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:
3
/ \
9 20
/ \
15 7
这道题要求用先序和中序遍历来建立二叉树，跟之前那道 Construct Binary Tree from Inorder and Postorder Traversal 原理基本相同，针对这道题，由于先序的顺序的第一个肯定是根，所以原二叉树的根节点可以知道，题目中给了一个很关键的条件就是树中没有相同元素，有了这个条件就可以在中序遍历中也定位出根节点的位置，并以根节点的位置将中序遍历拆分为左右两个部分，分别对其递归调用原函数，参见代码如下：
class Solution {
public:
TreeNode *buildTree(vector<int> &preorder, vector<int> &inorder) {
return buildTree(preorder, , preorder.size() - , inorder, , inorder.size() - );
}
TreeNode *buildTree(vector<int> &preorder, int pLeft, int pRight, vector<int> &inorder, int iLeft, int iRight) {
if (pLeft > pRight || iLeft > iRight) return NULL;
int i = ;
for (i = iLeft; i <= iRight; ++i) {
if (preorder[pLeft] == inorder[i]) break;
}
TreeNode *cur = new TreeNode(preorder[pLeft]);
cur->left = buildTree(preorder, pLeft + , pLeft + i - iLeft, inorder, iLeft, i - );
cur->right = buildTree(preorder, pLeft + i - iLeft + , pRight, inorder, i + , iRight);
return cur;
}
};
下面来看一个例子, 某一二叉树的中序和后序遍历分别为：
Preorder: 5 4 11 8 13 9
Inorder: 11 4 5 13 8 9
4 11 8 13 9 => 5
11 4 13 8 9 / \
11 13 9 => 5
11 13 9 / \
4 8
11 13 9 => 5
11 13 9 / \
4 8
/ / \
11 13 9
做完这道题后，大多人可能会有个疑问，怎么没有由先序和后序遍历建立二叉树呢，这是因为先序和后序遍历不能唯一的确定一个二叉树，比如下面五棵树：
1 preorder: 1 2 3
/ \ inorder: 2 1 3
2 3 postorder: 2 3 1
1 preorder: 1 2 3
/ inorder: 3 2 1
2 postorder: 3 2 1
/
3
1 preorder: 1 2 3
/ inorder: 2 3 1
2 postorder: 3 2 1
\
3
1 preorder: 1 2 3
\ inorder: 1 3 2
2 postorder: 3 2 1
/
3
1 preorder: 1 2 3
\ inorder: 1 2 3
2 postorder: 3 2 1
\
3
从上面我们可以看出，对于先序遍历都为 1 2 3 的五棵二叉树，它们的中序遍历都不相同，而它们的后序遍历却有相同的，所以只有和中序遍历一起才能唯一的确定一棵二叉树。但可能会有小伙伴指出，那第 889 题 Construct Binary Tree from Preorder and Postorder Traversal 不就是从先序和后序重建二叉树么？难道博主被啪啪打脸了么？难道博主的一世英名就此毁于一旦了么？不，博主向命运的不公说不，请仔细看那道题的要求 "Return any binary tree that matches the given preorder and postorder traversals."，是让返回任意一棵二叉树即可，所以这跟博主的结论并不矛盾。长舒一口气，博主的晚节保住了～
Github 同步地址：
https://github.com/grandyang/leetcode/issues/105
类似题目：
Construct Binary Tree from Inorder and Postorder Traversal
Construct Binary Tree from Preorder and Postorder Traversal
参考资料：
https://leetcode.com/problems/construct-binary-tree-from-preorder-and-inorder-traversal/
https://leetcode.com/problems/construct-binary-tree-from-preorder-and-inorder-traversal/discuss/34538/My-Accepted-Java-Solution
https://leetcode.com/problems/construct-binary-tree-from-preorder-and-inorder-traversal/discuss/34562/Sharing-my-straightforward-recursive-solution
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