🔨 Building Your First Merkle Tree

Learn how to construct a Merkle tree from leaf nodes to root hash

Previous
Introduction

🔨 Building a Merkle Tree

Let's build a Merkle tree step by step! Watch how data at the leaves gets hashed and combined up to a single root hash.

📋 Construction Algorithm

1️⃣
Hash the Leaves

Take each transaction and compute its hash. These become the leaf nodes.

Leaf₁ = Hash("TX1")
Leaf₂ = Hash("TX2")
Leaf₃ = Hash("TX3")
Leaf₄ = Hash("TX4")
2️⃣
Combine Pairs

Concatenate adjacent hashes and hash them together to create parent nodes.

Parent₁ = Hash(Leaf₁ + Leaf₂)
Parent₂ = Hash(Leaf₃ + Leaf₄)
3️⃣
Repeat Until Root

Continue combining pairs level by level until only one hash remains - the Merkle root!

Root = Hash(Parent₁ + Parent₂)

🎮 Interactive Tree Builder

Add or remove transactions, then watch the tree build automatically:

Current Transactions: 4
TX1
TX2
TX3
TX4

🧮 Complexity Analysis

Building the Tree
Time Complexity:O(n)
Space Complexity:O(n)
Tree Height:log₂(n)

Linear time to build, but logarithmic height makes verification efficient!

Example: 1000 Transactions
Leaf Nodes:1,000
Total Nodes:~2,000
Tree Height:10 levels

Only 10 hashes needed to verify any single transaction!

⚠️ Edge Cases

Odd Number of Transactions

If you have an odd number of nodes at any level, duplicate the last node.

[TX1, TX2, TX3] → [TX1, TX2, TX3, TX3]
Then pair: Hash(TX1+TX2), Hash(TX3+TX3)
Single Transaction

With just one transaction, the hash of that transaction IS the Merkle root.

[TX1] → Merkle Root = Hash(TX1)
Empty Block

Bitcoin blocks always have at least a coinbase transaction, so never truly empty.

Minimum: [Coinbase TX] → Valid block with Merkle root

💡 Key Insights

🎯
Bottom-Up Construction

Always build from leaves up to root. Can't start from root and work down!

🔄
Deterministic Process

Same transactions always produce same Merkle root. Order matters!

Parallel Construction

Each level can be computed in parallel - great for performance!