Consider the given tree below. Calculate the value at the root of the tree…

Key insight: Traverse the tree left-to-right applying alpha-beta pruning. The root is a Max node.

• Step 1: Evaluate the left subtree (Min). Visit its left Max-child: max(3,5) = 5. This returns 5 to the Min node.

• Step 2: At the left Min parent, beta becomes 5. Evaluate its right Max-child: first child is 6. Since this Max-child already yields 6 which is >= beta (5), alpha-beta prunes the sibling 9. The right Max-child would be at least 6, so the Min parent keeps min(5,6) = 5. Thus the entire left subtree returns 5.

• Step 3: Back at the root (Max), alpha becomes 5. Evaluate the right subtree (Min) with alpha = 5. Visit its left Max-child: max(1,2) = 2. The Min parent now has beta = 2.

• Step 4: Since beta (2) is <= alpha (5), alpha-beta prunes the right Max-child subtree (values 0 and -1) entirely. So the right subtree returns 2.

• Step 5: The root (Max) chooses max( left subtree 5, right subtree 2 ) = 5.

Pruned leaves/subtrees: leaf 9 is pruned during evaluation of the left subtree; the entire right sibling subtree with leaves 0 and -1 is pruned during evaluation of the right subtree.

Final answer: 5