8() { TREE_NODE* pTreeNode = NULL; assert(TRUE == insert_node_into_tree(&pTreeNode, 10)); assert(TRUE == insert_node_into_tree(&pTreeNode, 6)); assert(6 == pTreeNode->left_child->data); assert(TRUE == insert_node_into_tree(&pTreeNode, 15)); assert(TRUE == delete_node_from_tree(&pTreeNode, 6)); assert(NULL == pTreeNode->left_child); free(pTreeNode->right_child); free(pTreeNode); } 测试用例2：删除节点15

/* * * 10 ======> 10 * / \ / * 6 15 6 * */ static void test9() { TREE_NODE* pTreeNode = NULL; assert(TRUE == insert_node_into_tree(&pTreeNode, 10)); assert(TRUE == insert_node_into_tree(&pTreeNode, 6)); assert(TRUE == insert_node_into_tree(&pTreeNode, 15)); assert(15 == pTreeNode->right_child->data); assert(TRUE == delete_node_from_tree(&pTreeNode, 15)); assert(NULL == pTreeNode->right_child); free(pTreeNode->right_child); free(pTreeNode); } 那么代码应该怎么编写呢？

测试用例1：测试节点6

/* * * 10 ======> 10 * / / * 6 3 * / * 3 */ static void test10() { TREE_NODE* pTreeNode = NULL; assert(TRUE == insert_node_into_tree(&pTreeNode, 10)); assert(TRUE == insert_node_into_tree(&pTreeNode, 6)); assert(TRUE == insert_node_into_tree(&pTreeNode, 3)); assert(TRUE == delete_node_from_tree(&pTreeNode, 6)); assert(3 == pTreeNode->left_child->data); assert(pTreeNode = pTreeNode->left_child->parent); free(pTreeNode->left_child); free(pTreeNode); } 测试用例2：删除节点15

/* * * 10 ======> 10 * \ \ * 15 12 * / * 12 */ static void test11() { TREE_NODE* pTreeNode = NULL; assert(TRUE == insert_node_into_tree(&pTreeNode, 10)); assert(TRUE == insert_node_into_tree(&pTreeNode, 15)); assert(TRUE == insert_node_into_tree(&pTreeNode, 12)); assert(TRUE == delete_node_from_tree(&pTreeNode, 15)); assert(12 == pTreeNode->right_child->data); assert(pTreeNode = pTreeNode->right_child->parent); free(pTreeNode->right_child); free(pTreeNode); } 添加左子树不为空，右子树为空的处理代码，如下所示：

测试用例1：删除数据6

/* * * 10 ======> 10 * / / * 6 8 * \ * 8 */ static void test12() { TREE_NODE* pTreeNode = NULL; assert(TRUE == insert_node_into_tree(&pTreeNode, 10)); assert(TRUE == insert_node_into_tree(&pTreeNode, 6)); assert(TRUE == insert_node_into_tree(&pTreeNode, 8)); assert(TRUE == delete_node_from_tree(&pTreeNode, 6)); assert(8 == pTreeNode->left_child->data); assert(pTreeNode = pTreeNode->left_child->parent); free(pTreeNode->left_child); free(pTreeNode); } 测试用例2：删除数据15

/* * * 10 ======> 10 * \ \ * 15 20 * \ * 20 */ static void test13() { TREE_NODE* pTreeNode = NULL; assert(TRUE == insert_node_into_tree(&pTreeNode, 10)); assert(TRUE == insert_node_into_tree(&pTreeNode, 15)); assert(TRUE == insert_node_into_tree(&pTreeNode, 20)); assert(TRUE == delete_node_from_tree(&pTreeNode, 15)); assert(20 == pTreeNode->right_child->data); assert(pTreeNode = pTreeNode->right_child->parent); free(pTreeNode->right_child); free(pTreeNode); } 添加左子树为空，右子树不为空的处理情形。代码如下：

1）左节点是删除节点左侧的最大节点（删除节点6）

/* * * 10 ======> 10 * / / * 6 5 * / \ \ * 5 8 8 */ static void test14() { TREE_NODE* pTreeNode = NULL; assert(TRUE == insert_node_into_tree(&pTreeNode, 10)); assert(TRUE == insert_node_into_tree(&pTreeNode, 6)); assert(TRUE == insert_node_into_tree(&pTreeNode, 5)); assert(TRUE == insert_node_into_tree(&pTreeNode, 8)); assert(TRUE == delete_node_from_tree(&pTreeNode, 6)); assert(5 == pTreeNode->left_child->data); assert(pTreeNode = pTreeNode->left_child->parent); assert( 8 == pTreeNode->left_child->right_child->data); assert(pTreeNode->left_child = pTreeNode->left_child->right_child->parent); free(pTreeNode->left_child->right_child); free(pTreeNode->left_child); free(pTreeNode); } 2）左节点不是删除节点左侧的最大节点（删除节点5）

