Min Heap API

Author:

Kuan-Wei Chiu <visitorckw@gmail.com>

Introduction

The Min Heap API provides a set of functions and macros for managing min-heapsin the Linux kernel. A min-heap is a binary tree structure where the value ofeach node is less than or equal to the values of its children, ensuring thatthe smallest element is always at the root.

This document provides a guide to the Min Heap API, detailing how to define anduse min-heaps. Users should not directly call functions with__min_heap_*()prefixes, but should instead use the provided macro wrappers.

In addition to the standard version of the functions, the API also includes aset of inline versions for performance-critical scenarios. These inlinefunctions have the same names as their non-inline counterparts but include an_inline suffix. For example,__min_heap_init_inline and itscorresponding macro wrappermin_heap_init_inline. The inline versions allowcustom comparison and swap functions to be called directly, rather than throughindirect function calls. This can significantly reduce overhead, especiallywhen CONFIG_MITIGATION_RETPOLINE is enabled, as indirect function calls becomemore expensive. As with the non-inline versions, it is important to use themacro wrappers for inline functions instead of directly calling the functionsthemselves.

Data Structures

Min-Heap Definition

The core data structure for representing a min-heap is defined using theMIN_HEAP_PREALLOCATED andDEFINE_MIN_HEAP macros. These macros allowyou to define a min-heap with a preallocated buffer or dynamically allocatedmemory.

Example:

#define MIN_HEAP_PREALLOCATED(_type, _name, _nr)struct_name{size_tnr;/* Number of elements in the heap */size_tsize;/* Maximum number of elements that can be held */_type*data;/* Pointer to the heap data */_typepreallocated[_nr];/* Static preallocated array */}#define DEFINE_MIN_HEAP(_type, _name) MIN_HEAP_PREALLOCATED(_type, _name, 0)

A typical heap structure will include a counter for the number of elements(nr), the maximum capacity of the heap (size), and a pointer to an array ofelements (data). Optionally, you can specify a static array for preallocatedheap storage usingMIN_HEAP_PREALLOCATED.

Min Heap Callbacks

Thestructmin_heap_callbacks provides customization options for orderingelements in the heap and swapping them. It contains two function pointers:

structmin_heap_callbacks{bool(*less)(constvoid*lhs,constvoid*rhs,void*args);void(*swp)(void*lhs,void*rhs,void*args);};

  • less is the comparison function used to establish the order of elements.

  • swp is a function for swapping elements in the heap. If swp is set toNULL, the default swap function will be used, which swaps the elements based on their size

Macro Wrappers

The following macro wrappers are provided for interacting with the heap in auser-friendly manner. Each macro corresponds to a function that operates on theheap, and they abstract away direct calls to internal functions.

Each macro accepts various parameters that are detailed below.

Heap Initialization

min_heap_init(heap,data,size);

  • heap: A pointer to the min-heap structure to be initialized.

  • data: A pointer to the buffer where the heap elements will be stored. IfNULL, the preallocated buffer within the heap structure will be used.

  • size: The maximum number of elements the heap can hold.

This macro initializes the heap, setting its initial state. Ifdata isNULL, the preallocated memory inside the heap structure will be used forstorage. Otherwise, the user-provided buffer is used. The operation isO(1).

Inline Version: min_heap_init_inline(heap, data, size)

Accessing the Top Element

element=min_heap_peek(heap);

  • heap: A pointer to the min-heap from which to retrieve the smallestelement.

This macro returns a pointer to the smallest element (the root) of the heap, orNULL if the heap is empty. The operation isO(1).

Inline Version: min_heap_peek_inline(heap)

Heap Insertion

success=min_heap_push(heap,element,callbacks,args);

  • heap: A pointer to the min-heap into which the element should be inserted.

  • element: A pointer to the element to be inserted into the heap.

  • callbacks: A pointer to astructmin_heap_callbacks providing theless andswp functions.

  • args: Optional arguments passed to theless andswp functions.

This macro inserts an element into the heap. It returnstrue if the insertionwas successful andfalse if the heap is full. The operation isO(log n).

Inline Version: min_heap_push_inline(heap, element, callbacks, args)

Heap Removal

success=min_heap_pop(heap,callbacks,args);

  • heap: A pointer to the min-heap from which to remove the smallest element.

  • callbacks: A pointer to astructmin_heap_callbacks providing theless andswp functions.

