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578 lines
23 KiB
578 lines
23 KiB
// SPDX-License-Identifier: MIT
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// This file was procedurally generated from scripts/generate/templates/Heap.js.
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pragma solidity ^0.8.20;
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import {Math} from "../math/Math.sol";
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import {SafeCast} from "../math/SafeCast.sol";
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import {Comparators} from "../Comparators.sol";
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import {Panic} from "../Panic.sol";
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/**
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* @dev Library for managing https://en.wikipedia.org/wiki/Binary_heap[binary heap] that can be used as
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* https://en.wikipedia.org/wiki/Priority_queue[priority queue].
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*
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* Heaps are represented as an array of Node objects. This array stores two overlapping structures:
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* * A tree structure where the first element (index 0) is the root, and where the node at index i is the child of the
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* node at index (i-1)/2 and the father of nodes at index 2*i+1 and 2*i+2. Each node stores the index (in the array)
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* where the corresponding value is stored.
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* * A list of payloads values where each index contains a value and a lookup index. The type of the value depends on
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* the variant being used. The lookup is the index of the node (in the tree) that points to this value.
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*
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* Some invariants:
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* ```
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* i == heap.data[heap.data[i].index].lookup // for all indices i
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* i == heap.data[heap.data[i].lookup].index // for all indices i
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* ```
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*
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* The structure is ordered so that each node is bigger than its parent. An immediate consequence is that the
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* highest priority value is the one at the root. This value can be looked up in constant time (O(1)) at
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* `heap.data[heap.data[0].index].value`
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*
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* The structure is designed to perform the following operations with the corresponding complexities:
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*
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* * peek (get the highest priority value): O(1)
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* * insert (insert a value): O(log(n))
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* * pop (remove the highest priority value): O(log(n))
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* * replace (replace the highest priority value with a new value): O(log(n))
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* * length (get the number of elements): O(1)
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* * clear (remove all elements): O(1)
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*/
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library Heap {
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using Math for *;
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using SafeCast for *;
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/**
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* @dev Binary heap that support values of type uint256.
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*
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* Each element of that structure uses 2 storage slots.
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*/
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struct Uint256Heap {
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Uint256HeapNode[] data;
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}
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/**
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* @dev Internal node type for Uint256Heap. Stores a value of type uint256.
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*/
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struct Uint256HeapNode {
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uint256 value;
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uint64 index; // position -> value
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uint64 lookup; // value -> position
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}
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/**
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* @dev Lookup the root element of the heap.
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*/
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function peek(Uint256Heap storage self) internal view returns (uint256) {
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// self.data[0] will `ARRAY_ACCESS_OUT_OF_BOUNDS` panic if heap is empty.
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return _unsafeNodeAccess(self, self.data[0].index).value;
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}
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/**
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* @dev Remove (and return) the root element for the heap using the default comparator.
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*
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* NOTE: All inserting and removal from a heap should always be done using the same comparator. Mixing comparator
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* during the lifecycle of a heap will result in undefined behavior.
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*/
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function pop(Uint256Heap storage self) internal returns (uint256) {
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return pop(self, Comparators.lt);
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}
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/**
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* @dev Remove (and return) the root element for the heap using the provided comparator.
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*
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* NOTE: All inserting and removal from a heap should always be done using the same comparator. Mixing comparator
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* during the lifecycle of a heap will result in undefined behavior.
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*/
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function pop(
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Uint256Heap storage self,
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function(uint256, uint256) view returns (bool) comp
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) internal returns (uint256) {
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unchecked {
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uint64 size = length(self);
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if (size == 0) Panic.panic(Panic.EMPTY_ARRAY_POP);
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uint64 last = size - 1;
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// get root location (in the data array) and value
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Uint256HeapNode storage rootNode = _unsafeNodeAccess(self, 0);
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uint64 rootIdx = rootNode.index;
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Uint256HeapNode storage rootData = _unsafeNodeAccess(self, rootIdx);
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Uint256HeapNode storage lastNode = _unsafeNodeAccess(self, last);
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uint256 rootDataValue = rootData.value;
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// if root is not the last element of the data array (that will get popped), reorder the data array.
