Question $17$

$2$ pts

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When value $27$ is removed from the binary search tree shown below, which procedure will result in a reduced binary search tree with greatest balance.

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Use this definition of "balance": Compute the absolute difference Ddiff between the depths of both subtrees of the root node. Smaller Ddiff means greater balance.

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Example: The initial BST has Ddiff $=|2-4|=2(2$ nodes along longest path in left subtree, $4$ nodes along longest path in right subtree$).$

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The binary search tree property is restored and the best balance is achieved with: $46$ becomes the new root, the and subtree rooted in $31$ becomes a left subtree of $55.$

The binary search tree property tree is restored and the best balance is achieved with: $31$ takes the place of $27$ and the subtree rooted in $35$ becomes the new left subtree of $46.$

The binary search tree property is restored and the best balance is achieved with: $32$ takes the place of $27$ and leaf $32$ is deleted.

The binary search tree property is restored and the best balance is achieved with: $16$ takes the place of $27$ and leaf $16$ is deleted.