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

The following code simply treats every possible cases. Tree height is obtained along the way to avoid another recursion.

enum CompleteType
{
    kNotComplete = 0,
    kComplete = 1, // Complete but not full
    kFull = 2,
    kEmpty = 3
};

CompleteType isTreeComplete(Node* node, int* height)
{
    if (node == NULL)
    {
        *height = 0;
        return kEmpty;
    }

    int leftHeight, rightHeight;

    CompleteType leftCompleteType = isTreeComplete(node->left, &leftHeight);
    CompleteType rightCompleteType = isTreeComplete(node->right, &rightHeight);

    *height = max(leftHeight, rightHeight) + 1;

    // Straight forwardly treat all possible cases
    if (leftCompleteType == kComplete && 
        rightCompleteType == kEmpty &&
        leftHeight == rightHeight + 1)
        return kComplete;

    if (leftCompleteType == Full)
    {
        if (rightCompleteType == kEmpty && leftHeight == rightHeight + 1)
            return kComplete;
        if (leftHeight == rightHeight)
        {
            if (rightCompleteType == kComplete)
                return kComplete;
            if (rightCompleteType == kFull)
                return kFull;
        }
    }

    if (leftCompleteType == kEmpty && rightCompleteType == kEmpty)
        return kFull;

    return kNotComplete;
}

bool isTreeComplete(Node* node)
{
    int height;
    return (isTreeComplete(node, &height) != kNotComplete);
}