引言 - 資料結構堆

　　堆結構都很耳熟, 從堆排序到優先順序佇列, 我們總會看見它的身影. 相關的資料太多了,

堆 - https://zh.wikipedia.org/wiki/%E5%A0%86%E7%A9%8D

無數漂亮的圖片接二連三, 但目前沒搜到一個工程中可以舒服用的程式碼庫. 本文由此痛點而來.

寫一篇奇妙資料結構堆的終結程式碼. 耳熟終究比不過手熱 ->---

對於 heap 介面思考, 我是這樣設計

#ifndef _H_HEAP
#define _H_HEAP

//
// cmp_f - 比較行為 > 0 or = 0  or < 0
// : int add_cmp(const void * now, const void * node)
 
//
typedef int (* cmp_f)();

//
// node_f - 銷燬行為
// : void list_die(void * node)
//
typedef void (* node_f)(void * node);

//
// head_t 堆的型別結構
//
typedef struct heap * heap_t;

//
// heap_create - 建立符合規則的堆
// fcmp     : 比較行為, 規則 fcmp() <= 0
// return   : 返回建立好的堆物件
//
extern heap_t heap_create(cmp_f fcmp);

 
//
// heap_delete - 銷燬堆
// h        : 堆物件
// fdie     : 銷燬行為, 預設 NULL
// return   : void
//
extern void heap_delete(heap_t h, node_f fdie);

//
// heap_insert - 堆插入資料
// h        : 堆物件
// node     : 操作物件
// return   : void
//
extern void heap_insert(heap_t h, void * node);

//
// heap_remove - 堆刪除資料
// h        : 堆物件
 
// arg      : 操作引數
// fcmp     : 比較行為, 規則 fcmp() == 0
// return   : 找到的堆節點
//
extern void * heap_remove(heap_t h, void * arg, cmp_f fcmp);

//
// heap_top - 檢視堆頂結點資料
// h        : 堆物件
// return   : 堆頂節點
//
extern void * heap_top(heap_t h);

//
// heap_top - 摘掉堆頂結點資料
// h        : 堆物件
// return   : 返回堆頂節點
//
extern void * heap_pop(heap_t h);

#endif//_H_HEAP

heap_t 是不完全型別實體指標, 其中 struct heap 是這樣設計

#include "heap.h"
#include <stdlib.h>
#include <assert.h>

#define UINT_HEAP       (1<<5u)

struct heap {
    cmp_f   fcmp;       // 比較行為
    unsigned len;       // heap 長度
    unsigned cap;       // heap 容量
    void ** data;       // 資料節點陣列
};

// heap_expand - 新增節點擴容
inline void heap_expand(struct heap * h) {
    if (h->len >= h->cap) {
        h->data = realloc(h->data, h->cap<<=1);
        assert(h->data);
    }
}

從中可以看出當前堆結構是可以儲存 void * 資料. 其中通過 heap::fcmp 比較行為來調整關係.

有了堆的資料結構定義, 那麼堆的建立和銷燬業務程式碼就被無腦的確定了 ~

//
// heap_create - 建立符合規則的堆
// fcmp     : 比較行為, 規則 fcmp() <= 0
// return   : 返回建立好的堆物件
//
inline heap_t 
heap_create(cmp_f fcmp) {
    struct heap * h = malloc(sizeof(struct heap));
    assert(h && fcmp);
    h->fcmp = fcmp;
    h->len = 0;
    h->cap = UINT_HEAP;
    h->data = malloc(sizeof(void *) * UINT_HEAP);
    assert(h->data && UINT_HEAP > 0);
    return h;
}

//
// heap_delete - 銷燬堆
// h        : 堆物件
// fdie     : 銷燬行為, 預設 NULL
// return   : void
//
void 
heap_delete(heap_t h, node_f fdie) {
    if (NULL == h || h->data == NULL) return;
    if (fdie && h->len > 0)
        for (unsigned i = 0; i < h->len; ++i)
            fdie(h->data[i]);
    free(h->data);
    h->data = NULL;
    h->len = 0;
    free(h);
}

隨後將迎接這個終結者堆的全貌. 此刻讀者可以先喝口水 : )

前言 - 寫一段終結程式碼

　　堆結構中最核心兩處就是向下調整和向上調整過程程式碼

// down - 堆節點下沉, 從上到下沉一遍
static void down(cmp_f fcmp, void * data[], unsigned len, unsigned x) {
    void * m = data[x];
    for (unsigned i = x * 2 + 1; i < len; i = x * 2 + 1) {
        if (i + 1 < len && fcmp(data[i+1], data[i]) < 0)
            ++i;
        if (fcmp(m, data[i]) <= 0)
            break;
        data[x] = data[i];
        x = i;
    }
    data[x] = m;
}

// up - 堆節點上浮, 從下到上浮一遍
static void up(cmp_f fcmp, void * node, void * data[], unsigned x) {
    while (x > 0) {
        void * m = data[(x-1)>>1];
         if (fcmp(m, node) <= 0)
            break;
        data[x] = m;
        x = (x-1)>>1;
    }
    data[x] = node;
}

如何理解其中奧妙呢. 可以這麼看, 索引 i 節點的左子樹索引為 2i+1, 右子樹樹索引為 2i+2 = (2i+1)+1.

