用二叉樹作爲存儲結構時,取到一個節點,只能獲取節點的左孩子和右孩子,不能直接得到節點的任一遍歷序列的前驅或者後繼。但是常常我們會想要更加直觀的知道節點的前驅後繼。線索二叉樹顯得尤爲的重要。
線索二叉樹的關鍵就是要定義一個全局變量來存放上一個訪問過的結點。
Node* prev;
(一)前序線索二叉樹
void PrevOrderTag() { _PrevOrderTag(_root); } void _PrevOrderTag(Node* root)//前序線索二叉樹 { if (root == NULL) return; if (!root->_left) { root->_leftTag = THREAD; root->_left = prev; } if (prev && !prev->_right) { prev->_rightTag = THREAD; prev->_right = root; } prev = root; if (root->_leftTag == LINK)//只有當_leftTag爲LINK時遞歸修改前驅後繼 _PrevOrderTag(root->_left); if (root->_rightTag == LINK) _PrevOrderTag(root->_right); } void PrevOrderTagPrint()//前序線索化打印 { Node* cur = _root; //while (cur) //{ // while (cur->_leftTag == LINK) // { // cout << cur->_data << " "; // cur = cur->_left; // } // cout << cur->_data << " "; // cur = cur->_right; //} //2. while (cur) { cout << cur->_data << " "; if (cur->_leftTag == LINK) { cur = cur->_left; } else { cur = cur->_right; } } }
使用二叉樹的線索打印二叉樹是比較方便的,不用遞歸就能解決問題。只要cur不爲NULL就一直尋找後繼打印。
(二)中序線索二叉樹
void MidOrderTag() { _MidOrderTag(_root); } void _MidOrderTag(Node* root)//中序線索二叉樹 { if (root == NULL) { return; } if (root->_leftTag == LINK)//只有當_leftTag爲LINK時遞歸修改前驅後繼 _MidOrderTag(root->_left); if (!root->_left) { root->_leftTag = THREAD; root->_left = prev; } if (prev&&!prev->_right) { prev->_rightTag = THREAD; prev->_right = root; } prev = root; if (root->_rightTag == LINK) _MidOrderTag(root->_right); } void MidOrderTagPrint()//中序線索打印 { Node* cur = _root; while (cur) { while (cur->_leftTag == LINK) { cur = cur->_left; } cout << cur->_data << " "; while (cur->_rightTag == THREAD) { cur = cur->_right; cout << cur->_data << " "; } cur = cur->_right;//在打印右子樹之前一定保證左子樹已經打印過了 } cout << endl; }
前序的線索化打印不難懂,但是中序得知道什麼時候訪問右結點,在訪問了左節點後才能訪問右節點。
(三)後序線索二叉樹
void RearOrderTag() { _RearOrderTag(_root); } void _RearOrderTag(Node* root)//後序線索二叉樹 { if (root == NULL) { return; } if (root->_leftTag == LINK)//只有當_leftTag爲LINK時遞歸修改前驅後繼 _RearOrderTag(root->_left); if (root->_rightTag == LINK) _RearOrderTag(root->_right); if (!root->_left) { root->_leftTag = THREAD; root->_left = prev; } if (prev&&!prev->_right) { prev->_rightTag = THREAD; prev->_right = root; } prev = root; }
注意,線索二叉樹只有當tag的類型爲LINK時才修改結點的前驅和後繼