[TIV-EXAM]二叉树的非递归遍历算法

二叉树的非递归遍地算法：提供一种最简洁的先序遍历算法，利用stack实现。

 

二叉树方便起见用满二叉树数组的形式实现。

注意这种形式压栈的时候是先右子树后左子树，这样pop出栈的时候就会先左而后右。这种简洁的形式和树的程序遍历用queue实现很像。

另外后续遍历也有一种最简洁的形式。

(1--先序遍历的非递归算法的最简洁形式)

(2--后序遍历的非递归算法的最简洁形式)

(3--中序遍历的非递归算法的最简洁形式)

(4--二叉树求树高的算法可以采用层序遍历中加FLAG点的方式实现)

 

程序如下：

 /********************************************************************* DESCRIPTION: TelNav-1 BinaryTree's Non Recursive Tour Algorithm** AUTHOR: Neesky** DATE:2009-10-24********************************************************************//** include files **/#include <iostream>#include <stack>#include <queue>#define MAXSIZE 15using namespace std;int BinaryTreeArray[MAXSIZE+1]={-1,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15};/** * Get the Index Of Left/Right Son Node * * @param i :Node Index * * @return int :Son Node Index */int GetLeftSonNode(int i){ return (i>0&&i<=MAXSIZE/2)?2*i:-1;}int GetRightSonNode(int i){ return (i>0&&i<=MAXSIZE/2)?2*i+1:-1;}/** * Visiting the No.k Node * * @param k */void VisitNode(int _BinaryTree[],int k){ cout<<_BinaryTree[k]<<" "; return;}/** * [1]PreOrder Binary Tree ,Not Recursive Method * * @param _BinaryTree * @param N */void PreOrderBinaryTree(int _BinaryTree[]){ stack<int> s; /*stack for path*/ int i=1,son=-1;s.push(i); cout<<"/nPreOrder Visit: "; while(!s.empty()) { i=s.top();s.pop(); /*The left node ahead of the right node being poped.*/ VisitNode(_BinaryTree,i); /*Visit the Node*/ son=GetRightSonNode(i); /*Right Pushed first.*/ if(son!=-1)s.push(son); /*[Key]: Visit the Right Son Node*/ son=GetLeftSonNode(i); /*Left Pushed then. */ if(son!=-1) s.push(son); /*Visit the Left Son Node */ } return;}/** * [2]InOrder Binary Tree ,Not Recursive Method * * @author NeeSky (2009-10-30) * * @param _BinaryTree */void InOrderBinaryTree(int _BinaryTree[]){ stack<int> s; /*Stack for path */ int p=1; cout<<"/nInOrder Visit: "; while((!s.empty())||(p!=-1)) { while(p!=-1) { s.push(p); p=GetLeftSonNode(p); /*Go to the Left */ } if(!s.empty()) { p=s.top(); VisitNode(_BinaryTree,p); /*Visit the Root */ s.pop(); p=GetRightSonNode(p); /*Go to the Right*/ } } return;}/** * [3]PostOrder Binary Tree, Not Recursive Method * * @author NeeSky (2009-10-31) * * @param _BinaryTree */void PostOrderBinaryTree(int _BinaryTree[]){ stack<int> s;int p=1,pre=0; cout<<"/nPostOrder Visit: "; while(!s.empty()||p!=-1) { if(p!=-1) { s.push(p); p=GetLeftSonNode(p); continue; } p=s.top(); /*p == -1*/ if(GetRightSonNode(p)!=-1&&GetRightSonNode(p)!=pre) { p=GetRightSonNode(p); continue; } p=pre=s.top(); /*GetRightSonNode(p)==-1*/ VisitNode(_BinaryTree,p); s.pop(); p=-1; } return;}/** * Get The Depth of Binary Tree * * @author NeeSky (2009-11-3) * * @param _Binary * @param N */void GetDepthOfBinaryTree_asLevelOrder(int _BinaryTree[]){ queue<int> que;int p=1;int dep=0; que.push(p);que.push(-1); cout<<"/nLeveOrder Visit: "; while(!que.empty()) { p=que.front();que.pop(); if(p==-1){ dep++;if(que.empty())break; que.push(-1);continue; } VisitNode(_BinaryTree,p); /*left child EnQue*/ int left=GetLeftSonNode(p); if(left!=-1)que.push(left); /*right child EnQue*/ int right=GetRightSonNode(p); if(right!=-1)que.push(right); } cout<<" Depth(NoRec) = "<<dep; return;}int GetDepthGetDepthOfBinaryTree_asRecMethod(int _BinaryTree[],int root=1){ if(root!=-1) { int leftDep=GetDepthGetDepthOfBinaryTree_asRecMethod(_BinaryTree,GetLeftSonNode(root)); int rightDep=GetDepthGetDepthOfBinaryTree_asRecMethod(_BinaryTree,GetRightSonNode(root)); return leftDep>rightDep?1+leftDep:1+rightDep; }else return 0;}/** *The Main Programming * * @param argc * @param argv * * @return int */int main (int argc, char *argv[]){ PreOrderBinaryTree(BinaryTreeArray); InOrderBinaryTree(BinaryTreeArray); PostOrderBinaryTree(BinaryTreeArray); GetDepthOfBinaryTree_asLevelOrder(BinaryTreeArray); cout<<" Depth(RecMD) = "<<GetDepthGetDepthOfBinaryTree_asRecMethod(BinaryTreeArray); return(0);}

 

输出：

make -f "Makefile" CFG=Debug
mingw32-make: Nothing to be done for `all'.
Debug/TelNav20091020.exe 

PreOrder  Visit: 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 
InOrder   Visit: 8 4 9 2 10 5 11 1 12 6 13 3 14 7 15 
PostOrder Visit: 8 9 4 10 11 5 2 12 13 6 14 15 7 3 1 
LeveOrder Visit: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  Depth(NoRec) = 4 Depth(RecMD) = 4