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if (rootIdx != last) {
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// get details about the value stored in the last element of the array (that will get popped)
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uint64 lastDataIdx = lastNode.lookup;
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uint256 lastDataValue = lastNode.value;
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// copy these values to the location of the root (that is safe, and that we no longer use)
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rootData.value = lastDataValue;
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rootData.lookup = lastDataIdx;
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// update the tree node that used to point to that last element (value now located where the root was)
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_unsafeNodeAccess(self, lastDataIdx).index = rootIdx;
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}
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// get last leaf location (in the data array) and value
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uint64 lastIdx = lastNode.index;
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uint256 lastValue = _unsafeNodeAccess(self, lastIdx).value;
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// move the last leaf to the root, pop last leaf ...
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rootNode.index = lastIdx;
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_unsafeNodeAccess(self, lastIdx).lookup = 0;
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self.data.pop();
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// ... and heapify
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_siftDown(self, last, 0, lastValue, comp);
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// return root value
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return rootDataValue;
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}
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}
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/**
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* @dev Insert a new element in the heap using the default comparator.
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*
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* NOTE: All inserting and removal from a heap should always be done using the same comparator. Mixing comparator
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* during the lifecycle of a heap will result in undefined behavior.
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*/
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function insert(Uint256Heap storage self, uint256 value) internal {
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insert(self, value, Comparators.lt);
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}
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/**
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* @dev Insert a new element in the heap using the provided comparator.
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*
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* NOTE: All inserting and removal from a heap should always be done using the same comparator. Mixing comparator
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* during the lifecycle of a heap will result in undefined behavior.
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*/
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function insert(
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Uint256Heap storage self,
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uint256 value,
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function(uint256, uint256) view returns (bool) comp
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) internal {
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uint64 size = length(self);
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if (size == type(uint64).max) Panic.panic(Panic.RESOURCE_ERROR);
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self.data.push(Uint256HeapNode({index: size, lookup: size, value: value}));
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_siftUp(self, size, value, comp);
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}
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/**
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* @dev Return the root element for the heap, and replace it with a new value, using the default comparator.
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* This is equivalent to using {pop} and {insert}, but requires only one rebalancing operation.
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*
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* NOTE: All inserting and removal from a heap should always be done using the same comparator. Mixing comparator
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* during the lifecycle of a heap will result in undefined behavior.
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*/
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function replace(Uint256Heap storage self, uint256 newValue) internal returns (uint256) {
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return replace(self, newValue, Comparators.lt);
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}
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/**
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* @dev Return the root element for the heap, and replace it with a new value, using the provided comparator.
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* This is equivalent to using {pop} and {insert}, but requires only one rebalancing operation.
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*
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* NOTE: All inserting and removal from a heap should always be done using the same comparator. Mixing comparator
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* during the lifecycle of a heap will result in undefined behavior.
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*/
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function replace(
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Uint256Heap storage self,
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uint256 newValue,
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function(uint256, uint256) view returns (bool) comp
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) internal returns (uint256) {
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uint64 size = length(self);
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if (size == 0) Panic.panic(Panic.EMPTY_ARRAY_POP);
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// position of the node that holds the data for the root
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uint64 rootIdx = _unsafeNodeAccess(self, 0).index;
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// storage pointer to the node that holds the data for the root
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Uint256HeapNode storage rootData = _unsafeNodeAccess(self, rootIdx);
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// cache old value and replace it
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uint256 oldValue = rootData.value;
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rootData.value = newValue;
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// re-heapify
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_siftDown(self, size, 0, newValue, comp);
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// return old root value
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return oldValue;
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}
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/**
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* @dev Returns the number of elements in the heap.
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*/
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function length(Uint256Heap storage self) internal view returns (uint64) {
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return self.data.length.toUint64();
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}
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/**
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* @dev Removes all elements in the heap.
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*/
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function clear(Uint256Heap storage self) internal {
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Uint256HeapNode[] storage data = self.data;
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/// @solidity memory-safe-assembly
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assembly {
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sstore(data.slot, 0)
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}
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}
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/**
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* @dev Swap node `i` and `j` in the tree.
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*/
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function _swap(Uint256Heap storage self, uint64 i, uint64 j) private {
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Uint256HeapNode storage ni = _unsafeNodeAccess(self, i);
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Uint256HeapNode storage nj = _unsafeNodeAccess(self, j);
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uint64 ii = ni.index;
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uint64 jj = nj.index;
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// update pointers to the data (swap the value)
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ni.index = jj;
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nj.index = ii;
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// update lookup pointers for consistency
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_unsafeNodeAccess(self, ii).lookup = j;
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_unsafeNodeAccess(self, jj).lookup = i;
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}
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/**
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* @dev Perform heap maintenance on `self`, starting at position `pos` (with the `value`), using `comp` as a
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* comparator, and moving toward the leafs of the underlying tree.
