summaryrefslogtreecommitdiff
path: root/Documentation/core-api/min_heap.rst
blob: 0c636c8b7aa5813b346fbd168fb0af210f09b770 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
.. SPDX-License-Identifier: GPL-2.0

============
Min Heap API
============

Introduction
============

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

This document provides a guide to the Min Heap API, detailing how to define and
use 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 a
set of inline versions for performance-critical scenarios. These inline
functions have the same names as their non-inline counterparts but include an
**_inline** suffix. For example, **__min_heap_init_inline** and its
corresponding macro wrapper **min_heap_init_inline**. The inline versions allow
custom comparison and swap functions to be called directly, rather than through
indirect function calls. This can significantly reduce overhead, especially
when CONFIG_MITIGATION_RETPOLINE is enabled, as indirect function calls become
more expensive. As with the non-inline versions, it is important to use the
macro wrappers for inline functions instead of directly calling the functions
themselves.

Data Structures
===============

Min-Heap Definition
-------------------

The core data structure for representing a min-heap is defined using the
**MIN_HEAP_PREALLOCATED** and **DEFINE_MIN_HEAP** macros. These macros allow
you to define a min-heap with a preallocated buffer or dynamically allocated
memory.

Example:

.. code-block:: c

    #define MIN_HEAP_PREALLOCATED(_type, _name, _nr)
    struct _name {
        int nr;         /* Number of elements in the heap */
        int size;       /* Maximum number of elements that can be held */
        _type *data;    /* Pointer to the heap data */
        _type preallocated[_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 of
elements (`data`). Optionally, you can specify a static array for preallocated
heap storage using **MIN_HEAP_PREALLOCATED**.

Min Heap Callbacks
------------------

The **struct min_heap_callbacks** provides customization options for ordering
elements in the heap and swapping them. It contains two function pointers:

.. code-block:: c

    struct min_heap_callbacks {
        bool (*less)(const void *lhs, const void *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 to
  NULL, 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 a
user-friendly manner. Each macro corresponds to a function that operates on the
heap, and they abstract away direct calls to internal functions.

Each macro accepts various parameters that are detailed below.

Heap Initialization
--------------------

.. code-block:: c

    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. If
  `NULL`, 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. If `data` is
`NULL`, the preallocated memory inside the heap structure will be used for
storage. Otherwise, the user-provided buffer is used. The operation is **O(1)**.

**Inline Version:** min_heap_init_inline(heap, data, size)

Accessing the Top Element
-------------------------

.. code-block:: c

    element = min_heap_peek(heap);

- **heap**: A pointer to the min-heap from which to retrieve the smallest
  element.

This macro returns a pointer to the smallest element (the root) of the heap, or
`NULL` if the heap is empty. The operation is **O(1)**.

**Inline Version:** min_heap_peek_inline(heap)

Heap Insertion
--------------

.. code-block:: c

    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 a `struct min_heap_callbacks` providing the
  `less` and `swp` functions.
- **args**: Optional arguments passed to the `less` and `swp` functions.

This macro inserts an element into the heap. It returns `true` if the insertion
was successful and `false` if the heap is full. The operation is **O(log n)**.

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

Heap Removal
------------

.. code-block:: c

    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 a `struct min_heap_callbacks` providing the
  `less` and `swp` functions.
- **args**: Optional arguments passed to the `less` and `swp` functions.

This macro removes the smallest element (the root) from the heap. It returns
`true` if the element was successfully removed, or `false` if the heap is
empty. The operation is **O(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:

.. code-block:: c

    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 a `struct min_heap_callbacks` providing the
  `less` and `swp` functions.
- **args**: Optional arguments passed to the `less` and `swp` functions.

This macro restores the heap property by moving the element at the specified
index (`pos`) down the heap until it is in the correct position. The operation
is **O(log n)**.

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

.. code-block:: c

    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 a `struct min_heap_callbacks` providing the
  `less` and `swp` functions.
- **args**: Optional arguments passed to the `less` and `swp` functions.

This macro restores the heap property by moving the element at the specified
index (`idx`) up the heap. The operation is **O(log n)**.

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

.. code-block:: c

    min_heapify_all(heap, callbacks, args);

- **heap**: A pointer to the min-heap.
- **callbacks**: A pointer to a `struct min_heap_callbacks` providing the
  `less` and `swp` functions.
- **args**: Optional arguments passed to the `less` and `swp` functions.

This macro ensures that the entire heap satisfies the heap property. It is
called when the heap is built from scratch or after many modifications. The
operation is **O(n)**.

**Inline Version:** min_heapify_all_inline(heap, callbacks, args)

Removing Specific Elements
--------------------------

.. code-block:: c

    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 a `struct min_heap_callbacks` providing the
  `less` and `swp` functions.
- **args**: Optional arguments passed to the `less` and `swp` functions.

This macro removes an element at the specified index (`idx`) from the heap and
restores the heap property. The operation is **O(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)**.

.. code-block:: c

    bool full = min_heap_full(heap);

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

This macro returns `true` if the heap is full, otherwise `false`.

**Inline Version:** min_heap_full_inline(heap)

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

.. code-block:: c

    bool empty = min_heap_empty(heap);

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

This macro returns `true` if the heap is empty, otherwise `false`.

**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.

.. code-block:: c

    #include <linux/min_heap.h>

    int my_less_function(const void *lhs, const void *rhs, void *args) {
        return (*(int *)lhs < *(int *)rhs);
    }

    struct min_heap_callbacks heap_cb = {
        .less = my_less_function,    /* Comparison function for heap order */
        .swp  = NULL,                /* Use default swap function */
    };

    void example_usage(void) {
        /* Pre-populate the buffer with elements */
        int buffer[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 */
        int new_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);
    }