How to determine whether a binary tree is complete?

Question

A complete binary tree is defined as a binary tree in which every level, except possibly the deepest, is completely filled. At deepest level, all nodes must be as far left a

Answer 1

Thanks for @Jonathan Graehl 's pseudo code. I've implemented it in Java. I've tested it against iterative version. It works like a charm!

public static boolean isCompleteBinaryTreeRec(TreeNode root){
//      Pair notComplete = new Pair(-1, false);
//      return !isCompleteBinaryTreeSubRec(root).equalsTo(notComplete);
    return isCompleteBinaryTreeSubRec(root).height != -1;
}

public static boolean isPerfectBinaryTreeRec(TreeNode root){
    return isCompleteBinaryTreeSubRec(root).isFull;
}

public static Pair isCompleteBinaryTreeSubRec(TreeNode root){
    if(root == null){
        return new Pair(0, true);
    }

    Pair left = isCompleteBinaryTreeSubRec(root.left);
    Pair right = isCompleteBinaryTreeSubRec(root.right);

    if(left.isFull && left.height==right.height){
        return new Pair(1+left.height, right.isFull);
    }

    if(right.isFull && left.height==right.height+1){
        return new Pair(1+left.height, false);
    }

    return new Pair(-1, false);
}

private static class Pair{
    int height;         
    boolean isFull;     

    public Pair(int height, boolean isFull) {
        this.height = height;
        this.isFull = isFull;
    }

    public boolean equalsTo(Pair obj){
        return this.height==obj.height && this.isFull==obj.isFull;
    }
}