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*
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* NOTE: This is a private function that is called in a trusted context with already cached parameters. `length`
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* and `value` could be extracted from `self` and `pos`, but that would require redundant storage read. These
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* parameters are not verified. It is the caller role to make sure the parameters are correct.
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*/
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function _siftDown(
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Uint256Heap storage self,
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uint64 size,
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uint64 pos,
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uint256 value,
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function(uint256, uint256) view returns (bool) comp
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) private {
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uint256 left = 2 * pos + 1; // this could overflow uint64
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uint256 right = 2 * pos + 2; // this could overflow uint64
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if (right < size) {
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// the check guarantees that `left` and `right` are both valid uint64
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uint64 lIndex = uint64(left);
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uint64 rIndex = uint64(right);
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uint256 lValue = _unsafeNodeAccess(self, _unsafeNodeAccess(self, lIndex).index).value;
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uint256 rValue = _unsafeNodeAccess(self, _unsafeNodeAccess(self, rIndex).index).value;
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if (comp(lValue, value) || comp(rValue, value)) {
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uint64 index = uint64(comp(lValue, rValue).ternary(lIndex, rIndex));
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_swap(self, pos, index);
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_siftDown(self, size, index, value, comp);
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}
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} else if (left < size) {
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// the check guarantees that `left` is a valid uint64
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uint64 lIndex = uint64(left);
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uint256 lValue = _unsafeNodeAccess(self, _unsafeNodeAccess(self, lIndex).index).value;
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if (comp(lValue, value)) {
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_swap(self, pos, lIndex);
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_siftDown(self, size, lIndex, value, comp);
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}
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}
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}
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/**
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* @dev Perform heap maintenance on `self`, starting at position `pos` (with the `value`), using `comp` as a
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* comparator, and moving toward the root of the underlying tree.
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*
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* NOTE: This is a private function that is called in a trusted context with already cached parameters. `value`
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* could be extracted from `self` and `pos`, but that would require redundant storage read. These parameters are not
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* verified. It is the caller role to make sure the parameters are correct.
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*/
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function _siftUp(
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Uint256Heap storage self,
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uint64 pos,
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uint256 value,
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function(uint256, uint256) view returns (bool) comp
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) private {
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unchecked {
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while (pos > 0) {
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uint64 parent = (pos - 1) / 2;
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uint256 parentValue = _unsafeNodeAccess(self, _unsafeNodeAccess(self, parent).index).value;
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if (comp(parentValue, value)) break;
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_swap(self, pos, parent);
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pos = parent;
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}
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}
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}
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function _unsafeNodeAccess(
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Uint256Heap storage self,
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uint64 pos
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) private pure returns (Uint256HeapNode storage result) {
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assembly ("memory-safe") {
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mstore(0x00, self.slot)
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result.slot := add(keccak256(0x00, 0x20), mul(pos, 2))
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}
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}
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/**
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* @dev Binary heap that support values of type uint208.
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*
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* Each element of that structure uses 1 storage slots.
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*/
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struct Uint208Heap {
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Uint208HeapNode[] data;
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}
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/**
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* @dev Internal node type for Uint208Heap. Stores a value of type uint208.
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*/
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struct Uint208HeapNode {
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uint208 value;
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uint24 index; // position -> value
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uint24 lookup; // value -> position
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}
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/**
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* @dev Lookup the root element of the heap.
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*/
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function peek(Uint208Heap storage self) internal view returns (uint208) {
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// self.data[0] will `ARRAY_ACCESS_OUT_OF_BOUNDS` panic if heap is empty.
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return _unsafeNodeAccess(self, self.data[0].index).value;
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}
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/**
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* @dev Remove (and return) the root element for the heap using the default comparator.
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*
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* NOTE: All inserting and removal from a heap should always be done using the same comparator. Mixing comparator
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* during the lifecycle of a heap will result in undefined behavior.
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*/
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function pop(Uint208Heap storage self) internal returns (uint208) {
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return pop(self, Comparators.lt);
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}
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/**
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* @dev Remove (and return) the root element for the heap using the provided comparator.
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*
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* NOTE: All inserting and removal from a heap should always be done using the same comparator. Mixing comparator
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* during the lifecycle of a heap will result in undefined behavior.
