面试经典二叉树算法
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#include <iostream>#include <cstdlib>#include <cassert>#include <stack>#include <cmath>#include <queue>#include <list>using namespace std;//面试经典二叉树算法typedef char ElemType;#define END '#'template <typename T>const T & Max(const T& a,const T & b){ return a>b?a:b;}typedef struct BtNode{ //BtNode *parent; BtNode *leftchild; BtNode *rigthchild; ElemType data;}BtNode , *BinaryTree;BtNode * _Buynode(){ BtNode *s = (BtNode *)malloc(sizeof(BtNode)); if(NULL == s) exit(1); memset(s,0,sizeof(BtNode)); return s;}void _Freenode(BtNode *p){ free(p);}//利用出栈的顺序进行遍历struct StkNode{ BtNode * Btnode; int PopNum;public: StkNode(BtNode * ptr = NULL) :Btnode(ptr),PopNum(0) {}};//中序void IsTree_struct_pop_num(BtNode *ptr){ if(ptr == NULL) { return ; } stack<StkNode> st; st.push(StkNode(ptr)); while (!st.empty()) { StkNode p = st.top(); st.pop(); p.PopNum++; if( p.PopNum == 2 ) { cout<<p.Btnode->data<< " "; if( p.Btnode->rigthchild != NULL ) { st.push(StkNode(p.Btnode->rigthchild)); } } else { st.push(StkNode(p)); if(p.Btnode->leftchild != NULL) { st.push(StkNode(p.Btnode->leftchild)); } } }}//后序void PassTree_struct_pop_num(BtNode *ptr){ if(ptr == NULL) { return ; } stack<StkNode> st; st.push(StkNode(ptr)); while (!st.empty()) { StkNode pt = st.top(); st.pop(); pt.PopNum++; if(pt.PopNum == 3) //第三次出栈，打印 { cout<<pt.Btnode->data<<" "; } else { st.push(ptr); if(pt.PopNum == 1 && pt.Btnode->leftchild != NULL) { st.push(StkNode(pt.Btnode->leftchild)); } else if(pt.PopNum == 2 && pt.Btnode->rigthchild != NULL) { st.push(StkNode(pt.Btnode->rigthchild)); } } }}//创建二叉树BtNode* Create_Tree(const char * &str){ BtNode * s = NULL; if(str == NULL) { return NULL; } if(*str != END) { s = _Buynode(); s->data = *str; s->leftchild = Create_Tree(++str); s->rigthchild = Create_Tree(++str); } return s;}//前序递归void PreTree(BtNode *ptr){ if(ptr == NULL) { return ; } else { cout<<ptr->data<<" "; PreTree(ptr->leftchild); PreTree(ptr->rigthchild); }}//前序非递归void PreOrder2(BtNode *ptr){ if(ptr == NULL) { return; } stack<BtNode *>st; st.push(ptr); while (!st.empty()) { ptr = st.top(); st.pop(); cout <<ptr->data<<" "; if(ptr->rigthchild != NULL) //right { st.push(ptr->rigthchild); } if(ptr->leftchild != NULL)//left { st.push(ptr->leftchild); } }}//前序非递归void PreOrder1(BtNode *ptr){ if(ptr == NULL) { return; } stack<BtNode*> st; while (ptr != NULL || !st.empty()) { while (ptr != NULL) { cout<<ptr->data<<" "; st.push(ptr); ptr = ptr->leftchild; } ptr = st.top(); st.pop(); ptr = ptr->rigthchild; }}//中序非递归void IsOrder(BtNode * ptr){ if(ptr == NULL) { return; } stack<BtNode *> st; while(ptr != NULL || !st.empty()) { while(ptr != NULL) { st.push(ptr); ptr = ptr->leftchild; } ptr = st.top(); st.pop(); cout<<ptr->data<<" "; ptr = ptr->rigthchild; }}//后续非递归void PassOrder(BtNode *ptr){ if(ptr == NULL) { return; } stack<BtNode*> st; BtNode *flag = NULL; while (ptr != NULL || !st.empty()) { while (ptr != NULL) { st.push(ptr); ptr = ptr->leftchild; } ptr = st.top(); st.pop(); if(ptr->rigthchild == NULL || flag == ptr->rigthchild) { cout<<ptr->data<<" "; flag = ptr; ptr = NULL; //如果已经访问了的数据节点，则此节点将会失去生命周期，没有意义 } else { st.push(ptr); //他的右子树还没有访问 ptr = ptr->rigthchild; } } cout<<endl;}//树高int Hight_Tree(BtNode *ptr){ if(ptr == NULL) { return 0; } if(ptr->leftchild == NULL && ptr->rigthchild == NULL) { return 1; } int lefthight = Hight_Tree(ptr->leftchild); int righthight = Hight_Tree(ptr->rigthchild); return Max(lefthight,righthight)+1;}//节点个数int Size_Tree(BtNode *ptr){ if(ptr == NULL) { return 0; } return Size_Tree(ptr->leftchild)+Size_Tree(ptr->rigthchild)+1;}//叶节点个数int leave_Tree(BtNode *ptr){ if(ptr == NULL) { return 0; } if(ptr->leftchild == NULL && ptr->rigthchild == NULL) { return 1; } return leave_Tree(ptr->rigthchild)+leave_Tree(ptr->leftchild)+1;}//完全二叉树bool Is_Comp_Binary_Tree(BtNode *ptr){ if(ptr == NULL) { return true; } queue<BtNode *> qu; qu.push(ptr); bool result = true; bool flag = false; while (!qu.empty()) { ptr = qu.front(); qu.pop(); if(flag) { if(ptr->leftchild != NULL || ptr->rigthchild !=NULL) { result = false; break; } } if(ptr->leftchild != NULL && ptr->rigthchild == NULL) { qu.push(ptr->leftchild); flag = true; } if(ptr->leftchild == NULL && ptr->rigthchild == NULL) { flag = true; } if(ptr->leftchild == NULL && ptr->rigthchild != NULL) { result = false; break; } if(ptr->leftchild != NULL && ptr->rigthchild !=NULL) { qu.push(ptr->leftchild); qu.push(ptr->rigthchild); } } return result;}//满二叉树bool Is_Full_Binary_Tree(BtNode *ptr){ if(ptr == NULL) { return true; } int higth = Hight_Tree(ptr); int sizecount = Size_Tree(ptr); int leave = leave_Tree(ptr); if((sizecount == pow(2,higth)-1) && leave == pow(2,higth-1)) { return true; } else { return false; } }//树节点int GetNumTree(BtNode *ptr){ if(ptr == NULL) { return 0; } return GetNumTree(ptr->leftchild)+GetNumTree(ptr->rigthchild)+1;}//打印倒数第k个void PrintCompBTree(BtNode *ptr, int k)//倒数第k个节点{ assert(ptr != NULL); int len = GetNumTree(ptr); if(ptr == NULL ||k < 0 || k > len) { return; } int k1 = len-k; int i = 0; queue<BtNode*> queue; queue.push(ptr); while (!queue.empty()) { ptr = queue.front(); queue.pop(); i++; if( i == k1) { cout<<"倒数第"<<k<<"个节点:"<<ptr->data<<endl; break; } if(ptr->leftchild != NULL) { queue.push(ptr->leftchild); } if(ptr->rigthchild != NULL) { queue.push(ptr->rigthchild); } }}int GetBinaryTreeLevel(BtNode *ptr, int k){ if(ptr == NULL || k < 0) { return 0; } if(k == 1) { return 1; } int leftcount = GetBinaryTreeLevel(ptr->leftchild,k-1); int rightcount = GetBinaryTreeLevel(ptr->rigthchild,k-1); return leftcount+rightcount;}//平衡二叉树bool IsBalance_BinaryTree(BtNode *ptr,int &hight){ if(ptr == NULL) { hight = 0; return false; } if(ptr->leftchild == NULL && ptr->rigthchild != NULL) { return false; } if(ptr->rigthchild != NULL && ptr->leftchild == NULL) { return false; } int lefthight = 0; int righthight = 0; bool boolleft = IsBalance_BinaryTree(ptr->leftchild,lefthight); bool boolright = IsBalance_BinaryTree(ptr->rigthchild,righthight); return boolright && boolleft && (abs(lefthight - righthight) <=1);}//查找节点bool FindNode_Tree(BtNode *ptr,BtNode *child){ if(ptr == NULL || child == NULL) { return false; } if(ptr == child) { return true; } bool flag = FindNode_Tree(ptr->leftchild ,child); if(!flag) { flag = FindNode_Tree(ptr->rigthchild,child); } return flag;}//寻找相同祖父BtNode * FindComParent(BtNode *ptr, BtNode *child1,BtNode *child2){ if(ptr == NULL || child1 == NULL || child2 == NULL) { return NULL; } if(FindNode_Tree(ptr->leftchild,child1)) // 左右 ---- { if(FindNode_Tree(ptr->rigthchild,child2)) { return ptr; } else { return FindComParent(ptr->leftchild,child1,child2); } } if(FindNode_Tree(ptr->rigthchild,child1))//not else //may be no this child in ptr { if(FindNode_Tree(ptr->leftchild,child2)) //右左 { return ptr; } else { return FindComParent(ptr->rigthchild,child1,child2); } } return NULL;}//2bool Get_Child_Tree_Path(BtNode *ptr,BtNode *child,list<BtNode*>& path) { if(ptr == NULL || child == NULL ) { return false; } if(ptr == child) { path.push_back(ptr); return