链表声明：
//基本结构声明 #include<iostream> #include<queue> #include<stack> #include<cstdio> #define NoInfo 0 // 0表示没有结点 using namespace std; typedef int ElementType; typedef struct TNode* Position; typedef Position BinTree; //二叉树链表结构 struct TNode{ ElementType Data; //结点数据 BinTree Left; //左子树 BinTree Right; //右子树 };
1.先序建立二叉树
//先序建立二叉树 BinTree CreateBinTree(){ ElementType data; scanf("%d",&data); if(data==NoInfo) return NULL; BinTree P; P=new TNode; P->Data=data; P->Left=CreateBinTree(); P->Right =CreateBinTree(); return P; }
2.层序建立二叉树
//层序建立二叉树 BinTree CreateBinTree(){ ElementType data; BinTree BT,T; queue<BinTree> q;//创建队列 scanf("%d",&data); if(data!=NoInfo){ BT=new TNode; BT->Data =data; BT->Left =BT->Right =NULL; q.push(BT); } else return NULL;//第一个数据为0则返回空树 while(!q.empty()){ T=q.front();//取出结点 q.pop(); scanf("%d",&data);//读入T的左孩子 if(data==NoInfo) T->Left =NULL; else{ T->Left =new TNode; T->Left ->Data=data; T->Left ->Left=T->Left ->Right=NULL; q.push(T->Left ); } scanf("%d",&data);//读入T的右孩子 if(data==NoInfo) T->Right =NULL; else{ T->Right =new TNode; T->Right ->Data=data; T->Right ->Left=T->Right ->Right=NULL; q.push(T->Right ); } } return BT; }
3.递归先序遍历
void PreorderTraversal_1(BinTree BT){ if(BT){ printf("%d",BT->Data ); PreorderTraversal_1(BT->Left ); PreorderTraversal_1(BT->Right ); } }
4.非递归先序遍历
void PreorderTraversal_2(BinTree BT){ BinTree T=BT; stack<BinTree> s; while(T||!s.empty()){ while(T){ printf("%d",T->Data ); s.push(T); T=T->Left ; } T=s.top(); s.pop(); T=T->Right ; } }
5.递归中序遍历
void InorderTraversal_1(BinTree BT){ if(BT){ InorderTraversal_1(BT->Left ); printf("%d",BT->Data ); InorderTraversal_1(BT->Right ); } }
6.非递归中序遍历
//非递归中序遍历 void InorderTraversal_2(BinTree BT){ BinTree T=BT; stack<BinTree> s; while(T||!s.empty()){ while(T){ s.push(T); T=T->Left ; } T=s.top(); s.pop(); printf("%d",T->Data ); T=T->Right ; } }
7.递归后序遍历
//递归后序遍历 void PostorderTraversal_1(BinTree BT){ if(BT){ PostorderTraversal_1(BT->Left ); PostorderTraversal_1(BT->Right ); printf("%d",BT->Data ); } }
8.非递归后序遍历
//非递归后序遍历 void PostorderTraversal_2(BinTree BT){ BinTree T,Pre=NULL; stack<BinTree> s; s.push(BT); while(!s.empty()){ T=s.top(); if( (T->Left ==NULL&&T->Right ==NULL) || (Pre!=NULL&& (T->Left==Pre ||T->Right==Pre ) ) ){ printf("%d",T->Data ); s.pop(); Pre=T; } else{ if(T->Right !=NULL) s.push(T->Right ); if(T->Left !=NULL) s.push(T->Left ); } } }
9.层序遍历
void LevelorderTravelsal(BinTree BT){ queue<BTree> q; BinTree T; if(!BT) return; q.push(BT); while(!q.empty()){ T=q.front(); q.pop(); printf("%d ",T->Data); if(T->Left ) q.push(T->Left ); if(T->Right ) q.push(T->Right ); } }
10.二叉树高度