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*/
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function pop(
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Uint208Heap storage self,
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function(uint256, uint256) view returns (bool) comp
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) internal returns (uint208) {
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unchecked {
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uint24 size = length(self);
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if (size == 0) Panic.panic(Panic.EMPTY_ARRAY_POP);
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uint24 last = size - 1;
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// get root location (in the data array) and value
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Uint208HeapNode storage rootNode = _unsafeNodeAccess(self, 0);
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uint24 rootIdx = rootNode.index;
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Uint208HeapNode storage rootData = _unsafeNodeAccess(self, rootIdx);
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Uint208HeapNode storage lastNode = _unsafeNodeAccess(self, last);
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uint208 rootDataValue = rootData.value;
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// if root is not the last element of the data array (that will get popped), reorder the data array.
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if (rootIdx != last) {
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// get details about the value stored in the last element of the array (that will get popped)
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uint24 lastDataIdx = lastNode.lookup;
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uint208 lastDataValue = lastNode.value;
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// copy these values to the location of the root (that is safe, and that we no longer use)
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rootData.value = lastDataValue;
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rootData.lookup = lastDataIdx;
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// update the tree node that used to point to that last element (value now located where the root was)
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_unsafeNodeAccess(self, lastDataIdx).index = rootIdx;
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}
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// get last leaf location (in the data array) and value
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uint24 lastIdx = lastNode.index;
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uint208 lastValue = _unsafeNodeAccess(self, lastIdx).value;
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// move the last leaf to the root, pop last leaf ...
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rootNode.index = lastIdx;
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_unsafeNodeAccess(self, lastIdx).lookup = 0;
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self.data.pop();
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// ... and heapify
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_siftDown(self, last, 0, lastValue, comp);
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// return root value
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return rootDataValue;
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}
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}
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/**
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* @dev Insert a new element in the heap using the default comparator.
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*
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* NOTE: All inserting and removal from a heap should always be done using the same comparator. Mixing comparator
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* during the lifecycle of a heap will result in undefined behavior.
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*/
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function insert(Uint208Heap storage self, uint208 value) internal {
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insert(self, value, Comparators.lt);
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}
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/**
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* @dev Insert a new element in the heap using the provided comparator.
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*
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* NOTE: All inserting and removal from a heap should always be done using the same comparator. Mixing comparator
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* during the lifecycle of a heap will result in undefined behavior.
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*/
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function insert(
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Uint208Heap storage self,
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uint208 value,
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function(uint256, uint256) view returns (bool) comp
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) internal {
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uint24 size = length(self);
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if (size == type(uint24).max) Panic.panic(Panic.RESOURCE_ERROR);
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self.data.push(Uint208HeapNode({index: size, lookup: size, value: value}));
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_siftUp(self, size, value, comp);
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}
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/**
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* @dev Return the root element for the heap, and replace it with a new value, using the default comparator.
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* This is equivalent to using {pop} and {insert}, but requires only one rebalancing operation.
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*
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* NOTE: All inserting and removal from a heap should always be done using the same comparator. Mixing comparator
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* during the lifecycle of a heap will result in undefined behavior.
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*/
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function replace(Uint208Heap storage self, uint208 newValue) internal returns (uint208) {
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return replace(self, newValue, Comparators.lt);
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}
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/**
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* @dev Return the root element for the heap, and replace it with a new value, using the provided comparator.
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* This is equivalent to using {pop} and {insert}, but requires only one rebalancing operation.
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*
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* NOTE: All inserting and removal from a heap should always be done using the same comparator. Mixing comparator
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* during the lifecycle of a heap will result in undefined behavior.
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*/
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function replace(
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Uint208Heap storage self,
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uint208 newValue,
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function(uint256, uint256) view returns (bool) comp
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) internal returns (uint208) {
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uint24 size = length(self);
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if (size == 0) Panic.panic(Panic.EMPTY_ARRAY_POP);
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// position of the node that holds the data for the root
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uint24 rootIdx = _unsafeNodeAccess(self, 0).index;
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// storage pointer to the node that holds the data for the root
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Uint208HeapNode storage rootData = _unsafeNodeAccess(self, rootIdx);
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// cache old value and replace it
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uint208 oldValue = rootData.value;
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rootData.value = newValue;
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// re-heapify
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_siftDown(self, size, 0, newValue, comp);
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// return old root value
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return oldValue;
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}
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/**
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* @dev Returns the number of elements in the heap.
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*/
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function length(Uint208Heap storage self) internal view returns (uint24) {
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return self.data.length.toUint24();
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}
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/**
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* @dev Removes all elements in the heap.
