how to rebuild BST using {pre,in,post}order traversals results

问题

We know the pre-order, in-order and post-order traversals. What algorithm will reconstruct the BST?

回答1:

Because it is BST, in-order can be sorted from pre-order or post-order <1>. Actually, either pre-order or post-order is needed only....

<1> if you know what the comparison function is

From pre-order and in-order, to construct a binary tree

BT createBT(int* preOrder, int* inOrder, int len)
{
    int i;
    BT tree;
    if(len <= 0)
        return NULL;
    tree = new BTNode;
    t->data = *preOrder;
    for(i = 0; i < len; i++)
        if(*(inOrder + i) == *preOrder)
            break;
    tree->left = createBT(preOrder + 1, inOrder, i);
    tree->right = createBT(preOrder + i + 1, inOrder + i + 1, len - i - 1);
    return tree;
}

The rationale behind this:

In pre-order, the first node is the root. Find the root in the in-order. Then the tree can be divided into left and right. Do it recursively.

Similar for post-order and in-order.

回答2:

I personally found Dante's answer a little hard to follow. I worked my way through the solution and found it to be similar to the one posted here http://geeksforgeeks.org/?p=6633

Complexity is O(N^2).

Here's another approach for building a tree using post-order traversal: http://www.technicallyidle.com/2011/02/15/build-binary-search-tree-using-post-order-traversal-trace/

Hope this helps

回答3:

For reconstruction of a binary tree either preorder+inorder or postorder+inorder is needed. As already pointed out for a BST we can reconstruct using either preorder or postorder as sorting either of them will give us the inorder.

You can use the following function which is modification of the code given by @brainydexter to reconstruct the tree without using the static variable:

struct node* buildTree(char in[],char pre[], int inStrt, int inEnd,int preIndex){

    // start index > end index..base condition return NULL.
    if(inStrt > inEnd)
        return NULL;

    // build the current node with the data at pre[preIndex].
    struct node *tNode = newNode(pre[preIndex]);

    // if all nodes are constructed 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,preIndex+1);
    tNode->right = buildTree(in, pre, inIndex+1, inEnd,preIndex+inIndex+1);

    return tNode;
}

回答4:

Here is a Ruby recursive solution

def rebuild(preorder, inorder)
  root = preorder.first
  root_inorder = inorder.index root
  return root unless root_inorder
  root.left = rebuild(preorder[1, root_inorder], inorder[0...root_inorder])
  root.right = rebuild(preorder[root_inorder+1..-1], inorder[root_inorder+1..-1])
  root
end

And an example

class Node
  attr_reader :val
  attr_accessor :left, :right

  def initialize(val)
    @val = val
  end

  def ==(node)
    node.val == val
  end

  def inspect
    "val: #{val}, left: #{left && left.val || "-"}, right: #{right && right.val || "-"}"
  end
end

inorder = [4, 7, 2, 5, 1, 3, 8, 6, 9].map{|v| Node.new v }
preorder = [1, 2, 4, 7, 5, 3, 6, 8, 9].map{|v| Node.new v }

tree = rebuild(preorder, inorder)
tree
# val: 1, left: 2, right: 3
tree.left
# val: 2, left: 4, right: 5
tree.left.left
# val: 4, left: -, right: 7

来源：https://stackoverflow.com/questions/5367358/how-to-rebuild-bst-using-pre-in-postorder-traversals-results

标签

algorithm

binary-tree

binary-search-tree