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    Question

    In a binomial heap, if the root is greater than the left child and less than the right child, which of the following statements is correct?

    A This violates the properties of a binomial heap. Correct Answer Incorrect Answer
    B This is a common property of a min-heap. Correct Answer Incorrect Answer
    C This is a common property of a max-heap. Correct Answer Incorrect Answer
    D This situation indicates the heap is balanced. Correct Answer Incorrect Answer
    E This is typical in a Fibonacci heap. Correct Answer Incorrect Answer

    Solution

    In a binomial heap, the fundamental property is that it follows the min-heap or max-heap order property across its trees. For a min-heap binomial heap, the root of each tree must be the smallest element, meaning it should be less than all its children. Conversely, in a max-heap binomial heap, the root should be greater than all its children. The situation described in the question, where the root is greater than the left child and less than the right child, violates these properties because it suggests an inconsistent ordering.

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