相反的索引為 i 節點的父親節點就是 (i-1)/2 = (i-1)>>1. 這就是堆節點調整的無上奧妙.  隨後的程式碼就

很輕鬆出手了

//
// heap_insert - 堆插入資料
// h        : 堆物件
// node     : 操作物件
// return   : void
//
inline void 
heap_insert(heap_t h, void * node) {
    heap_expand(h);
    up(h->fcmp, node, h->data, h->len++);
}

//
// heap_top - 檢視堆頂結點資料
// h        : 堆物件
// return   : 堆頂節點
//
inline void * 
heap_top(heap_t h) {
    return h->len <= 0 ? NULL : *h->data;
}

//
// heap_top - 摘掉堆頂結點資料
// h        : 堆物件
// return   : 返回堆頂節點
//
inline void * 
heap_pop(heap_t h) {
    void * node = heap_top(h);
    if (node && --h->len > 0) {
        // 尾巴節點一定比小堆頂節點大, 那麼要下沉
        h->data[0] = h->data[h->len];
        down(h->fcmp, h->data, h->len, 0);
    }
    return node;
}

看完上面程式碼可以再回看下 down 和 up 程式碼佈局. 是不是堆節點調整全部技巧已經瞭然於胸 ~

隨後我們介紹堆刪除任意節點大致演算法思路

　　1' 迴圈遍歷, 找到要刪除節點

　　2' 如果刪除後堆空, 或者刪除的是最後節點, 那直接搞定

　　3' 最後節點複製到待刪除節點位置處

　　4' 最後節點和待刪除節點權值相等, 不調整節點關係

　　5' 最後節點比待刪除節點權值大, 向下調整節點關係(基於小頂堆設計)

　　6' 最後節點比待刪除節點權值小, 向上調整節點關係

從上可以看出堆刪除節點演算法複雜度是 O(n) + O(logn) = O(n). 請欣賞具體程式碼

//
// heap_remove - 堆刪除資料
// h        : 堆物件
// arg      : 操作引數
// fcmp     : 比較行為, 規則 fcmp() == 0
// return   : 找到的堆節點
//
void * 
heap_remove(heap_t h, void * arg, cmp_f fcmp) {
    if (h == NULL || h->len <= 0)
        return NULL;

    // 開始查詢這個節點
    unsigned i = 0;
    fcmp = fcmp ? fcmp : h->fcmp;
    do {
        void * node = h->data[i];
        if (fcmp(arg, node) == 0) {
            if (--h->len > 0 && h->len != i) {
                // 尾巴節點和待刪除節點比較
                int ret = h->fcmp(h->data[h->len], node);

                // 小頂堆, 新的值比老的值小, 那麼上浮
                if (ret < 0)
                    up(h->fcmp, h->data[h->len], h->data, i);
                else if (ret > 0) {
                    // 小頂堆, 新的值比老的值大, 那麼下沉
                    h->data[i] = h->data[h->len];
                    down(h->fcmp, h->data, h->len, i);
                }
            }

            return node;
        }
    } while (++i < h->len);

    return NULL;
}

到這堆資料結構基本程式碼都已經搞定. 開始寫寫測試用例跑跑

#include "heap.h"
#include <stdio.h>

struct node {
    int value;
};

static inline int node_cmp(const struct node * l, const struct node * r) {
    return l->value - r->value;
}

static void heap_print(heap_t h) {
    struct heap {
        cmp_f   fcmp;       // 比較行為
        unsigned len;       // heap 長度
        unsigned cap;       // heap 容量
        void ** data;       // 資料節點陣列
    } * x = (struct heap *)h;

    // 資料列印for (unsigned i = 0; i < x->len; ++i) {
        struct node * node = x->data[i];
        printf("%d ", node->value);
    }
    putchar('\n');
}

int main() {
    heap_t h = heap_create(node_cmp);
    struct node a[] = { { 53 }, { 17 }, { 78 }, { 9 }, { 45 }, { 65 }, { 87 }, { 23} };
    for (int i = 0; i < sizeof a / sizeof *a; ++i)
        heap_insert(h, a + i);

    heap_print(h);

    // 資料列印
    struct node * node;
    while ((node = heap_pop(h))) {
        printf("%d ", node->value);
    }
    putchar('\n');

