重建二叉树（剑指offer）

输入某二叉树的前序遍历和中序遍历的结果，请重建出该二叉树。假设输入的前序遍历和中序遍历的结果中都不含重复的数字。例如输入前序遍历序列{1,2,4,7,3,5,6,8}和中序遍历序列{4,7,2,1,5,3,8,6}，则重建二叉树并返回。

1、二叉树相关

1.1、二叉树节点定义

typedef struct TreeNode
{
    int val; 
    struct TreeNode *left;
    struct TreeNode *next;  
}TNode;

1.2、二叉树前序遍历

void preOrder(TNode *node)
{
    if(!node)
        return;
    cout<<node->val<<" ";
    preOrder(node->left);
    preOrder(node->right);
}

1.3、二叉树中序遍历

void inOrder(TNode *node)
{
    if(!node)
        return;
    inOrder(node->left);
    cout<<node->val<<" ";
    inOrder(node->right);
}

1.4、二叉树后序遍历

void posOrder(TNode *node)
{
    if(!node)
        return;
    posOrder(node->left);
    posOrder(node->right);
    cout<<node->val<<" ";
}

2、根据前序遍历与中序遍历重建二叉树

TNode* reConstructBinaryTree(vector<int> pre,vector<int> in)
{
    //如果pre与in任一个为空则返回空
    if(pre.empty() || in.empty())
        return NULL;

    //新建结点，以当前前序遍历的第一个值为当前子树根结点的值
    TNode *node = new TreeNode();
    node->val = pre[0];

    //求左子树前序遍历(preLeft)和中序遍历(InLeft)
    vector<int> preLeft;
    vector<int> InLeft;
    int i = 0;
    while(pre[0] != in[i] && i < (int)in.size())
    {
        preLeft.push_back(pre[i+1]);
        InLeft.push_back(in[i]);
        i++;
    }

    //求右子树前序遍历(preRight)和中序遍历(InRight)
    i++;
    vector<int> preRight;
    vector<int> InRight;

    while(i < (int)in.size())
    {
        preRight.push_back(pre[i]);
        InRight.push_back(in[i]);
        i++;
    }

    //重建左子树
    node->left = reConstructBinaryTree(preLeft,InLeft);
    //重建右子树
    node->right = reConstructBinaryTree(preRight,InRight);

    return node;
}

3、演示

#include <vector>
#include <iostream>
using namespace std;
int main(int argc, char **argv)
{
    vector<int> pre = {1,2,4,7,3,5,6,8};
    vector<int> in = {4,7,2,1,5,3,8,6};

    TNode *pp =reConstructBinaryTree(pre,in);
    //前序遍历
    cout<<"前序遍历：";
    preOrder(pp);
    cout<<endl;
    //中序遍历
    cout<<"中序遍历：";
    inOrder(pp);
    cout<<endl;
    //后序遍历
    cout<<"后序遍历：";
    posOrder(pp);
    cout<<endl;
    return 0;
}

输出：

前序遍历：1 2 4 7 3 5 6 8 
中序遍历：4 7 2 1 5 3 8 6 
后序遍历：7 4 2 5 8 6 3 1