leetcode105.从前序与中序遍历序列构造二叉树

根据一棵树的前序遍历与中序遍历构造二叉树。

注意:
你可以假设树中没有重复的元素。

例如，给出

前序遍历 preorder = [3,9,20,15,7]
中序遍历 inorder = [9,3,15,20,7]

返回如下的二叉树：

    3
   / \
  9  20
    /  \
   15   7

来源：力扣（LeetCode）
链接：https://leetcode-cn.com/problems/construct-binary-tree-from-preorder-and-inorder-traversal
著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。

完整代码

递归
基本思想：

• 先构造根节点，根节点是先序序列的第一个节点
• 再在中序遍历序列中找根节点的位置
• 递归构造根的左子树，右子树

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    TreeNode* buildTree(vector<int>& preorder, vector<int>& inorder) {
        if(preorder.size()==0||inorder.size()==0)
            return NULL;
        return build(preorder,0,preorder.size()-1,inorder,0,inorder.size()-1);
    }
    TreeNode* build(vector<int>& preorder,int ps,int pe,vector<int>& inorder,int is,int ie){
        //构建根节点
        TreeNode* root=new TreeNode(preorder[ps]);
        root->left=NULL;
        root->right=NULL;
        
        //在中序序列中寻找根节点
        int i=is;
        while(i<=ie&&preorder[ps]!=inorder[i])
            ++i;
        //i指向中序序列中根节点的位置
        int ll=i-is;//左子树的序列长度
        int rl=ie-i;//右子树的序列长度
        
        //构建左右子树        
        if(ll>0){
            root->left=build(preorder,ps+1,ps+ll,inorder,is,is+ll-1);
        }
        if(rl>0){
            root->right=build(preorder,ps+ll+1,pe,inorder,is+ll+1,ie);
        }
        return root;
        
    }
};

由于每次在中序遍历中寻找根节点的位置时，都需要遍历中序遍历序列，这里我们可以定义一个map记录序列中每个节点和它对应位置的映射，于是有了如下的优化代码形式.
下述代码未能通过所有的测试用例：一共203个测试用例，只通过了202个，最后一个运行超时

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    TreeNode* buildTree(vector<int>& preorder, vector<int>& inorder) {
        if(preorder.size()==0||inorder.size()==0)
            return NULL;
        //构建中序序列节点和位置的映射
        map<int,int> m;
        for(int i=0;i<inorder.size();++i){
            m[inorder[i]]=i;
            //cout<
        }
        return build(preorder,0,preorder.size()-1,inorder,0,inorder.size()-1,m);
    }
    TreeNode* build(vector<int>& preorder,int ps,int pe,vector<int>& inorder,int is,int ie,map<int,int> m){
        //构建根节点
        TreeNode* root=new TreeNode(preorder[ps]);
        root->left=NULL;
        root->right=NULL;
        
        //在中序序列中寻找根节点
        int i=m[preorder[ps]];
        
        //i指向中序序列中根节点的位置
        int ll=i-is;//左子树的序列长度
        int rl=ie-i;//右子树的序列长度
        
        //构建左右子树        
        if(ll>0){
            root->left=build(preorder,ps+1,ps+ll,inorder,is,is+ll-1,m);
        }
        if(rl>0){
            root->right=build(preorder,ps+ll+1,pe,inorder,is+ll+1,ie,m);
        }
        return root;
        
    }
};

运行结果：

202 / 203 个通过测试用例
状态：超出时间限制
提交时间：3 分钟之前
最后执行的输入：
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非递归形式
先序遍历构造二叉树，借助栈来实现，定义一个指针指向中序遍历的数组

• 遍历二叉树的先序序列的数组，如果栈顶节点和当前指针指向的值不相等，那么当前节点就是栈顶节点的左孩子，并将左孩子入栈
• 如果栈顶节点和当前指针指向的值相等，说明此时已经访问到了最左端的节点，那么当前节点是栈中某个节点的右孩子。此时将栈中的节点依次出栈，指向中序遍历序列的指针依次往右移动，如果当前栈顶节点和指针指向的节点的值不相等，停止出栈，那么说明当前节点是刚刚出栈节点的右孩子，将右孩子入栈。

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    TreeNode* buildTree(vector<int>& preorder, vector<int>& inorder) {
        //非递归形式，借助栈
        //根据先序遍历的顺序构造二叉树
        stack<TreeNode*> st;
        if(preorder.size() == 0)
            return NULL;
        TreeNode *root = new TreeNode(preorder[0]);
        st.push(root);
        int index = 0;
        for(int i = 1; i < preorder.size(); ++i){
            TreeNode *cur = st.top();
            if(cur->val != inorder[index]){
                cur->left = new TreeNode(preorder[i]);
                st.push(cur->left);
            }
            else{//此时说明栈中某个节点的右子树出现了
                //如果节点没有右子树，那么中序遍历和先序遍历恰好是逆序的形式
                //如果当前节点和栈中的顶部的节点不相等，那么这个节点是上次出栈的右孩子
                while(!st.empty() && st.top()->val == inorder[index]){
                    cur = st.top();
                    st.pop();
                    index++;
                }
                cur->right = new TreeNode(preorder[i]);
                st.push(cur->right);
            }
            
        }
        return root;
    }
};