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What is the difference between the binary-search-tree property and the min-heap property (see page 129)? Can...

What is the difference between the binary-search-tree property and the min-heap property (see page 129)? Can the min-heap property be used to print out the keys of an n-node tree in sorted order in O(n) time? Explain how or why not.

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The difference between the binary-search-tree property and the min-heap property is that the binary-search-tree requires that the key of left child be less than or equal to its parent and that the key of the right child be greater than or equal to its parent. The min-heap, on the other hand, requires that both the keys of the children be less than or equal to the key of the parent. The difference is that in the BST the right child is greater than or equal the parent and in the min-heap the right child is less than or equal to the parent.

The min-heap cannot be used to print out the keys of an n-node tree in sorted order in O(n) time since the min-heap says nothing about the ordering of child nodes with respect to each other. Additional sorting and comparisons would have to be done, which would automatically bump the algorithm to greater than O(n).

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