    // 重新插入資料
    for (int i = 0; i < sizeof a / sizeof *a; ++i)
        heap_insert(h, a + i);

    // 刪除操作 - 下沉
    heap_remove(h, &(struct node){ 17 }, NULL);
    heap_print(h);

    // 插入操作
    heap_insert(h, &(struct node){ 17 });
    heap_print(h);

    // 刪除操作 - 上浮
    heap_remove(h, &(struct node){ 78 }, NULL);
    heap_print(h);

    heap_delete(h, NULL);
    return 0;
}

最終執行結果如下

後續堆相關程式碼變化, 可以參照  heap - https://github.com/wangzhione/structc/blob/master/structc/struct/heap.c

說到引用 github 想起一個 git 好用配置安利給大家 ~ 從此 git ll 就活了.

git config --global color.diff auto
git config --global color.status auto
git config --global color.branch auto
git config --global color.interactive auto
git config --global alias.ll "log --graph --all --pretty=format:'%Cred%h %Creset -%C(yellow)%d%Creset %s %Cgreen(%cr) %C(bold blue)<%an>%Creset' --abbrev-commit --date=relative"

奇妙資料結構堆, 終結在這裡, 後面內容可以忽略. 期待下次再扯了 ~

正文 - 順帶贈送個點心

　　其實到這本不該再說什麼. 單純看上面就足夠了. 但不知道有沒有朋友覺得你總是說 C 資料結構. 效

果好嗎? 對技術提升效果明顯嗎? 這裡不妨利用我們對 C 理解, 來分析一個業務程式碼. 感受下一通百通.

我試著用 Go 中資料結構原始碼舉例子. 重點看下 Go 原始碼包中 "container/list" 連結串列用法(比較簡單)

package main

import (
	"container/list"
	"fmt"
)

func main() {
	// 構造連結串列物件
	pers := list.New()

	// Persion 普通人物件
	type Persion struct {
		Name string
		Age  int
	}

	// 連結串列物件資料填充
	pers.PushBack(&Persion{"wang", 27})
	pers.PushFront(&Persion{"zhi", 27})

	// 開始遍歷處理
	for e := pers.Front(); e != nil; e = e.Next() {
		per, ok := e.Value.(*Persion)
		if !ok {
			panic(fmt.Sprint("Persion List faild", e.Value))
		}
		fmt.Println(per)
	}

	for e := pers.Front(); e != nil; {
		next := e.Next()
		pers.Remove(e)
		e = next
	}
	fmt.Println(pers.Len())
}

執行結果是

$ go run list-demo.go
&{zhi 27}
&{wang 27}
0

通過上面演示 Demo, 大致知道了 list 包用法. 隨後開始著手解析 "container/list" 原始碼

// Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

// Package list implements a doubly linked list.
//
// To iterate over a list (where l is a *List):
//	for e := l.Front(); e != nil; e = e.Next() {
//		// do something with e.Value
//	}
//
package list

// Element is an element of a linked list.
type Element struct {
	// Next and previous pointers in the doubly-linked list of elements.
	// To simplify the implementation, internally a list l is implemented
	// as a ring, such that &l.root is both the next element of the last
	// list element (l.Back()) and the previous element of the first list
	// element (l.Front()).
	next, prev *Element

	// The list to which this element belongs.
	list *List

	// The value stored with this element.
	Value interface{}
}

// Next returns the next list element or nil.
func (e *Element) Next() *Element {
	if p := e.next; e.list != nil && p != &e.list.root {
		return p
	}
	return nil
}

// Prev returns the previous list element or nil.
func (e *Element) Prev() *Element {
	if p := e.prev; e.list != nil && p != &e.list.root {
		return p
	}
	return nil
}

// List represents a doubly linked list.
// The zero value for List is an empty list ready to use.
type List struct {
	root Element // sentinel list element, only &root, root.prev, and root.next are used
	len  int     // current list length excluding (this) sentinel element
}

// Init initializes or clears list l.
func (l *List) Init() *List {
	l.root.next = &l.root
	l.root.prev = &l.root
	l.len = 0
	return l
}

// New returns an initialized list.
func New() *List { return new(List).Init() }

// Len returns the number of elements of list l.
// The complexity is O(1).
func (l *List) Len() int { return l.len }

// Front returns the first element of list l or nil if the list is empty.
func (l *List) Front() *Element {
	if l.len == 0 {
		return nil
	}
	return l.root.next
}

// Back returns the last element of list l or nil if the list is empty.
func (l *List) Back() *Element {
	if l.len == 0 {
		return nil
	}
	return l.root.prev
}

// lazyInit lazily initializes a zero List value.
func (l *List) lazyInit() {
	if l.root.next == nil {
		l.Init()
	}
}

