# Construct Binary Tree from Preorder and Inorder Traversal

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

## Solution

/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode(int x) { val = x; }
* }
*/
class Solution {
public TreeNode buildTree(int[] preorder, int[] inorder) {
if (preorder == null || inorder == null || preorder.length != inorder.length) {
return null;
}
return buildTreeHelper(preorder, inorder, 0, preorder.length - 1, 0, inorder.length - 1) ;
}
TreeNode buildTreeHelper(int[] preorder, int[] inorder, int preStart, int preEnd, int inStart, int inEnd) {
if (inStart > inEnd) {
return null;
}
int rootPosition = findPosition(inStart, inEnd, inorder, preorder[preStart]);
TreeNode root = new TreeNode(preorder[preStart]);
root.left = buildTreeHelper(preorder, inorder, preStart + 1, preStart + rootPosition - inStart, inStart, rootPosition - 1 );
root.right = buildTreeHelper(preorder, inorder, preEnd - inEnd + rootPosition + 1, preEnd, rootPosition + 1, inEnd );
return root;
}
int findPosition (int start, int end, int[] arr, int target) {
int i;
for (i = start; i <= end; i++) {
if (arr[i] == target) {
return i;
}
}
return -1;
}
}

### Using Pre-built Hashmap for Index Lookup

via @yavinci: use HashMap to cache the inorder[] position.
public TreeNode buildTree(int[] preorder, int[] inorder) {
Map<Integer, Integer> inMap = new HashMap<Integer, Integer>();
for(int i = 0; i < inorder.length; i++) {
inMap.put(inorder[i], i);
}
TreeNode root = buildTree(preorder, 0, preorder.length - 1, inorder, 0, inorder.length - 1, inMap);
return root;
}
public TreeNode buildTree(int[] preorder, int preStart, int preEnd, int[] inorder, int inStart, int inEnd, Map<Integer, Integer> inMap) {
if(preStart > preEnd || inStart > inEnd) return null;
TreeNode root = new TreeNode(preorder[preStart]);
int inRoot = inMap.get(root.val);
int numsLeft = inRoot - inStart;
root.left = buildTree(preorder, preStart + 1, preStart + numsLeft, inorder, inStart, inRoot - 1, inMap);
root.right = buildTree(preorder, preStart + numsLeft + 1, preEnd, inorder, inRoot + 1, inEnd, inMap);
return root;
}

### *LeetCode Official Solution

Depth First Search (DFS) - Recursion - ID Map
class Solution {
// start from first preorder element
int pre_idx = 0;
int[] preorder;
int[] inorder;
HashMap<Integer, Integer> idx_map = new HashMap<Integer, Integer>();
public TreeNode helper(int in_left, int in_right) {
// if there is no elements to construct subtrees
if (in_left == in_right)
return null;
// pick up pre_idx element as a root
int root_val = preorder[pre_idx];
TreeNode root = new TreeNode(root_val);
// root splits inorder list
// into left and right subtrees
int index = idx_map.get(root_val);
// recursion
pre_idx++;
// build left subtree
root.left = helper(in_left, index);
// build right subtree
root.right = helper(index + 1, in_right);
return root;
}
public TreeNode buildTree(int[] preorder, int[] inorder) {
this.preorder = preorder;
this.inorder = inorder;
// build a hashmap value -> its index
int idx = 0;
for (Integer val : inorder) {
idx_map.put(val, idx++);
}
return helper(0, inorder.length);
}
}