A binary search tree is built by inserting these chars in this order: G R O U N D H O G Assume that nodes greater than or equal to the parent will go right, less than the parent will go left. What is the post-order traversal of the tree? Enter JUST the characters, all caps, no spaces:
Question
A binary search tree is built by inserting these chars in this order: G R O U N D H O G
Assume that nodes greater than or equal to the parent will go right, less than the parent will go left. What is the post-order traversal of the tree? Enter JUST the characters, all caps, no spaces:
Solution
To solve this problem, we first need to build the binary search tree (BST) using the given order of characters: G R O U N D H O G.
- Start with the first character 'G'. This becomes the root of the tree.
- The next character is 'R'. Since 'R' is greater than 'G', it goes to the right of 'G'.
- The next character is 'O'. 'O' is less than 'R' but greater than 'G', so it goes to the left of 'R'.
- The next character is 'U'. 'U' is greater than 'R', so it goes to the right of 'R'.
- The next character is 'N'. 'N' is less than 'U' but greater than 'O', so it goes to the right of 'O' and left of 'U'.
- The next character is 'D'. 'D' is less than 'N' and 'O', so it goes to the left of 'N'.
- The next character is 'H'. 'H' is greater than 'G' but less than 'O', so it goes to the right of 'G' and left of 'O'.
- The next character is 'O'. 'O' is equal to the existing 'O' in the tree, so it goes to the right of the existing 'O'.
- The last character is 'G'. 'G' is equal to the root 'G', so it goes to the right of the root 'G'.
Now, to find the post-order traversal of the tree, we follow the rule: Left, Right, Root.
The post-order traversal of the tree is: D N O G O H U R G
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