一步一步写算法（之排序二叉树删除-2）
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2.4 删除节点的左右子树都存在，此时又会分成两种情形
1）左节点是当前左子树的最大节点，此时只需要用左节点代替根节点即可
/*
*
* 10 ======> 6
* / \ / \
* 6 15 5 15
* /
* 5
*/
/*
*
* 10 ======> 6
* / \ / \
* 6 15 5 15
* /
* 5
*/ 代码该怎么编写呢？
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;
}
}
free(pTreeNode);
return TRUE;
}
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;
}
}
free(pTreeNode);
return TRUE;
}
return TRUE;
} 上面的代码中添加的内容表示了我们介绍的这一情形。为此，我们可以设计一种测试用例。依次插入10、6、5、15，然后删除10即可。
static void test6()
{
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, 15));
assert(TRUE == delete_node_from_tree(&pTreeNode, 10));
assert(6 == pTreeNode->data);
assert(NULL == pTreeNode->parent);
assert(15 == pTreeNode->right_child->data);
assert(pTreeNode = pTreeNode->right_child->parent);
assert(NULL == pTreeNode->parent);
free(pTreeNode->left_child);
free(pTreeNode->right_child);
free(pTreeNode);
}
static void test6()
{
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, 15));
assert(TRUE == delete_node_from_tree(&pTreeNode, 10));
assert(6 == pTreeNode->data);
assert(NULL == pTreeNode->parent);
assert(15 == pTreeNode->right_child->data);
assert(pTreeNode = pTreeNode->right_child->parent);
assert(NULL == pTreeNode->parent);
free(pTreeNode->left_child);
free(pTreeNode->right_child);
free(pTreeNode);
} 如果上面的测试用例通过，表示我们添加的代码没有问题。
2）左节点不是当前左子树的最大节点，情形如下所示
/*
*
* 10 ======> 8
* / \ / \
* 6 15 5 15
* \
* 8
*/
/*
*
* 10 ======> 8
* / \ / \
* 6 15 5 15
* \
* 8
*/ 此时，我们应该用10左侧的最大节点8代替删除的节点10即可。
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 = NULL;
pTreeNode = pLeftMax;
}
}
free(pTreeNode);
return TRUE;
}
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 = NULL;
pTreeNode = pLeftMax;
}
}
free(pTreeNode);
return TRUE;
}
return TRUE;
} 那么，这个场景下面测试用例又该怎么设计呢？其实只需要按照上面给出的示意图进行即可。依次插入数据10、6、8、15，然后删除数据10。
static void test7()
{
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 == insert_node_into_tree(&pTreeNode, 15));
assert(TRUE == delete_node_from_tree(&pTreeNode, 10));
assert(8 == pTreeNode->data);
assert(NULL == pTreeNode->parent);
assert(NULL == pTreeNode->left_child->right_child);
assert(NULL == pTreeNode->parent);
free(pTreeNode->left_child);
free(pTreeNode->right_child);
free(pTreeNode);
}
static void test7()
{
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 == insert_node_into_tree(&pTreeNode, 15));
assert(TRUE == delete_node_from_tree(&pTreeNode, 10));
assert(8 == pTreeNode->data);
assert(NULL == pTreeNode->parent);
assert(NULL == pTreeNode->left_child->right_child);
assert(NULL == pTreeNode->parent);
free(pTreeNode->left_child);
free(pTreeNode->right_child);
free(pTreeNode);
} 至此，删除节点为根节点的情形全部讨论完毕，那么如果删除的节点是普通节点呢，那应该怎么解决呢？
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 = NULL;
pTreeNode = pLeftMax;
}
}
free(pTreeNode);
return TRUE;
}
return _delete_node_from_tree(pTreeNode);
}
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 = NULL;
pTreeNode = pLeftMax;
}
}
free(pTreeNode);
return TRUE;
}
return _delete_node_from_tree(pTreeNode);
} 我们在当前函数的最后一行添加_delete_node_from_tree，这个函数用来处理普通节点的删除情况，我们会在下面一篇博客中继续介绍。
3、 普通节点的删除
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