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*/
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function clear(Uint208Heap storage self) internal {
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Uint208HeapNode[] storage data = self.data;
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/// @solidity memory-safe-assembly
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|
assembly {
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sstore(data.slot, 0)
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|
}
|
|
}
|
|
|
|
/**
|
|
* @dev Swap node `i` and `j` in the tree.
|
|
*/
|
|
function _swap(Uint208Heap storage self, uint24 i, uint24 j) private {
|
|
Uint208HeapNode storage ni = _unsafeNodeAccess(self, i);
|
|
Uint208HeapNode storage nj = _unsafeNodeAccess(self, j);
|
|
uint24 ii = ni.index;
|
|
uint24 jj = nj.index;
|
|
// update pointers to the data (swap the value)
|
|
ni.index = jj;
|
|
nj.index = ii;
|
|
// update lookup pointers for consistency
|
|
_unsafeNodeAccess(self, ii).lookup = j;
|
|
_unsafeNodeAccess(self, jj).lookup = i;
|
|
}
|
|
|
|
/**
|
|
* @dev Perform heap maintenance on `self`, starting at position `pos` (with the `value`), using `comp` as a
|
|
* comparator, and moving toward the leafs of the underlying tree.
|
|
*
|
|
* NOTE: This is a private function that is called in a trusted context with already cached parameters. `length`
|
|
* and `value` could be extracted from `self` and `pos`, but that would require redundant storage read. These
|
|
* parameters are not verified. It is the caller role to make sure the parameters are correct.
|
|
*/
|
|
function _siftDown(
|
|
Uint208Heap storage self,
|
|
uint24 size,
|
|
uint24 pos,
|
|
uint208 value,
|
|
function(uint256, uint256) view returns (bool) comp
|
|
) private {
|
|
uint256 left = 2 * pos + 1; // this could overflow uint24
|
|
uint256 right = 2 * pos + 2; // this could overflow uint24
|
|
|
|
if (right < size) {
|
|
// the check guarantees that `left` and `right` are both valid uint24
|
|
uint24 lIndex = uint24(left);
|
|
uint24 rIndex = uint24(right);
|
|
uint208 lValue = _unsafeNodeAccess(self, _unsafeNodeAccess(self, lIndex).index).value;
|
|
uint208 rValue = _unsafeNodeAccess(self, _unsafeNodeAccess(self, rIndex).index).value;
|
|
if (comp(lValue, value) || comp(rValue, value)) {
|
|
uint24 index = uint24(comp(lValue, rValue).ternary(lIndex, rIndex));
|
|
_swap(self, pos, index);
|
|
_siftDown(self, size, index, value, comp);
|
|
}
|
|
} else if (left < size) {
|
|
// the check guarantees that `left` is a valid uint24
|
|
uint24 lIndex = uint24(left);
|
|
uint208 lValue = _unsafeNodeAccess(self, _unsafeNodeAccess(self, lIndex).index).value;
|
|
if (comp(lValue, value)) {
|
|
_swap(self, pos, lIndex);
|
|
_siftDown(self, size, lIndex, value, comp);
|
|
}
|
|
}
|
|
}
|
|
|
|
/**
|
|
* @dev Perform heap maintenance on `self`, starting at position `pos` (with the `value`), using `comp` as a
|
|
* comparator, and moving toward the root of the underlying tree.
|
|
*
|
|
* NOTE: This is a private function that is called in a trusted context with already cached parameters. `value`
|
|
* could be extracted from `self` and `pos`, but that would require redundant storage read. These parameters are not
|
|
* verified. It is the caller role to make sure the parameters are correct.
|
|
*/
|
|
function _siftUp(
|
|
Uint208Heap storage self,
|
|
uint24 pos,
|
|
uint208 value,
|
|
function(uint256, uint256) view returns (bool) comp
|
|
) private {
|
|
unchecked {
|
|
while (pos > 0) {
|
|
uint24 parent = (pos - 1) / 2;
|
|
uint208 parentValue = _unsafeNodeAccess(self, _unsafeNodeAccess(self, parent).index).value;
|
|
if (comp(parentValue, value)) break;
|
|
_swap(self, pos, parent);
|
|
pos = parent;
|
|
}
|
|
}
|
|
}
|
|
|
|
function _unsafeNodeAccess(
|
|
Uint208Heap storage self,
|
|
uint24 pos
|
|
) private pure returns (Uint208HeapNode storage result) {
|
|
assembly ("memory-safe") {
|
|
mstore(0x00, self.slot)
|
|
result.slot := add(keccak256(0x00, 0x20), pos)
|
|
}
|
|
}
|
|
}
|
|
|