//二叉树高度 int GetHeight(BinTree BT){ if(BT) return max(GetHeight(BT->Left),GetHeight(BT->Right ))+1; else return 0;//空树高度为0 }
11.求二叉树所有结点
//求二叉树所有结点 int CountNode(BinTree BT){ if(BT) return CountNode(BT->Left )+CountNode(BT->Right )+1; else return 0; }
12.求二叉树叶子结点
void LeaveCount(BinTree BT){ if(BT){ if(BT->Left ==NULL&&BT->Right ==NULL) count++; LeaveCount(BT->Left ); LeaveCount(BT->Right ); } }
int LeafcountofBinTree(BinTree BT){ if(BT){ if(BT->Left ==NULL&&BT->Right ==NULL) return LeafcountofBinTree(BT->Left )+LeafcountofBinTree(BT->Right )+1; } else return 0; }
13.先序输出二叉树叶子结点
void PreorderPrintLeaves(BinTree BT){ if(BT!=NULL){ if((BT->Left==NULL)&&(BT->Right==NULL)) printf(" %c",BT->Data); PreorderPrintLeaves(BT->Left); PreorderPrintLeaves(BT->Right); } }
14.镜面反转，将所有非叶结点的左右孩子对换
void Inversion(BinTree BT){ if(BT){ Inversion(BT->Left); Inversion(BT->Right); BinTree temp; temp=BT->Left ; BT->Left =BT->Right ; BT->Right =temp; } }
15.销毁二叉树
void DestroyBinTree(BinTree BT){ if(BT){ DestroyBinTree(BT->Left ); DestroyBinTree(BT->Right ); delete BT; BT=NULL; } }
16.根据前序和中序遍历还原二叉树
1. 根据前序序列的第一个元素建立根结点；
2. 在中序序列中找到该元素，确定根结点的左右子树的中序序列；
3. 在前序序列中确定左右子树的前序序列；
4. 由左子树的前序序列和中序序列建立左子树；
5. 由右子树的前序序列和中序序列建立右子树。
//根据前序和中序遍历还原二叉树 BinTree PreInoRestoreBinTree(int* inorder ,int* preorder, int length) { if(length==0) return NULL; BinTree T=new TNode; int rootIndex; T->Data = *preorder; for(rootIndex=0;rootIndex < length; rootIndex++) if(inorder[rootIndex] == *preorder) break; T->Left = PreInoRestoreBinTree(inorder,preorder +1 , rootIndex); T->Right = PreInoRestoreBinTree(inorder + rootIndex + 1 ,preorder + rootIndex + 1 , length - (rootIndex + 1)); return T; }
17.根据后序和中序遍历还原二叉树
1. 根据后序序列的最后一个元素建立根结点；
2. 在中序序列中找到该元素，确定根结点的左右子树的中序序列；
3. 在后序序列中确定左右子树的后序序列；
4. 由左子树的后序序列和中序序列建立左子树；
5. 由右子树的后序序列和中序序列建立右子树
BinTree InoPosRestoreBinTree(int *inorder,int *postorder,int length) { if(length==0) return NULL; BinTree T; int rootindex; T =new TNode; T->Data=postorder[length-1]; T->Left=T->Right=NULL; for(rootindex=0; rootindex < length; rootindex++) if(inorder[rootindex] == postorder[length-1]) break; T->Left =InoPosRestoreBinTree(inorder,postorder,rootindex); T->Right =InoPosRestoreBinTree(inorder+rootindex+1,postorder+rootindex,length-(rootindex+1)); return T; }
17.1 根据中序和后序输出前序
#include<iostream> #include<vector> #include<string> using namespace std; string in, post, ans=""; void pre(int root, int l, int r){ if(l>r) return ; int i=l; while(in[i] != post[root]) i++; //printf("%d %d %d %d ",root,l,r,i); ans += post[root]; //cout<<"L"<<endl; pre(root-r+i-1, l, i-1); //cout<<"R"<<endl; pre(root-1, i+1, r); } int main(){ cin>>in>>post; pre(post.size()-1,0,post.size()-1); cout<<ans<<endl; return 0; }