diff --git a/contracts/utils/structs/MaxHeap.sol b/contracts/utils/structs/MaxHeap.sol
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+++ b/contracts/utils/structs/MaxHeap.sol
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+// SPDX-License-Identifier: MIT
+
+pragma solidity ^0.8.20;
+
+/**
+ *  TODO:
+ *  - optimizations
+ *  - changeset
+ *  - add tests
+ *  - add docs
+ *  - add base impl link here
+ *
+ * @dev Library for managing a max heap data structure.
+ *
+ * A max heap is a complete binary tree where each node has a value greater than or equal to its children.
+ * The root node contains the maximum value in the heap.
+ *
+ * This library provides functions to insert, update, and remove elements from the max heap, as well as to
+ * retrieve the maximum element (peek) and check the validity of the heap.
+ *
+ * The max heap has the following properties:
+ *
+ * - Insertion: O(log n)
+ * - Deletion of maximum element: O(log n)
+ * - Retrieval of maximum element (peek): O(1)
+ * - Update of an element: O(log n)
+ *
+ * The max heap is implemented using two mappings:
+ * - `tree`: Maps the position in the heap to the item ID.
+ * - `items`: Maps the item ID to its corresponding `Node` struct, which contains the value and heap index.
+ *
+ * Example usage:
+ *
+ * ```solidity
+ * contract Example {
+ *     using MaxHeap for MaxHeap.MaxHeap;
+ *
+ *     MaxHeap.MaxHeap private heap;
+ *
+ *     function addItem(uint256 itemId, uint256 value) public {
+ *         heap.insert(itemId, value);
+ *     }
+ *
+ *     function removeMax() public returns (uint256, uint256) {
+ *         return heap.pop();
+ *     }
+ *
+ *     function getMax() public view returns (uint256, uint256) {
+ *         return heap.peek();
+ *     }
+ * }
+ * ```
+ */
+library MaxHeap {
+    /**
+     * @dev The position doesn't have a _parent as it's the root.
+     */
+    error InvalidPositionZero();
+
+    struct Node {
+        uint256 value;
+        uint256 heapIndex;
+    }
+
+    struct MaxHeap {
+        mapping(uint256 => uint256) tree;
+        mapping(uint256 => Node) items;
+        uint256 size;
+    }
+
+    function _parent(uint256 pos) private pure returns (uint256) {
+        if (pos == 0) revert InvalidPositionZero();
+        return (pos - 1) / 2;
+    }
+
+    function _swap(MaxHeap storage heap, uint256 fpos, uint256 spos) private {
+        (heap.tree[fpos], heap.tree[spos]) = (heap.tree[spos], heap.tree[fpos]);
+        (heap.items[heap.tree[fpos]].heapIndex, heap.items[heap.tree[spos]].heapIndex) = (fpos, spos);
+    }
+
+    function heapify(MaxHeap storage heap, uint256 pos) internal {
+        if (pos >= (heap.size / 2) && pos <= heap.size) return;
+
+        uint256 left = 2 * pos + 1;
+        uint256 right = left + 1;
+
+        uint256 leftValue = left < heap.size ? heap.items[heap.tree[left]].value : 0;
+        uint256 rightValue = right < heap.size ? heap.items[heap.tree[right]].value : 0;
+        uint256 posValue = heap.items[heap.tree[pos]].value;
+
+        if (posValue < leftValue || posValue < rightValue) {
+            if (leftValue > rightValue) {
+                _swap(heap, pos, left);
+                heapify(heap, left);
+            } else {
+                _swap(heap, pos, right);
+                heapify(heap, right);
+            }
+        }
+    }
+
+    function insert(MaxHeap storage heap, uint256 itemId, uint256 value) internal {
+        heap.tree[heap.size] = itemId;
+        heap.items[itemId] = Node({value: value, heapIndex: heap.size});
+
+        uint256 current = heap.size;
+        uint256 parentOfCurrent = _parent(current);
+
+        while (current != 0 && heap.items[heap.tree[current]].value > heap.items[heap.tree[parentOfCurrent]].value) {
+            uint256 parentOfCurrent = _parent(current);
+            _swap(heap, current, parentOfCurrent);
+            current = parentOfCurrent;
+            parentOfCurrent = _parent(current);
+        }
+        heap.size++;
+    }
+
+    function update(MaxHeap storage heap, uint256 itemId, uint256 newValue) internal {
+        // Check that itemId exists in heap
+        // TODO: update return with revert?
+        if (heap.items[itemId].heapIndex >= heap.size) return;
+
+        uint256 position = heap.items[itemId].heapIndex;
+        uint256 oldValue = heap.items[itemId].value;
+
+        heap.items[itemId].value = newValue;
+
+        if (newValue > oldValue) {
+            while (
+                position != 0 && heap.items[heap.tree[position]].value > heap.items[heap.tree[_parent(position)]].value
+            ) {
+                uint256 parentOfPosition = _parent(position);
+                _swap(heap, position, parentOfPosition);
+                position = parentOfPosition;
+            }
+        } else heapify(heap, position);
+    }
+
+    function pop(MaxHeap storage heap) internal returns (uint256, uint256) {
+        // TODO: should it revert if empty?
+
+        uint256 popped = heap.tree[0];
+        uint256 returnValue = heap.items[popped].value;
+
+        delete heap.items[popped];
+
+        heap.tree[0] = heap.tree[--heap.size];
+
+        heap.items[heap.tree[0]].heapIndex = 0;
+
+        delete heap.tree[heap.size];
+
+        heapify(heap, 0);
+
+        return (popped, returnValue);
+    }
+
+    function peek(MaxHeap storage heap) internal view returns (uint256, uint256) {
+        // TODO: should it revert if empty?
+        return (heap.tree[0], heap.items[heap.tree[0]].value);
+    }
+}