使用廣義表建立二叉樹
阿新 • • 發佈：2018-11-03
- 利用廣義表A(B(D,E),C(F,G))建立二叉樹，利用棧來輔助，這裡使用陣列模擬棧。原則如下：
（4）遇到右括號，表明子樹建立結束，根節點出棧。
2. 圖示：待補充
3.示例程式碼：
void CreateBTreeUseList( BTree<char>*& node) { char ch; //節點資料 BTree<char>* st[100]{nullptr}; //用陣列模擬棧 BTree<char>* p = nullptr; //節點 char flag = 2; //左右子樹的標識 int8_t top = -1; //棧頂指標 while ((ch = getchar()) != '\n') //遇到換行符二叉樹建立結束 { switch (ch) { case '(': //遇到左括號，根節點入棧， st[++top] = p; flag = 0; //左子樹開始 break; case ',': flag = 1; //右子樹開始 break; case ')': //遇到右括號，根節點出棧 top--; break; default: //遇到節點資料，分配記憶體，建立新節點 p = new BTree<char>(); p->leftSubTree = nullptr; p->rightSubTree = nullptr; p->data = ch; if (nullptr == mRoot) //儲存整個樹的根節點 mRoot = p; else { switch (flag) //節點的左右子樹 { case 0: //左子樹 st[top]->leftSubTree = p; break; case 1: //右子樹 st[top]->rightSubTree = p; break; default: break; } } break; } } }
4.執行結果：
int main()
{
BinaryTree<char> bt;
cout << "後序遍歷：";
bt.postOrderVisit();
cout << endl << "列印二叉樹:";
bt.PrintBTree();
return 0;
}A(B(C,D(,F(E,G))),H(I(J(,L(,M)),K)))
後序遍歷：C E G F D B M L J K I H A
列印二叉樹:A(B(C,D(,F(E,G))),H(I(J(,L(,M)),K))
5.附錄：完整的二叉樹C++檔案：
#ifndef BINARYTREE_H_INCLUDED #define BINARYTREE_H_INCLUDED #include <iostream> using namespace std; template <typename T> struct BTree { T data; struct BTree* leftSubTree; struct BTree* rightSubTree; }; template <class T> class BinaryTree { }; template <> class BinaryTree<char> { public: BinaryTree() { mRoot = nullptr; //CreateBTree(mRoot); //AB#E##C#G## CreateBTreeUseList(mRoot); } virtual ~BinaryTree() { DestroyBTree(mRoot); } void postOrderVisit() { PostOrderVisit(mRoot); } size_t high() { return High(mRoot); } size_t width() { return Width(); } //查詢 bool findBTree(char ch) { return FindBTree(mRoot,ch); } //輸出 void PrintBTree() { printBTree(mRoot); } private: //以廣義表的形式輸出樹 void printBTree(BTree<char>* node) { if (nullptr != node) { cout << node->data; if (node->leftSubTree != nullptr ) { cout << "("; printBTree(node->leftSubTree); } if (node->rightSubTree != nullptr) { if (node->leftSubTree == nullptr) cout << "("; cout << ","; printBTree(node->rightSubTree); cout << ")"; } } else return; } //查詢 bool FindBTree(BTree<char>* node,char ch) { if (nullptr == node)return false; else { if (ch == node->data) return true; else { if (FindBTree(node->leftSubTree,ch)) return true; if (FindBTree(node->rightSubTree,ch)) return true; return false; } } } //銷燬二叉樹 void DestroyBTree(BTree<char>* node) { if (nullptr == node) { return; }else { DestroyBTree(node->leftSubTree); DestroyBTree(node->rightSubTree); delete node; } } //建立二叉樹 void CreateBTree( BTree<char>*& node) { char ch = getchar(); if ('\n' == ch) return; else if (ch == '#') { node = nullptr; }else { node = new BTree<char>(); node->data = ch; /* if (nullptr == mRoot) { mRoot = node; } */ CreateBTree(node->leftSubTree); CreateBTree(node->rightSubTree); } } //利用廣義表建立二叉樹 void CreateBTreeUseList( BTree<char>*& node) { char ch; BTree<char>* st[100]{nullptr}; BTree<char>* p = nullptr; char flag = 2; int8_t top = -1; while ((ch = getchar()) != '\n') { switch (ch) { case '(': st[++top] = p; flag = 0; //左子樹開始 break; case ',': flag = 1; //右子樹開始 break; case ')': top--; break; default: p = new BTree<char>(); p->leftSubTree = nullptr; p->rightSubTree = nullptr; p->data = ch; if (nullptr == mRoot) mRoot = p; else { switch (flag) { case 0: //左子樹 st[top]->leftSubTree = p; break; case 1: //右子樹 st[top]->rightSubTree = p; break; default: break; } } break; } } } //後序遍歷 void PostOrderVisit(BTree<char>*& node) { if (nullptr == node) return; else { PostOrderVisit(node->leftSubTree); PostOrderVisit(node->rightSubTree); cout << node->data << " "; } } //求樹的高度 size_t High(BTree<char>*& node) { if (nullptr == node) return 0; else return Max(High(node->leftSubTree),High(node->rightSubTree)) + 1; } size_t Max(size_t a,size_t b) { return a>b ? a: b; } //求樹的寬度 #define MAX_SIZE (50) size_t Width() { if (nullptr == mRoot) return 0; BTree<char>* q[MAX_SIZE]={nullptr}; size_t last = 0,fr=0,rear=1; size_t tmp=0; size_t maxw=0; q[rear] = mRoot; BTree<char>* p = nullptr; while (fr <= last) { fr++; fr = fr % MAX_SIZE; p = q[fr]; if (nullptr != p) tmp++; if (nullptr != p && p->leftSubTree != nullptr) { rear++; rear = rear % MAX_SIZE; q[rear] = p->leftSubTree; } if (nullptr != p && p->rightSubTree != nullptr) { rear++; rear = rear % MAX_SIZE; q[rear] = p->rightSubTree; } if (fr >= last) { last = rear; if (tmp > maxw) maxw = tmp; tmp = 0; }/* if (nullptr == p) break; */ } return maxw; } private : BTree<char>* mRoot; }; #endif // BINARYTREE_H_INCLUDED