  • args: Optional arguments passed to theless andswp functions.

This macro removes the smallest element (the root) from the heap. It returnstrue if the element was successfully removed, orfalse if the heap isempty. The operation isO(log n).

Inline Version: min_heap_pop_inline(heap, callbacks, args)

Heap Maintenance

You can use the following macros to maintain the heap’s structure:

min_heap_sift_down(heap,pos,callbacks,args);

  • heap: A pointer to the min-heap.

  • pos: The index from which to start sifting down.

  • callbacks: A pointer to astructmin_heap_callbacks providing theless andswp functions.

  • args: Optional arguments passed to theless andswp functions.

This macro restores the heap property by moving the element at the specifiedindex (pos) down the heap until it is in the correct position. The operationisO(log n).

Inline Version: min_heap_sift_down_inline(heap, pos, callbacks, args)

min_heap_sift_up(heap,idx,callbacks,args);

  • heap: A pointer to the min-heap.

  • idx: The index of the element to sift up.

  • callbacks: A pointer to astructmin_heap_callbacks providing theless andswp functions.

  • args: Optional arguments passed to theless andswp functions.

This macro restores the heap property by moving the element at the specifiedindex (idx) up the heap. The operation isO(log n).

Inline Version: min_heap_sift_up_inline(heap, idx, callbacks, args)

min_heapify_all(heap,callbacks,args);

  • heap: A pointer to the min-heap.

  • callbacks: A pointer to astructmin_heap_callbacks providing theless andswp functions.

  • args: Optional arguments passed to theless andswp functions.

This macro ensures that the entire heap satisfies the heap property. It iscalled when the heap is built from scratch or after many modifications. Theoperation isO(n).

Inline Version: min_heapify_all_inline(heap, callbacks, args)

Removing Specific Elements

success=min_heap_del(heap,idx,callbacks,args);

  • heap: A pointer to the min-heap.

  • idx: The index of the element to delete.

  • callbacks: A pointer to astructmin_heap_callbacks providing theless andswp functions.

  • args: Optional arguments passed to theless andswp functions.

This macro removes an element at the specified index (idx) from the heap andrestores the heap property. The operation isO(log n).

Inline Version: min_heap_del_inline(heap, idx, callbacks, args)

Other Utilities

  • min_heap_full(heap): Checks whether the heap is full.Complexity:O(1).

boolfull=min_heap_full(heap);

  • heap: A pointer to the min-heap to check.

This macro returnstrue if the heap is full, otherwisefalse.

Inline Version: min_heap_full_inline(heap)

  • min_heap_empty(heap): Checks whether the heap is empty.Complexity:O(1).

boolempty=min_heap_empty(heap);

  • heap: A pointer to the min-heap to check.

This macro returnstrue if the heap is empty, otherwisefalse.

Inline Version: min_heap_empty_inline(heap)

Example Usage

An example usage of the min-heap API would involve defining a heap structure,initializing it, and inserting and removing elements as needed.

#include<linux/min_heap.h>intmy_less_function(constvoid*lhs,constvoid*rhs,void*args){return(*(int*)lhs<*(int*)rhs);}structmin_heap_callbacksheap_cb={.less=my_less_function,/* Comparison function for heap order */.swp=NULL,/* Use default swap function */};voidexample_usage(void){/* Pre-populate the buffer with elements */intbuffer[5]={5,2,8,1,3};/* Declare a min-heap */DEFINE_MIN_HEAP(int,my_heap);/* Initialize the heap with preallocated buffer and size */min_heap_init(&my_heap,buffer,5);/* Build the heap using min_heapify_all */my_heap.nr=5;/* Set the number of elements in the heap */min_heapify_all(&my_heap,&heap_cb,NULL);/* Peek at the top element (should be 1 in this case) */int*top=min_heap_peek(&my_heap);pr_info("Top element: %d\n",*top);/* Pop the top element (1) and get the new top (2) */min_heap_pop(&my_heap,&heap_cb,NULL);top=min_heap_peek(&my_heap);pr_info("New top element: %d\n",*top);/* Insert a new element (0) and recheck the top */intnew_element=0;min_heap_push(&my_heap,&new_element,&heap_cb,NULL);top=min_heap_peek(&my_heap);pr_info("Top element after insertion: %d\n",*top);}