原文地址：Construct Tree from given Inorder and Preorder traversals
我们考虑下下面的遍历：
中序遍历：D B E A F C
先序遍历：A B D E C F
在一个先序序列中，最左端的元素就是树根。所以我们知道A是已知序列的根。通过查询A的中序序列，我们可以得到A左边左子树的所有元素和右边右子树的所有元素。所以我们现在知道了以下结构。
A
/ \
/ \
D B E F C我们递归上述步骤，然后得到下面的树：
A
/ \
/ \
B C
/ \ /
/ \ /
D E F算法： buildTree()
1）从先序序列中选一个元素。增加一个先序索引变量（下面代码中的preIndex）来选择下一次递归调用的下一个元素。
2）用已选择的元素的值创建一个新的树节点tNode。
3）找到已选择元素在中序遍历中的索引。设这个索引为inIndex。
4）在inIndex之前调用buildTree，建立树作为tNode的左子树。
5）在inIndex之后调用buildTree，建立树作为tNode的右子树。
6）返回tNode。
// Java program to construct a tree using inorder and preorder traversal
/* A binary tree node has data, pointer to left child
and a pointer to right child */
class Node
{
char data;
Node left, right;
Node(char item)
{
data = item;
left = right = null;
}
}
class BinaryTree
{
Node root;
static int preIndex = 0;
/* Recursive function to construct binary of size len from
Inorder traversal in[] and Preorder traversal pre[].
Initial values of inStrt and inEnd should be 0 and len -1.
The function doesn't do any error checking for cases where
inorder and preorder do not form a tree */
Node buildTree(char in[], char pre[], int inStrt, int inEnd)
{
if (inStrt > inEnd)
return null;
/* Pick current node from Preorder traversal using preIndex
and increment preIndex */
Node tNode = new Node(pre[preIndex++]);
/* If this node has no children then return */
if (inStrt == inEnd)
return tNode;
/* Else find the index of this node in Inorder traversal */
int inIndex = search(in, inStrt, inEnd, tNode.data);
/* Using index in Inorder traversal, construct left and
right subtress */
tNode.left = buildTree(in, pre, inStrt, inIndex - 1);
tNode.right = buildTree(in, pre, inIndex + 1, inEnd);
return tNode;
}
/* UTILITY FUNCTIONS */
/* Function to find index of value in arr[start...end]
The function assumes that value is present in in[] */
int search(char arr[], int strt, int end, char value)
{
int i;
for (i = strt; i <= end; i++)
{
if (arr[i] == value)
return i;
}
return i;
}
/* This funtcion is here just to test buildTree() */
void printInorder(Node node)
{
if (node == null)
return;
/* first recur on left child */
printInorder(node.left);
/* then print the data of node */
System.out.print(node.data + " ");
/* now recur on right child */
printInorder(node.right);
}
// driver program to test above functions
public static void main(String args[])
{
BinaryTree tree = new BinaryTree();
char in[] = new char[]{'D', 'B', 'E', 'A', 'F', 'C'};
char pre[] = new char[]{'A', 'B', 'D', 'E', 'C', 'F'};
int len = in.length;
Node root = tree.buildTree(in, pre, 0, len - 1);
// building the tree by printing inorder traversal
System.out.println("Inorder traversal of constructed tree is : ");
tree.printInorder(root);
}
}
// This code has been contributed by Mayank Jaiswal输出：
Inorder traversal of constructed tree is :
D B E A F C时间复杂度：