BST-Rightmost/Leftmost
Starting with an empty tree, build a BST by inserting nodes in the order 12, 101, 23, 48, 3, 33, 105, 2, 4 11.

Which number will the rightmost node of the tree have?

[Fill in the blank]

Which number will the leftmost node of the tree have?

[Fill in the blank]

Question

BST-Rightmost/Leftmost
Starting with an empty tree, build a BST by inserting nodes in the order 12, 101, 23, 48, 3,  33, 105, 2, 4 11.

Which number will the rightmost node of the tree have?

[Fill in the blank]

Which  number will the leftmost node of the tree have?

[Fill in the blank]

BlackTom AI · Accepted Answer

In a binary search tree (BST), every left child is less than its parent and every right child is greater, so the rightmost node contains the maximum value and the leftmost node contains the minimum value. 1) Relevant knowledge points and concepts - BST property: left subtree < node < right subtree. - The maximum value in a BST is found by following right child pointers until none remain (rightmost node). - The minimum value is found by following left child pointers until none remain (leftmost node). 2) Step-by-step insertion reasoning (each insertion shows where the node goes) Starting with empty tree: - Insert 12: becomes root. - Insert 101: 101 > 12 → goes to right of 12. - Insert 23: 23 > 12 → go right to 101; 23 < 101 → goes to left of 101. - Insert 48: 48 > 12 → right to 101; 48 < 101 → left to 23; 48 > 23 → goes to right of 23. - Insert 3: 3 < 12 → goes to left of 12. - Insert 33: 33 > 12 → right to 101; 33 < 101 → left to 23; 33 > 23 → right to 48; 33 < 48 → goes to left of 48. - Insert 105: 105 > 12 → right to 101; 105 > 101 → goes to right of 101. - Insert 2: 2 < 12 → left to 3; 2 < 3 → goes to left of 3. - Insert 4: 4 < 12 → left to 3; 4 > 3 → goes to right of 3. - Insert 11: 11 < 12 → left to 3; 11 > 3 → right to 4; 11 > 4 → goes to right of 4. 3) Intermediate placements summarized (paths to extremes) - Leftmost path: 12 → left 3 → left 2. No further left child, so leftmost = 2. - Rightmost path: 12 → right 101 → right 105. No further right child, so rightmost = 105. 4) Why the correct answers are correct Because 105 is the largest inserted value and ends up as the node with no right child at the extreme right, it is the rightmost node. Because 2 is the smallest inserted value and ends up as the node with no left child at the extreme left, it is the leftmost node. 5) Why other options (other inserted numbers) are incorrect - Any other number less than 105 (e.g., 101, 48, 33, 23, 12, 4, 3, 2, 11) cannot be the rightmost because 105 is greater and positioned to the right of them. - Any other number greater than 2 cannot be the leftmost because 2 is smaller and positioned to the left of them. 6) Conclusion Rightmost node = 105; Leftmost node = 2. These match the provided answers: ["105", "2"].

BST-Rightmost/Leftmost Starting with an empty tree, build a BST by inserting nodes in the order 12, 101, 23, 48, 3, 33, 105, 2, 4 11. Which number will the rightmost node of the tree have? [Fill in the blank] Which number will the leftmost node of the tree have? [Fill in the blank] 多项填空题

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