一步一步写算法(之排序二叉树删除-3)
【 声明:版权所有,欢迎转载,请勿用于商业用途。 联系信箱:feixiaoxing @163.com】
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?
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 删除的节点有左子树,没有右子树
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:
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 删除的节点左子树为空,右子树节点不为空
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:
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 删除的节点左右子树均不为空,不过又要分为两种情形:
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?
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;pLeftMax->left_child->parent = pLeftMax->parent;pTreeNode = pLeftMax;}}free(pTreeNode);return TRUE;
}
结束总结:
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;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;pLeftMax->left_child->parent = pLeftMax->parent; 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;pLeftMax->left_child->parent = pLeftMax->parent;pTreeNode = pLeftMax;}}free(pTreeNode);return TRUE;}return _delete_node_from_tree(pTreeNode);
}
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