How to Build Tree Structures

🌲 Step 1: Decide the Tree Type

✅ Do you need a Binary Search Tree (BST)?

• Structure where left child < parent < right child
• Insertions follow value-based logic

✅ Do you need a Min/Max Heap?

• Often implemented with arrays
• Enforce ordering without necessarily being sorted

✅ Do you need a general N-ary tree?

• Any number of children per node
• Often used for hierarchical data like file systems or org charts

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🔧 Step 2: Build Strategies

▶️ A. Recursive Build (for BST)

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

def insert_bst(root, val):
    if not root:
        return Node(val)
    if val < root.val:
        root.left = insert_bst(root.left, val)
    else:
        root.right = insert_bst(root.right, val)
    return root

values = [4, 7, 3, 21, 15]
tree = None
for v in values:
    tree = insert_bst(tree, v)

🗂️ B. Map-Based Build (when you have parent references)

data = [
    { "id": 1, "parent_id": None },
    { "id": 2, "parent_id": 1 },
    { "id": 3, "parent_id": 1 },
    { "id": 4, "parent_id": 2 }
]

tree_map = {item["id"]: {**item, "children": []} for item in data}
root = None

for item in data:
    pid = item["parent_id"]
    if pid is None:
        root = tree_map[item["id"]]
    else:
        tree_map[pid]["children"].append(tree_map[item["id"]])

⬇️ C. Sorting + Heap Build (for binary heaps)

import heapq

values = [4, 7, 3, 21, 15]
heapq.heapify(values)

# Result is still array-based, but heap-ordered
print(values)  # Min-heap by default

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🧠 Build Direction: Top-Down vs Bottom-Up

Direction	Description	Common Use Cases	Constraint
Top-Down	Start from root, add children	File systems, org charts	Parents must be encountered before children
Bottom-Up	Start from leaves, combine upward	Merkle trees, expression trees	Each child must know its parent

Larger article on tree building direction here