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二叉树的建立:

对于二叉树,如果单纯通过前序遍历或后序遍历以及中序遍历是无法唯一确定一棵二叉树的前序+中序后序+中序才可以唯一确定一棵二叉树。
因此我们可以通过前序+中序或者后序+中序的结果对二叉树进行确定。重建二叉树-风君子博客
重建二叉树-风君子博客
假设一棵二叉树为如下:重建二叉树-风君子博客
则前序和中序遍历的结果是:重建二叉树-风君子博客
我们首先要对前序遍历和中序遍历的特点进行了解。如上图数组中,明显可以看到。在前序遍历中,数组第一个元素就是这棵树的Root,而中序遍历,则Root位于中间位置啦 ,但是在中序中Root(图中中序遍历数组 的“1”)左边是其左子树,而其右边是其右子树的节点值,于是我们大概可以确定这棵树了。重建二叉树-风君子博客
那么左子树又如何确定呢?前序遍历结果:重建二叉树-风君子博客                   中序遍历结果:重建二叉树-风君子博客
于是我们又可以确定如下:重建二叉树-风君子博客

那么又子树呢?同样的嘛:重建二叉树-风君子博客
一直这样迭代下去,肯定就可以了搞定了。

#ifndef RECONSTRUCT_BINARY_TREE_H#define RECONSTRUCT_BINARY_TREE_H#include<iostream>struct TreeNode{	int val; 	struct TreeNode *left; 	struct TreeNode *right; }; struct TreeNode *reconstructBinaryTree(int *preorder,int *midorder,int length); struct TreeNode *reconstructCore(int *startPreorder,int *endPreorder,int *startMidorder,int *endMidorder); 
struct TreeNode *reconstructBinaryTree(int *preorder,int *midorder,int length){ return reconstructCore(preorder,preorder+length-1,midorder,midorder+length-1); }struct TreeNode *reconstructCore( int *startPreorder,int *endPreorder, int *startMidorder,int *endMidorder){ //这里是关键,传入的参数是当前前序、中序的起始位置
int rootValue=*startPreorder; struct TreeNode *root=new TreeNode; //核心部分,构建一个节点 root->val=rootValue; root->left=root->right=NULL; if(startPreorder==endPreorder){ if(startMidorder==endMidorder&&*startPreorder==*startMidorder){ return root; //边界值的处理 }else{ throw("invalid input "); } } int *iter; int leftCount=0; for(iter=startMidorder; iter!=endMidorder; iter++){ if(*iter==rootValue){ break; } leftCount++; } if(iter!=startMidorder&&iter!=endMidorder){ //如果左右子树不为空 root->left=reconstructCore(startPreorder+1,startPreorder+leftCount,startMidorder,iter-1); root->right=reconstructCore(startPreorder+leftCount+1,endPreorder,iter+1,endMidorder); } if(iter==startMidorder&&iter!=endMidorder){ //如果左子树为空 root->left=NULL; root->right=reconstructCore(startPreorder+leftCount+1,endPreorder,iter+1,endMidorder); } if(iter!=startMidorder&&iter==endMidorder){ //如果右子树为空 root->left=reconstructCore(startPreorder+1,startPreorder+leftCount,startMidorder,iter-1); root->right=NULL; } return root; }void preorderPrint(struct TreeNode *root){ if(root==NULL){ return; } std::cout<<root->val<<std::endl; preorderPrint(root->left); preorderPrint(root->right); }void midorderPrint(struct TreeNode *root){ if(root==NULL){ return; } preorderPrint(root->left); std::cout<<root->val<<std::endl; preorderPrint(root->right);}#endif

int main(){	int pre[8]={1,2,4,7,3,5,6,8}; 	int mid[8]={4,7,2,1,5,3,8,6};	struct TreeNode *root=reconstructBinaryTree(pre,mid,8); 	/*std::cout<<root->left->val<<std::endl; 	std::cout<<root->left->left->right->val<<std::endl; 	std::cout<<root->left->left->val<<std::endl; 	std::cout<<root->right->left->val<<std::endl; 	std::cout<<root->right->right->val<<std::endl; 	std::cout<<root->right->right->left->val<<std::endl; */		preorderPrint(root); 	midorderPrint(root); }

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