true; } path.push_back(ptr); bool found = false; found = Get_Child_Tree_Path(ptr->leftchild,child,path); if(!found) { found = Get_Child_Tree_Path(ptr->rigthchild,child,path); } if(!found) { path.pop_back(); } return found;}BtNode * FindComParent2(BtNode *ptr, BtNode *child1,BtNode *child2){ if(NULL == ptr || NULL == child1 || NULL == child2) { return NULL; } list<BtNode *>path1; list<BtNode *>path2; bool boolchild1 = Get_Child_Tree_Path(ptr,child1,path1); bool boolchild2 = Get_Child_Tree_Path(ptr,child2,path2); BtNode * last = NULL; if(boolchild1 && boolchild2) { list<BtNode *>::iterator it1 = path1.begin(); list<BtNode *>::iterator it2 = path2.begin(); while(it1 != path1.end() && it2 != path2.end()) { if(*it1 == *it2) { last = *it1; } else { break; } ++it1; ++it2; } } else { last = NULL; } return last;}//转换成双链表BtNode * BinaryTreeToList(BtNode *ptr){ if(ptr == NULL ) { return NULL; } BtNode *head = NULL; stack<BtNode*> st; while (ptr != NULL || !st.empty() ) { while (ptr!=NULL) { st.push(ptr); ptr = ptr->leftchild; } BtNode *p = st.top(); ptr = p; st.pop(); if(NULL == head) { head = p; head->rigthchild = NULL; head->leftchild = NULL; } else { BtNode *pre = head; while (pre->rigthchild != NULL) { pre = pre->rigthchild; } pre->rigthchild = p; p->leftchild = pre; p->rigthchild = NULL; } ptr = ptr->rigthchild; } return head;}void BinaryTreeToList3(BtNode * &head,BtNode *&last){ if(head == NULL) return; BinaryTreeToList3(head->leftchild,last); head->leftchild = last; if(last != NULL) { last->rigthchild = head; } last = head; BinaryTreeToList3(head->rigthchild,last);}void BinaryTreeToList2(BtNode * ptr,BtNode *&first,BtNode *&last){ BtNode *pfirstleft; BtNode *plastleft; BtNode *pfirstright; BtNode *plastright; if(ptr == NULL) { first = NULL; last = NULL; return ; } if(ptr->leftchild == NULL) { first = ptr; } else { BinaryTreeToList2(ptr->leftchild,pfirstleft,plastleft); first = pfirstleft; //把根节点放置到在左子树中查找到的最后一个节点 ptr->leftchild = plastleft; plastleft->rigthchild = ptr; } if(ptr->rigthchild == NULL) { last = ptr; } else { BinaryTreeToList2(ptr->rigthchild,pfirstright,plastright); last = plastright; ptr->rigthchild = pfirstleft; pfirstleft->rigthchild = ptr; }}int main(){ //const char* p = "ABC##DE##F##G#H##"; //BtNode * root = Create_Tree(p); //PreTree(root); //cout<<endl; //PreOrder2(root); //cout<<endl; //IsOrder(root); //PassTree_struct_pop_num(root); //int hight = 0; //if(IsBalance_BinaryTree(root,hight)) //{ //cout<<"root is IsBalance_BinaryTree"<<endl; //} const char *str1 = "ABC##D##EF###"; const char *str2 = "ABCG###D##EF###"; BtNode *root = Create_Tree(str1); IsOrder(root); BtNode *p; BtNode *q = NULL; BinaryTreeToList3(root,q); //BinaryTreeToList2(root,p,q); for(p = root;p!=NULL;p = p->rigthchild) { cout<<p->data<<" "; } cout<<endl; //cout<<p->data<<" "<<p->rigthchild->data<<" "<<p->rigthchild->rigthchild->data<<endl; //for(;p!=q;p = p->rigthchild) //{ // cout<<p->data<<" "; //} //BtNode *root2 = Create_Tree(str2); ////PreTree(root); // //cout<<endl; //cout<<GetNumTree(root)<<endl; //BtNode * p = BinaryTreeToList(root); //cout<<endl; //while (p!=NULL) //{ // cout<<p->data<<" "; // p = p->rigthchild; //} //PassOrder(root); //if(Is_Comp_Binary_Tree(root)) //{ // cout<<"Ok Is_Comp_Binary_Tree"<<endl; //} //cout<<GetBinaryTreeLevel(root2,4)<<endl; /*PreTree(root2); cout<<endl; PassOrder(root2); if(Is_Comp_Binary_Tree(root2)) { cout<<"Ok Is_Comp_Binary_Tree"<<endl; }*/ return 0;}//如果有什么错误，希望不吝赐教 0 0
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