106. Construct Binary Tree from Inorder and Postorder Traversal

Problem

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

Note:

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

For example, given

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

Return the following binary tree:

    3
   / \
  9  20
    /  \
   15   7

Solution

/**
 * Definition for a binary tree node.
 * function TreeNode(val) {
 *     this.val = val;
 *     this.left = this.right = null;
 * }
 */
/**
 * @param {number[]} inorder
 * @param {number[]} postorder
 * @return {TreeNode}
 */
var buildTree = function(inorder, postorder) {
  return helper(inorder, postorder, 0, inorder.length - 1, postorder.length - 1);
};

var helper = function (inorder, postorder, inStart, inEnd, postIndex) {
  if (inStart > inEnd || postIndex < 0) return null;

  var index = 0;
  var root = new TreeNode(postorder[postIndex]);

  for (var i = inStart; i <= inEnd; i++) {
    if (inorder[i] === root.val) {
      index = i;
      break;
    }
  }

  root.right = helper(inorder, postorder, index + 1, inEnd, postIndex - 1);
  root.left = helper(inorder, postorder, inStart, index - 1, postIndex - 1 - (inEnd - index));

  return root;
};

Explain:

see Construct Binary Tree from Preorder and Inorder Traversal.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).