/* * * 10 ======> 10 * / / * 5 4 * / \ / \ * 2 6 2 6 * \ * 4 */ static void test15() { TREE_NODE* pTreeNode = NULL; assert(TRUE == insert_node_into_tree(&pTreeNode, 10)); assert(TRUE == insert_node_into_tree(&pTreeNode, 5)); assert(TRUE == insert_node_into_tree(&pTreeNode, 2)); assert(TRUE == insert_node_into_tree(&pTreeNode, 4)); assert(TRUE == insert_node_into_tree(&pTreeNode, 6)); assert(TRUE == delete_node_from_tree(&pTreeNode, 5)); assert(4 == pTreeNode->left_child->data); assert(NULL == pTreeNode->left_child->left_child->right_child); free(pTreeNode->left_child->left_child); free(pTreeNode->left_child->right_child); free(pTreeNode->left_child); free(pTreeNode); } 那么针对这两种类型，我们的代码究竟应该怎么处理呢？

上面的过程记录了我们的代码是怎么一步一步走过来的。最后我们给出一份完整的节点删除代码：

STATUS _delete_node_from_tree(TREE_NODE* pTreeNode) { TREE_NODE* pLeftMax; if(NULL == pTreeNode-> left_child && NULL == pTreeNode->right_child){ if(pTreeNode == pTreeNode->parent->left_child) pTreeNode->parent->left_child = NULL; else pTreeNode->parent->right_child = NULL; }else if(NULL != pTreeNode->left_child && NULL == pTreeNode->right_child){ pTreeNode->left_child->parent = pTreeNode->parent; if(pTreeNode == pTreeNode->parent->left_child) pTreeNode->parent->left_child = pTreeNode->left_child; else pTreeNode->parent->right_child = pTreeNode->left_child; }else if(NULL == pTreeNode->left_child && NULL != pTreeNode->right_child){ pTreeNode->right_child->parent = pTreeNode->parent; if(pTreeNode == pTreeNode->parent->left_child) pTreeNode->parent->left_child = pTreeNode->right_child; else pTreeNode->parent->right_child = pTreeNode->right_child; }else{ pLeftMax = find_max_node(pTreeNode->left_child); if(pLeftMax == pTreeNode->left_child){ if(pTreeNode == pTreeNode->parent->left_child) pTreeNode->parent->left_child = pTreeNode->left_child; else pTreeNode->parent->right_child = pTreeNode->left_child; pTreeNode->left_child->parent = pTreeNode->parent; pTreeNode->left_child->right_child = pTreeNode->right_child; pTreeNode->right_child->parent = pTreeNode-> left_child; }else{ pTreeNode->data = pLeftMax->data; pLeftMax->parent->right_child = pLeftMax->left_child; pTreeNode = pLeftMax; } } free(pTreeNode); return TRUE; } STATUS delete_node_from_tree(TREE_NODE** ppTreeNode, int data) { TREE_NODE* pTreeNode; TREE_NODE* pLeftMax; if(NULL == ppTreeNode || NULL == *ppTreeNode) return FALSE; pTreeNode = find_data_in_tree_node(*ppTreeNode, data); if(NULL == pTreeNode) return FALSE; if(*ppTreeNode == pTreeNode){ if(NULL == pTreeNode->left_child && NULL == pTreeNode->right_child){ *ppTreeNode = NULL; }else if(NULL != pTreeNode->left_child && NULL == pTreeNode->right_child){ *ppTreeNode = pTreeNode->left_child; pTreeNode->left_child->parent = NULL; }else if(NULL == pTreeNode->left_child && NULL != pTreeNode->right_child){ *ppTreeNode = pTreeNode->right_child; pTreeNode->right_child->parent = NULL; }else{ pLeftMax = find_max_node(pTreeNode->left_child); if(pLeftMax == pTreeNode->left_child){ *ppTreeNode = pTreeNode->left_child; (*ppTreeNode)->right_child = pTreeNode->right_child; (*ppTreeNode)->right_child->parent = *ppTreeNode; (*ppTreeNode)->parent = NULL; }else{ pTreeNode->data = pLeftMax->data; pLeftMax->parent->right_child = pLeftMax->left_child; pTreeNode = pLeftMax; } } free(pTreeNode); return TRUE; } return _delete_node_from_tree(pTreeNode); }