fix: handle the precondition in path length from key when the number …

…of leaves is <= 1 (#274)

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## Overview

Fix the issue with path length from key when the number of leaves is <=
1. This happens when the key and the number of leaves are consecutive
numbers.

## Checklist

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- [ ] New and updated code has appropriate documentation
- [ ] New and updated code has new and/or updated testing
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- [ ] Linked issues closed with keywords


<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit

- **Bug Fixes**
- Improved the `pathLengthFromKey` function to handle cases with minimal
leaves efficiently.

- **Tests**
- Added new test cases to ensure the reliability of binary Merkle proofs
with various key and leaves scenarios.
- Enhanced existing tests with additional assertions for better
coverage.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

src/lib/tree/Utils.sol

@@ -20,9 +20,12 @@ function getStartingBit(uint256 numLeaves) pure returns (uint256 startingBit) {
 /// @param key: The key of the leaf
 /// @param numLeaves: The total number of leaves in the tree
 /// @return pathLength : The length of the path to the leaf
-/// @dev A precondition to this function is that `numLeaves > 1`, so that `(pathLength - 1)` does not cause an underflow when pathLength = 0.
 // solhint-disable-next-line func-visibility
 function pathLengthFromKey(uint256 key, uint256 numLeaves) pure returns (uint256 pathLength) {
+    if (numLeaves <= 1) {
+        // if the number of leaves of the tree is 1 or 0, the path always is 0.
+        return 0;
+    }
     // Get the height of the left subtree. This is equal to the offset of the starting bit of the path
     pathLength = Constants.MAX_HEIGHT - getStartingBit(numLeaves);
 

src/lib/tree/binary/test/BinaryMerkleTree.t.sol

@@ -277,6 +277,28 @@ contract BinaryMerkleProofTest is DSTest {
         assertEq(result[1], data[2]);
     }
 
+    function testSameKeyAndLeavesNumber() external {
+        bytes32 root = 0xb855b42d6c30f5b087e05266783fbd6e394f7b926013ccaa67700a8b0c5a596f;
+        bytes32[] memory sideNodes = new bytes32[](0);
+        uint256 key = 3;
+        uint256 numLeaves = 3;
+        BinaryMerkleProof memory proof = BinaryMerkleProof(sideNodes, key, numLeaves);
+        bytes memory data = bytes(hex"01");
+        bool isValid = BinaryMerkleTree.verify(root, proof, data);
+        assert(!isValid);
+    }
+
+    function testConsecutiveKeyAndNumberOfLeaves() external {
+        bytes32 root = 0xb855b42d6c30f5b087e05266783fbd6e394f7b926013ccaa67700a8b0c5a596f;
+        bytes32[] memory sideNodes = new bytes32[](0);
+        uint256 key = 6;
+        uint256 numLeaves = 7;
+        BinaryMerkleProof memory proof = BinaryMerkleProof(sideNodes, key, numLeaves);
+        bytes memory data = bytes(hex"01");
+        bool isValid = BinaryMerkleTree.verify(root, proof, data);
+        assert(!isValid);
+    }
+
     function testInvalidSliceBeginEnd() public {
         bytes32[] memory data = new bytes32[](4);
         data[0] = "a";