Transform string to tree

Question

Convert the given array to tree structure following the specified rules.

Codemia · Accepted Answer

To transform an array into a tree structure, we can recognize that the problem resembles a recursive approach to building binary trees from sorted arrays. The key pattern here is the divide and conquer method. We can utilize the middle element of the array as the root of the tree, and recursively apply the same logic to the left and right halves of the array to create left and right subtrees. This process ensures that the resulting tree is balanced, as we consistently choose the middle element.

1. **Base Case**: If the input array is empty, return None since there's no tree to create.
2. **Recursive Case**: Find the middle index of the array. This will be the root node of the tree.
   - For example, given the array [1, 2, 3, 4, 5], the middle element is 3, which becomes the root.
3. **Construct Left Subtree**: Recursively call the function on the left half of the array (elements before the middle index).
   - For [1, 2], the middle is 2, which becomes the left child of 3.
4. **Construct Right Subtree**: Recursively call the function on the right half of the array (elements after the middle index).
   - For [4, 5], the middle is 5, which becomes the right child of 3.
5. Finally, return the root node. This will create a balanced binary tree from the sorted array.

Here’s the implementation of the above approach in Python:
```python
class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def sorted_array_to_bst(nums):
    if not nums:
        return None
    mid = len(nums) // 2
    root = TreeNode(nums[mid])
    root.left = sorted_array_to_bst(nums[:mid])
    root.right = sorted_array_to_bst(nums[mid + 1:])
    return root
```
This code creates a binary search tree from a sorted array by recursively finding the middle element as the root.

The time complexity of this approach is O(n), where n is the number of elements in the input array. This is because each element is processed once while creating the tree. The space complexity is O(log n) due to the recursive stack space used for the function calls (in the case of a balanced tree). If the input array were to be unbalanced, the space complexity could degrade to O(n), but given that we are working with a sorted array, it remains O(log n).

1. **Empty Array**: Input `[]` should return `None`.
2. **Single Element Array**: Input `[1]` should return a tree with a single node (1).
3. **Two Elements Array**: Input `[1, 2]` should return a tree where 2 is the root, and 1 is the left child.
4. **All Elements Equal**: Input `[2, 2, 2, 2]` should still create a valid tree, but all nodes will have the same value.
5. **Large Input**: Test with a larger sorted array (e.g., range of 1 to 1000) to ensure the solution handles scalability.

Transform string to tree

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