二叉树大总结1 ---- 排序二叉树的各种题
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#include <iostream>#include <queue>#include <stack>using namespace std;/* 二叉查找树中的保存指针 */template<class T>class BinarySearchTree{public: struct Node { T* value; Node* left; Node* right; Node* parent; Node(){left=0;right=0;parent=0;} }; private: static Node* root;public: void add(T& t) { if(!root) { root = new Node; root->value = &t; }else { Node* p = root; Node* q = root; bool isLeft = true; while(p) { q = p; if(*(p->value)>t) { isLeft = true; p = p->left; }else { isLeft = false; p = p->right; } } Node * temp = new Node; temp->value = const_cast<T*>(&t); temp->parent = q; if(isLeft) q->left = temp; else q->right = temp; } } void remove(const T& t) { if(!contain(t)) return; if(*(root->value)==t) { if(!root->left&&!root->right) //只有根 { delete root; root = 0; return; }else if(!root->right)//没有右子树 { //找左子树的最大值 Node *p = root->left; Node *q; while(p->right) { q = p; p = p->right; } q->right = 0; root->value = p->value; delete p; return; } } Node *p = root; Node *q = root; bool isLeft = true; while(p) { if(*p->value==t) break; else if(*p->value>t) { isLeft = true; q = p; p = p->left; }else { q = p; isLeft = false; p = p->right; } } if(!(p->left)&&!p->right) { if(isLeft) q->left = 0; else q->right = 0; delete p; }else if(!p->right) { if(isLeft) { q->left = p->left; }else { q->right = p->left; } p->left->parent = q; delete p; }else //右子树存在 { Node* p1 =p;q = p1;p1 = p1->right; while(p1->left) { q = p1;p1 = p1->left; }//可能右孩子没有左子树if(q->right==p1)q->right = p1->right;else q->left = p1->right; if(p1->right) p1->right->parent = q; p->value = p1->value; delete p1; } } bool contain(const T& t) { Node *p = root; while(p) { if(*(p->value)==t) return true; else if(*(p->value)<t) p = p->right; else p = p->left; } return false; } T findMin() { if(!root) throw "null"; //寻找最小数但里面什么都没有STL是怎么做的？ Node* p = root; while(p->left) { p = p->left; } return *(p->value); } T findMax() { if(!root) throw "null"; Node* p = root; while(p->right) p = p->right; return *(p->value); } bool isEmpty(){return root==0?true:false;} BinarySearchTree(){root=0;} virtual ~BinarySearchTree() { deleteTree(root); } //递归遍历 void postTraversal(Node* node=root) { if(node) { postTraversal(node->left); postTraversal(node->right); cout<< *(node->value)<<" "; } } void preTraversal(Node* node=root) { if(node) { cout<< *(node->value)<<" "; preTraversal(node->left); preTraversal(node->right); } } void inorderTraversal(Node* node=root) { if(node) { inorderTraversal(node->left); cout<< *(node->value)<<" "; inorderTraversal(node->right); } } //非递归遍历 void postTraversalUsingStack() { stack<Node*> s; Node* p = root; bool hasVisited = false; do { while(p) { s.push(p); p = p->left; } if(!s.empty()) { p = s.top(); s.pop(); }else break; bool copy = hasVisited; if(!s.empty()&&s.top()->right==p) hasVisited = true; else hasVisited = false; if(p->right&&!copy) { s.push(p); p = p->right; } else { cout<<*p->value<<" "; p = 0; } } while(true); } void preTraversalUsingStack() { stack<Node*> s; Node* p = root; do { while(p) { cout<< *p->value<<" "; s.push(p); p = p->left; } if(!s.empty()) { p = s.top(); s.pop(); }else break; if(p->right) p = p->right; else p = 0; } while(true); } void inorderTraversalUsingStack() { stack<Node*> s; Node* p = root; do { while(p) { s.push(p); p = p->left; } if(!s.empty()) { p = s.top(); s.pop(); }else break; cout<<*p->value<<" "; if(p->right) p = p->right; else p = 0; } while(true); } /* STL中的queue： push(x) 