Description:

Given preorder and inorder traversal of a tree, construct the binary tree.

Note:
You may assume that duplicates do not exist in the tree.

For example, given

preorder = [3,9,20,15,7]
inorder = [9,3,15,20,7]

Return the following binary tree:

Solutions:

Solution1: 搞了2個(gè)小時(shí)才解出來(lái)的Medium。。一種iterative解法

NOTE:
利用inorder 和 preorder的性質(zhì)可知：

1. inorder是“左中右”，preorder是“中左右”，那么在“右”之前，“中左”和“左中”是完全逆序的，可以因此分片，如圖：

   
   

2. 如果是從inorder從左往右遍歷，那么node1在搜索到的時(shí)候前面在preorder已經(jīng)出現(xiàn)過(guò)了，所以更合理的分片是：藍(lán)色豎線分割的5個(gè)分片。其中綠色刪除掉的inorder元素在preorder已經(jīng)出現(xiàn)過(guò)了。每個(gè)block內(nèi)部是按照preorder順序，每個(gè)元素都是前一個(gè)元素的左child。

   
   
3. 還剩每個(gè)block第一個(gè)node是前面哪個(gè)node的右child還不確定。但這個(gè)parent其實(shí)就是當(dāng)前這個(gè)block最后一個(gè)元素在inorder的前一個(gè)元素。比如6的parent就是7在inorder前面的2。

• 根據(jù)inorder的信息，6要么在1的左children里，或者6跟1有共同的祖先，6在一個(gè)左branch，1在右branch。6不可能在1的右children里。
• 根據(jù)preorder的信息，6要么是1的子孫，要么跟1有共同祖先，但是6在右branch，1在左branch。
  因此6不是1的右child，在1的左children里面。

=> 6是7之前的2的right child。后面以此類推，8是6的right child，9是1的right child，11是9的right child

6是7之前的2的right child；9是1的right child

class Solution:
    def buildTree(self, preorder: List[int], inorder: List[int]) -> TreeNode:
        if not preorder:
            return None
        
        dic = {}
        for i,n in enumerate(preorder):
            dic[n] = i
        
        last_head = preorder.index(inorder[0])
        node_hist = [TreeNode(preorder[i]) for i in range(last_head+1)]
        for k in range(len(node_hist)-1):
            node_hist[k].left = node_hist[k+1]
            
        i = 1
        j = last_head+1
        while j < len(preorder):
            index = dic[inorder[i]]
            if index >= j:
                cache = [TreeNode(preorder[k]) for k in range(j,index+1)]
                for k in range(len(cache)-1):
                    cache[k].left = cache[k+1]
                node_hist[last_head].right = cache[0]
                node_hist += cache
            last_head = index
            i += 1
            j = max(j,last_head+1)
        
        return node_hist[0]

Runtime: 48 ms, faster than 93.19% of Python3 online submissions for Construct Binary Tree from Preorder and Inorder Traversal.
Memory Usage: 14.3 MB, less than 95.75% of Python3 online submissions for Construct Binary Tree from Preorder and Inorder Traversal.

Solution2: 一種遞推的解法

inspired by http://bangbingsyb.blogspot.com/2014/11/leetcode-construct-binary-tree-from.html

class Solution:
    def buildTree(self, preorder: List[int], inorder: List[int]) -> TreeNode:
        if not preorder:
            return None
        root_val = preorder[0]
        root = TreeNode(root_val)
        index = inorder.index(root_val)
        
        root.left = self.buildTree(preorder[1:index+1],inorder[:index])
        root.right = self.buildTree(preorder[index+1:],inorder[index+1:])
        
        return root

Runtime: 188 ms, faster than 36.89% of Python3 online submissions for Construct Binary Tree from Preorder and Inorder Traversal.
Memory Usage: 87.8 MB, less than 19.44% of Python3 online submissions for Construct Binary Tree from Preorder and Inorder Traversal.

sample 120 ms submission:

class Solution:
    def buildTree(self, preorder: List[int], inorder: List[int]) -> TreeNode:
        if not inorder or not preorder:
            return None

        ind = inorder.index(preorder.pop(0))
        root = TreeNode(inorder[ind])
        root.left = self.buildTree(preorder, inorder[:ind])
        root.right = self.buildTree(preorder, inorder[ind+1:])
        
        return root

sample 36 ms submission:

class Solution:
    def buildTree(self, preorder: List[int], inorder: List[int]) -> TreeNode:
        #get root from preorder
        # save index from inorder to find range of index between which left and right child will be
        
        ln = len(inorder)
        mp = {}
        for idx, num in enumerate(inorder):
            mp[num] = idx
        
        l, r = 0, ln - 1
        self.idx = 0 #idx is for preorder
        return self.helper(preorder, mp, l, r)
        
    
    def helper(self, preorder, mp, l, r):
        if l > r:
            return None
        
        num = preorder[self.idx]
        newNode = TreeNode(num)
        self.idx += 1
        if l == r:
            return newNode
        else:
            newNode.left = self.helper(preorder, mp, l, mp[num]-1)
            newNode.right = self.helper(preorder, mp, mp[num]+1, r)
            return newNode

sample 32 ms submission: 對(duì)preorder進(jìn)行迭代

class Solution:
    def buildTree(self, preorder, inorder):
        ind = {}
        for i,v in enumerate(inorder):
            ind[v] = i
        
        stack, root = [], None
        
        for val in preorder:
            if not root:
                root = TreeNode(val)
                stack.append(root)
            else:
                idx = ind[val]
                node = TreeNode(val)
                if idx < ind[stack[-1].val]:
                    stack[-1].left = node
                else:
                    while stack and idx > ind[stack[-1].val]:
                        parent = stack.pop()
                    parent.right = node
                stack.append(node)
        return root