排序二叉樹刪除3

    3 普通節點的刪除

    3.1 刪除的節點沒有左子樹，也沒有右子樹

     測試案例1： 刪除節點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);}

測試案例2： 刪除節點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);}

  那麼代碼應該怎麼編寫呢？

 

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;elsepTreeNode->parent->right_child = NULL;}free(pTreeNode);return TRUE;}

  3.2 刪除的節點有左子樹，沒有右子樹

    測試案例1： 測試節點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);}

    測試案例2： 刪除節點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);}

  添加左子樹不為空白，右子樹為空白的處理代碼，如下所示：

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;elsepTreeNode->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;elsepTreeNode->parent->right_child = pTreeNode->left_child;}free(pTreeNode);return TRUE;}

    3.3 刪除的節點左子樹為空白，右子樹節點不為空白

    測試案例1： 刪除資料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);}

  測試案例2： 刪除資料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);}

    添加左子樹為空白，右子樹不為空白的處理情形。代碼如下：

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;elsepTreeNode->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;elsepTreeNode->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;elsepTreeNode->parent->right_child = pTreeNode->right_child;}free(pTreeNode);return TRUE;}

   3.4 刪除的節點左右子樹均不為空白，不過又要分為兩種情形：

    1） 左節點是刪除節點左側的最大節點 （刪除節點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） 左節點不是刪除節點左側的最大節點（刪除節點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);}

    那麼針對這兩種類型，我們的代碼究竟應該怎麼處理呢？

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;elsepTreeNode->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;elsepTreeNode->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;elsepTreeNode->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;elsepTreeNode->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;}

結束總結：

    上面的過程記錄了我們的代碼是怎麼一步一步走過來的。最後我們給出一份完整的節點刪除代碼：

 

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;elsepTreeNode->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;elsepTreeNode->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;elsepTreeNode->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;elsepTreeNode->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);}