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328 lines
12 KiB
328 lines
12 KiB
const format = require('../format-lines');
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const { TYPES } = require('./Heap.opts');
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const { capitalize } = require('../../helpers');
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/* eslint-disable max-len */
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const header = `\
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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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`;
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const generate = ({ struct, node, valueType, indexType, blockSize }) => `\
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/**
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* @dev Binary heap that support values of type ${valueType}.
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*
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* Each element of that structure uses ${blockSize} storage slots.
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*/
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struct ${struct} {
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${node}[] data;
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}
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/**
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* @dev Internal node type for ${struct}. Stores a value of type ${valueType}.
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*/
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struct ${node} {
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${valueType} value;
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${indexType} index; // position -> value
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${indexType} 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(${struct} storage self) internal view returns (${valueType}) {
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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(${struct} storage self) internal returns (${valueType}) {
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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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${struct} storage self,
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function(uint256, uint256) view returns (bool) comp
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) internal returns (${valueType}) {
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unchecked {
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${indexType} size = length(self);
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if (size == 0) Panic.panic(Panic.EMPTY_ARRAY_POP);
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${indexType} last = size - 1;
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// get root location (in the data array) and value
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${node} storage rootNode = _unsafeNodeAccess(self, 0);
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${indexType} rootIdx = rootNode.index;
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${node} storage rootData = _unsafeNodeAccess(self, rootIdx);
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${node} storage lastNode = _unsafeNodeAccess(self, last);
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${valueType} rootDataValue = rootData.value;
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// if root is not the last element of the data array (that will get popped), reorder the data array.
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if (rootIdx != last) {
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// get details about the value stored in the last element of the array (that will get popped)
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${indexType} lastDataIdx = lastNode.lookup;
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${valueType} lastDataValue = lastNode.value;
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// copy these values to the location of the root (that is safe, and that we no longer use)
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rootData.value = lastDataValue;
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rootData.lookup = lastDataIdx;
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// update the tree node that used to point to that last element (value now located where the root was)
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_unsafeNodeAccess(self, lastDataIdx).index = rootIdx;
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}
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// get last leaf location (in the data array) and value
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${indexType} lastIdx = lastNode.index;
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${valueType} lastValue = _unsafeNodeAccess(self, lastIdx).value;
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// move the last leaf to the root, pop last leaf ...
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rootNode.index = lastIdx;
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_unsafeNodeAccess(self, lastIdx).lookup = 0;
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self.data.pop();
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// ... and heapify
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_siftDown(self, last, 0, lastValue, comp);
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// return root value
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return rootDataValue;
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}
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}
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/**
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* @dev Insert a new element in the heap using the default comparator.
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*
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* NOTE: All inserting and removal from a heap should always be done using the same comparator. Mixing comparator
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* during the lifecycle of a heap will result in undefined behavior.
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*/
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function insert(${struct} storage self, ${valueType} value) internal {
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insert(self, value, Comparators.lt);
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}
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/**
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* @dev Insert a new element in the heap using the provided comparator.
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*
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* NOTE: All inserting and removal from a heap should always be done using the same comparator. Mixing comparator
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* during the lifecycle of a heap will result in undefined behavior.
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*/
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function insert(
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${struct} storage self,
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${valueType} value,
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function(uint256, uint256) view returns (bool) comp
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) internal {
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${indexType} size = length(self);
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if (size == type(${indexType}).max) Panic.panic(Panic.RESOURCE_ERROR);
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self.data.push(${struct}Node({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(${struct} storage self, ${valueType} newValue) internal returns (${valueType}) {
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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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${struct} storage self,
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${valueType} newValue,
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function(uint256, uint256) view returns (bool) comp
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) internal returns (${valueType}) {
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${indexType} 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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${indexType} rootIdx = _unsafeNodeAccess(self, 0).index;
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// storage pointer to the node that holds the data for the root
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${node} storage rootData = _unsafeNodeAccess(self, rootIdx);
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// cache old value and replace it
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${valueType} oldValue = rootData.value;
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rootData.value = newValue;
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// re-heapify
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_siftDown(self, size, 0, newValue, comp);
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// return old root value
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return oldValue;
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}
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/**
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* @dev Returns the number of elements in the heap.
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*/
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function length(${struct} storage self) internal view returns (${indexType}) {
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return self.data.length.to${capitalize(indexType)}();
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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(${struct} storage self) internal {
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${struct}Node[] 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(${struct} storage self, ${indexType} i, ${indexType} j) private {
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${node} storage ni = _unsafeNodeAccess(self, i);
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${node} storage nj = _unsafeNodeAccess(self, j);
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${indexType} ii = ni.index;
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${indexType} jj = nj.index;
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// update pointers to the data (swap the value)
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ni.index = jj;
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nj.index = ii;
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// update lookup pointers for consistency
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_unsafeNodeAccess(self, ii).lookup = j;
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_unsafeNodeAccess(self, jj).lookup = i;
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}
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/**
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* @dev Perform heap maintenance on \`self\`, starting at position \`pos\` (with the \`value\`), using \`comp\` as a
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* comparator, and moving toward the leafs of the underlying tree.
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*
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* NOTE: This is a private function that is called in a trusted context with already cached parameters. \`length\`
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* and \`value\` could be extracted from \`self\` and \`pos\`, but that would require redundant storage read. These
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* parameters are not verified. It is the caller role to make sure the parameters are correct.
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*/
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function _siftDown(
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${struct} storage self,
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${indexType} size,
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${indexType} pos,
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${valueType} 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 ${indexType}
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uint256 right = 2 * pos + 2; // this could overflow ${indexType}
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if (right < size) {
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// the check guarantees that \`left\` and \`right\` are both valid ${indexType}
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${indexType} lIndex = ${indexType}(left);
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${indexType} rIndex = ${indexType}(right);
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${valueType} lValue = _unsafeNodeAccess(self, _unsafeNodeAccess(self, lIndex).index).value;
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${valueType} rValue = _unsafeNodeAccess(self, _unsafeNodeAccess(self, rIndex).index).value;
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if (comp(lValue, value) || comp(rValue, value)) {
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${indexType} index = ${indexType}(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 ${indexType}
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${indexType} lIndex = ${indexType}(left);
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${valueType} 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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${struct} storage self,
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${indexType} pos,
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${valueType} value,
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function(uint256, uint256) view returns (bool) comp
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) private {
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unchecked {
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while (pos > 0) {
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${indexType} parent = (pos - 1) / 2;
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${valueType} parentValue = _unsafeNodeAccess(self, _unsafeNodeAccess(self, parent).index).value;
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if (comp(parentValue, value)) break;
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_swap(self, pos, parent);
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pos = parent;
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}
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}
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}
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function _unsafeNodeAccess(
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${struct} storage self,
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${indexType} pos
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) private pure returns (${node} 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), ${blockSize == 1 ? 'pos' : `mul(pos, ${blockSize})`})
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}
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}
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`;
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// GENERATE
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module.exports = format(
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header.trimEnd(),
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'library Heap {',
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format(
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[].concat(
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'using Math for *;',
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'using SafeCast for *;',
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'',
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TYPES.map(type => generate(type)),
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),
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).trimEnd(),
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'}',
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);
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