将x压入队列的末端 pop() 弹出队列的第一个元素(队顶元素)，注意此函数并不返回任何值 front() 返回第一个元素(队顶元素) back() 返回最后被压入的元素(队尾元素) empty() 当队列为空时，返回true size() 返回队列的长度 */ //层序遍历 void traversalByLayer() { queue<Node*> q; q.push(root); while(!q.empty()) { Node* temp = q.front(); q.pop(); if(temp->left) q.push(temp->left); if(temp->right) q.push(temp->right); cout<< *(temp->value)<<" "; } } //递归翻转镜像 void mirror(Node* node=root) { if(node) { mirror(node->left); mirror(node->right); Node* temp=node->left;node->left=node->right;node->right=temp; } } //非递归翻转镜像 void mirrorIteratively() { stack<Node*> s; Node* p = root; do { while(p) { Node* temp=p->left;p->left=p->right;p->right=temp; s.push(p); p = p->left; } if(!s.empty()) { p = s.top(); s.pop(); }else break; if(p->right) p = p->right; else p = 0; } while(true); } //寻找叶子数 int getLeafNumber(Node* node=root) { if(!node) return 0; if(!node->left&&!node->right) return 1; int left = getLeafNumber(node->left); int right = getLeafNumber(node->right); return left+right; } //寻找树的高度 int getHeight(Node* node=root) { if(!node) return 0; if(!node->left&&!node->right) return 1; int left = getHeight(node->left); int right = getHeight(node->right); int result = left>right?left:right; return result+1; } //寻找最大距离 int findMaxDistance(Node* node=root) { if(!node) return 0; int n1 = getHeight(node->left); int n2 = getHeight(node->right); return n1+n2+1; } //寻找共同最低父节点:等价于Y型链表求交点 T parent(const T& t1,const T& t2) { Node* node1 = getNode(t1); Node* node2 = getNode(t2); if(!node1||!node2) throw "null"; int num1 = 0; int num2 = 0; Node* p; p = node1; while(p->parent) { num1++; p = p->parent; } p = node2; while(p->parent) { num2++; p = p->parent; } if(num1<num2) { int n=num1;num1=num2;num2=n; Node* temp=node1;node1=node2;node2=temp; } int n = num1-num2; while(n--) { node1 = node1->parent; } while(true) { if(node1==node2) { cout<<*node1->value<<endl; return *node1->value; } node1 = node1->parent; node2 = node2->parent; } } //将二叉树变成排序的双向链表 Node* convert(Node* node=root,Node* last=0) { if(!node) return 0; if(node->left) last = convert(node->left,last); node->left = last; if(last) last->right = node; last = node; if(node->right) last = convert(node->right,last); return last; }private: void deleteTree(Node* node) { if(node) { deleteTree(node->left); deleteTree(node->right); delete node; } } Node* getNode(const T& t) { Node *p = root; while(p) { if(*(p->value)==t) return p; else if(*(p->value)<t) p = p->right; else p = p->left; } return 0; } };template<class T>BinarySearchTree<T>::Node* BinarySearchTree<T>::root = 0;void main(){ BinarySearchTree<int> bst; int a[] = {4,8,10,5,9,2,3,6,15,12,17}; for(int i=0;i<sizeof(a)/sizeof(int);i++) bst.add(a[i]); bst.inorderTraversal();cout<<endl;/*bst.inorderTraversalUsingStack();cout<<endl; bst.preTraversal();cout<<endl;bst.preTraversalUsingStack();cout<<endl;bst.postTraversal();cout<<endl;bst.postTraversalUsingStack();cout<<endl;*//*bst.remove(9);bst.inorderTraversal();cout<<endl;bst.remove(2);bst.inorderTraversal();cout<<endl;bst.remove(4);bst.inorderTraversal();cout<<endl;*//*cout<<bst.findMin()<<endl;cout<<bst.findMax()<<endl;bst.traversalByLayer();cout<<endl;*//*bst.mirror();bst.mirrorIteratively();bst.inorderTraversal();cout<<endl;*/cout<<bst.getLeafNumber()<<" "<<bst.getHeight()<<" "<<bst.findMaxDistance()<<" "<<bst.parent(15,6);cout<<endl;BinarySearchTree<int>::Node* p = bst.convert();while(p){ cout<<*p->value<<" "; p = p->left;}}- 二叉树大总结1 ---- 排序二叉树的各种题
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