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‎docs/reference/contracts/libs/data-structures/CartesianMerkleTree.md‎

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@@ -11,7 +11,7 @@ library CartesianMerkleTree
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Cartesian Merkle Tree Module
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A magnificent ZK-friendly data structure based on a Binary Search Tree + Heap + Merkle Tree. Short names: CMT, Treaple.
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Possesses deterministic and idemponent properties. Can be used as a substitute for a Sparse Merkle Tree (SMT).
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Possesses deterministic and idempotent properties. Can be used as a substitute for a Sparse Merkle Tree (SMT).
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Gas usage for adding and removing 1,000 elements to a CMT with the keccak256 and poseidon hash functions is detailed below:
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CartesianMerkleTree.Proof memory proof = uintTreaple.getProof(100, 0);
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uintTreaple.verifyProof(proof);
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uintTreaple.getNodeByKey(100);
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uintTreaple.remove(100);
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| :--- | :------------------------------- | :---------------- |
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| [0] | struct CartesianMerkleTree.Proof | CMT proof struct. |
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### verifyProof
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```solidity
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function verifyProof(
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CartesianMerkleTree.UintCMT storage treaple,
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CartesianMerkleTree.Proof memory proof_
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) internal view returns (bool)
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```
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The function to verify the proof for inclusion or exclusion of a node in the CMT.
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Complexity is O(log(n)), where n is the max depth of the treaple.
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Parameters:
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| Name | Type | Description |
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| :------ | :--------------------------------- | :--------------------- |
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| treaple | struct CartesianMerkleTree.UintCMT | self. |
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| proof_ | struct CartesianMerkleTree.Proof | The CMT proof struct. |
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Return values:
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| Name | Type | Description |
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| :--- | :--- | :------------------------------------------- |
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| [0] | bool | True if the proof is valid, false otherwise. |
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### getRoot
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```solidity
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| :--- | :------------------------------- | :---------------- |
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| [0] | struct CartesianMerkleTree.Proof | CMT proof struct. |
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### verifyProof
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```solidity
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function verifyProof(
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CartesianMerkleTree.Bytes32CMT storage treaple,
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CartesianMerkleTree.Proof memory proof_
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) internal view returns (bool)
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```
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The function to verify the proof for inclusion or exclusion of a node in the CMT.
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Complexity is O(log(n)), where n is the max depth of the treaple.
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Parameters:
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| Name | Type | Description |
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| :------ | :------------------------------------ | :--------------------- |
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| treaple | struct CartesianMerkleTree.Bytes32CMT | self. |
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| proof_ | struct CartesianMerkleTree.Proof | The CMT proof struct. |
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Return values:
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| Name | Type | Description |
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| :--- | :--- | :------------------------------------------- |
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| [0] | bool | True if the proof is valid, false otherwise. |
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### getRoot
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```solidity
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| :--- | :------------------------------- | :---------------- |
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| [0] | struct CartesianMerkleTree.Proof | CMT proof struct. |
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### verifyProof
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```solidity
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function verifyProof(
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CartesianMerkleTree.AddressCMT storage treaple,
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CartesianMerkleTree.Proof memory proof_
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) internal view returns (bool)
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```
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The function to verify the proof for inclusion or exclusion of a node in the CMT.
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Complexity is O(log(n)), where n is the max depth of the treaple.
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Parameters:
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| Name | Type | Description |
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| :------ | :------------------------------------ | :--------------------- |
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| treaple | struct CartesianMerkleTree.AddressCMT | self. |
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| proof_ | struct CartesianMerkleTree.Proof | The CMT proof struct. |
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Return values:
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| Name | Type | Description |
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| :--- | :--- | :------------------------------------------- |
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| [0] | bool | True if the proof is valid, false otherwise. |
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### getRoot
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```solidity

‎docs/reference/contracts/libs/data-structures/IncrementalMerkleTree.md‎

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| :--- | :------ | :-------------------------------- |
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| [0] | bytes32 | The root hash of the Merkle tree. |
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### verifyProof
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```solidity
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function verifyProof(
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IncrementalMerkleTree.UintIMT storage tree,
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bytes32[] memory siblings_,
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uint256 directionBits_,
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bytes32 leaf_
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) internal view returns (bool)
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```
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The function to verify a proof of a leaf's existence in the uint256 tree.
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Complexity is O(log(n)), where n is the number of elements in the tree.
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Parameters:
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| Name | Type | Description |
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| :------------- | :----------------------------------- | :------------------------------- |
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| tree | struct IncrementalMerkleTree.UintIMT | self. |
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| siblings_ | bytes32[] | The siblings of the leaf. |
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| directionBits_ | uint256 | The direction bits of the leaf. |
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| leaf_ | bytes32 | The leaf. |
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Return values:
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| Name | Type | Description |
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| :--- | :--- | :------------------------------------------- |
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| [0] | bool | True if the proof is valid, false otherwise. |
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### height
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```solidity
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The function to return the root hash of the bytes32 tree.
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Complexity is O(log(n) + h), where n is the number of elements in the tree and
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h is the height of the tree.
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### verifyProof
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```solidity
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function verifyProof(
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IncrementalMerkleTree.Bytes32IMT storage tree,
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bytes32[] memory siblings_,
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uint256 directionBits_,
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bytes32 leaf_
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) internal view returns (bool)
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```
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The function to verify a proof of a leaf's existence in the bytes32 tree.
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Complexity is O(log(n)), where n is the number of elements in the tree.
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Parameters:
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| Name | Type | Description |
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| :------------- | :-------------------------------------- | :------------------------------- |
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| tree | struct IncrementalMerkleTree.Bytes32IMT | self. |
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| siblings_ | bytes32[] | The siblings of the leaf. |
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| directionBits_ | uint256 | The direction bits of the leaf. |
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| leaf_ | bytes32 | The leaf. |
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Return values:
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| Name | Type | Description |
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| :--- | :--- | :------------------------------------------- |
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| [0] | bool | True if the proof is valid, false otherwise. |
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### height
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```solidity
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The function to return the root hash of the address tree.
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Complexity is O(log(n) + h), where n is the number of elements in the tree and
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h is the height of the tree.
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### verifyProof
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```solidity
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function verifyProof(
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IncrementalMerkleTree.AddressIMT storage tree,
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bytes32[] memory siblings_,
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uint256 directionBits_,
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bytes32 leaf_
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) internal view returns (bool)
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```
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The function to verify a proof of a leaf's existence in the address tree.
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Complexity is O(log(n)), where n is the number of elements in the tree.
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Parameters:
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| Name | Type | Description |
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| :------------- | :-------------------------------------- | :------------------------------- |
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| tree | struct IncrementalMerkleTree.AddressIMT | self. |
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| siblings_ | bytes32[] | The siblings of the leaf. |
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| directionBits_ | uint256 | The direction bits of the leaf. |
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| leaf_ | bytes32 | The leaf. |
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Return values:
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| Name | Type | Description |
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| :--- | :--- | :------------------------------------------- |
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| [0] | bool | True if the proof is valid, false otherwise. |
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### height
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```solidity

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