手寫實現搜索二叉樹:
- 樹的節點定義:
class TreeNode
{
public:
TreeNode(int v) :value(v){};
TreeNode* left_son = NULL;
TreeNode* right_son = NULL;
TreeNode* p = NULL; //一定保存雙親的指針
int value = 0;
};
- 節點插入:
bool TreeInsert(TreeNode*& pRoot,int value)
{
TreeNode* pNew = new TreeNode(value);//待插入的節點
TreeNode* pParent = NULL;//父節點
TreeNode* pCur = pRoot;//子節點
while (pCur != NULL)
{
pParent = pCur;
if (pCur->value < value)
{
pCur = pCur->right_son;
}
else if (pCur->value>value)
{
pCur = pCur->left_son;
}
else
{
return false;
}
}
if (pParent == NULL)//空樹
{
pRoot = pNew;
}
else if ( pParent->value<value )//插右邊
{
pParent->right_son = pNew;
pNew->p = pParent;
}
else//插左邊
{
pParent->left_son = pNew;
pNew->p = pParent;
}
return true;
}
- 最大值,最小值函數
TreeNode* TreeMax(TreeNode* pRoot)
{
while (pRoot!=NULL&&pRoot->right_son!=NULL)
{
pRoot = pRoot->right_son;
}
return pRoot;
}
TreeNode* TreeMin(TreeNode* pRoot)
{
while (pRoot!=NULL&&pRoot->left_son!=NULL)
{
pRoot = pRoot->left_son;
}
return pRoot;
}
- 前驅、後繼函數
TreeNode* Successor(TreeNode* pRoot)
{
/*
尋找節點的後繼節點
方法一:中序遍歷,後繼即 該節點輸出的後一個節點
方法二:若當前節點有右孩子,則後繼爲右孩子子樹的最小節點
若當前節點無右孩子,則後繼爲其最底層的祖先,條件是該結點位於此祖先的左子樹
*/
if (pRoot==NULL)
{
return pRoot;
}
if (pRoot->right_son != NULL)// 當前節點有右孩子
{
return TreeMin(pRoot->right_son);
}
TreeNode* pChild = pRoot;
TreeNode* pParent = pChild->p;
while (pParent != NULL&&pParent->right_son == pChild)//當前節點無右孩子,尋找滿足要求的最底層祖先
{
pChild = pParent;
pParent = pParent->p;
}
return pParent;
}
TreeNode* Processor(TreeNode* pRoot)
{
/*
尋找節點的前驅節點
若當前節點有左孩子,則前驅爲左孩子子樹的最大節點
若當前節點無左孩子,則後繼爲其最底層的祖先,條件是該結點位於此祖先的右子樹
*/
if (pRoot == NULL)
{
return pRoot;
}
if (pRoot->left_son != NULL)//有左孩子
{
return TreeMax(pRoot->left_son);
}
TreeNode* pChild = pRoot;
TreeNode* pParent = pChild->p;
while (pParent != NULL&&pParent->left_son == pChild)//無左孩子,尋找滿足要求的最底層祖先
{
pChild = pParent;
pParent = pParent->p;
}
return pParent;
}
- 替換函數,使用一棵樹接管另一棵樹的雙親
bool TransPlant(TreeNode *& pRoot, TreeNode* pOld, TreeNode* pNew)
{
/*
使用一棵樹接管另一棵樹的雙親
*/
if (pRoot == NULL||pOld == NULL)//舊子樹爲空
{
return false;
}
//調整父節點的指針
if (pOld->p == NULL)//父節點爲空:替換了根節點
{
pRoot = pNew;
}
else
{
if (pOld == pOld->p->left_son)
{
pOld->p->left_son = pNew;
}
else
{
pOld->p->right_son = pNew;
}
}
//調整指向父節點的指針
if (pNew != NULL)//新子樹不爲空
{
pNew->p = pOld->p;
}
return true;
}
- 刪除節點
void TreeDelete(TreeNode*& pRoot, TreeNode* pDelete)
{
/*
刪除指定節點
*/
if (pRoot == NULL || pDelete == NULL)
return;
if (pDelete->left_son == NULL)//沒有孩子或者只有一個孩子,直接將孩子提上來
{
TransPlant(pRoot,pDelete, pDelete->right_son);
}
else if (pDelete->right_son == NULL)
{
TransPlant(pRoot,pDelete, pDelete->left_son);
}
else//同時有兩個孩子時
{
TreeNode* successor = TreeMin(pDelete->right_son);//尋找後繼,後繼一定沒有左孩子節點
if (successor->p != pDelete)//後繼不是被刪除節點的右孩子節點
{
TransPlant(pRoot,successor, successor->right_son);//刪除後繼節點
successor->right_son = pDelete->right_son;//將後繼提到被刪除節點右孩子位置上:接管被刪除節點的右孩子
successor->right_son->p = successor;
}
TransPlant(pRoot,pDelete, successor);//後繼接管被刪節點的雙親
successor->left_son = pDelete->left_son;//後繼接管被刪節點的左孩子
successor->left_son->p = successor;
}
}
- 中序打印函數
- 測試主函數
void TreePrint(TreeNode* pRoot)
{
if (pRoot == NULL)
{
return;
}
TreePrint(pRoot->left_son);
cout << pRoot->value << " ";
TreePrint(pRoot->right_son);
}
int main()
{
TreeNode* pRoot(NULL);
TreeInsert(pRoot, 4);
TreeInsert(pRoot, 1);
TreeInsert(pRoot, 9);
TreeInsert(pRoot, 2);
TreeInsert(pRoot, 8);
TreeInsert(pRoot, 3);
TreeInsert(pRoot, 6);
TreePrint(pRoot);
cout << endl;
TreeDelete(pRoot,pRoot);
TreePrint(pRoot);
return 0;
}