// insert inserts e after at, increments l.len, and returns e.
func (l *List) insert(e, at *Element) *Element {
	n := at.next
	at.next = e
	e.prev = at
	e.next = n
	n.prev = e
	e.list = l
	l.len++
	return e
}

// insertValue is a convenience wrapper for insert(&Element{Value: v}, at).
func (l *List) insertValue(v interface{}, at *Element) *Element {
	return l.insert(&Element{Value: v}, at)
}

// remove removes e from its list, decrements l.len, and returns e.
func (l *List) remove(e *Element) *Element {
	e.prev.next = e.next
	e.next.prev = e.prev
	e.next = nil // avoid memory leaks
	e.prev = nil // avoid memory leaks
	e.list = nil
	l.len--
	return e
}

// Remove removes e from l if e is an element of list l.
// It returns the element value e.Value.
// The element must not be nil.
func (l *List) Remove(e *Element) interface{} {
	if e.list == l {
		// if e.list == l, l must have been initialized when e was inserted
		// in l or l == nil (e is a zero Element) and l.remove will crash
		l.remove(e)
	}
	return e.Value
}

// PushFront inserts a new element e with value v at the front of list l and returns e.
func (l *List) PushFront(v interface{}) *Element {
	l.lazyInit()
	return l.insertValue(v, &l.root)
}

// PushBack inserts a new element e with value v at the back of list l and returns e.
func (l *List) PushBack(v interface{}) *Element {
	l.lazyInit()
	return l.insertValue(v, l.root.prev)
}

// InsertBefore inserts a new element e with value v immediately before mark and returns e.
// If mark is not an element of l, the list is not modified.
// The mark must not be nil.
func (l *List) InsertBefore(v interface{}, mark *Element) *Element {
	if mark.list != l {
		return nil
	}
	// see comment in List.Remove about initialization of l
	return l.insertValue(v, mark.prev)
}

// InsertAfter inserts a new element e with value v immediately after mark and returns e.
// If mark is not an element of l, the list is not modified.
// The mark must not be nil.
func (l *List) InsertAfter(v interface{}, mark *Element) *Element {
	if mark.list != l {
		return nil
	}
	// see comment in List.Remove about initialization of l
	return l.insertValue(v, mark)
}

// MoveToFront moves element e to the front of list l.
// If e is not an element of l, the list is not modified.
// The element must not be nil.
func (l *List) MoveToFront(e *Element) {
	if e.list != l || l.root.next == e {
		return
	}
	// see comment in List.Remove about initialization of l
	l.insert(l.remove(e), &l.root)
}

// MoveToBack moves element e to the back of list l.
// If e is not an element of l, the list is not modified.
// The element must not be nil.
func (l *List) MoveToBack(e *Element) {
	if e.list != l || l.root.prev == e {
		return
	}
	// see comment in List.Remove about initialization of l
	l.insert(l.remove(e), l.root.prev)
}

// MoveBefore moves element e to its new position before mark.
// If e or mark is not an element of l, or e == mark, the list is not modified.
// The element and mark must not be nil.
func (l *List) MoveBefore(e, mark *Element) {
	if e.list != l || e == mark || mark.list != l {
		return
	}
	l.insert(l.remove(e), mark.prev)
}

// MoveAfter moves element e to its new position after mark.
// If e or mark is not an element of l, or e == mark, the list is not modified.
// The element and mark must not be nil.
func (l *List) MoveAfter(e, mark *Element) {
	if e.list != l || e == mark || mark.list != l {
		return
	}
	l.insert(l.remove(e), mark)
}

// PushBackList inserts a copy of an other list at the back of list l.
// The lists l and other may be the same. They must not be nil.
func (l *List) PushBackList(other *List) {
	l.lazyInit()
	for i, e := other.Len(), other.Front(); i > 0; i, e = i-1, e.Next() {
		l.insertValue(e.Value, l.root.prev)
	}
}

// PushFrontList inserts a copy of an other list at the front of list l.
// The lists l and other may be the same. They must not be nil.
func (l *List) PushFrontList(other *List) {
	l.lazyInit()
	for i, e := other.Len(), other.Back(); i > 0; i, e = i-1, e.Prev() {
		l.insertValue(e.Value, &l.root)
	}
}

list 包中最核心的資料結構無外乎 Element 和 List 互相引用的結構

// Element is an element of a linked list.
type Element struct {
	// Next and previous pointers in the doubly-linked list of elements.
	// To simplify the implementation, internally a list l is implemented
	// as a ring, such that &l.root is both the next element of the last
	// list element (l.Back()) and the previous element of the first list
	// element (l.Front()).
	next, prev *Element

	// The list to which this element belongs.
	list *List

	// The value stored with this element.
	Value interface{}
}

// Next returns the next list element or nil.
func (e *Element) Next() *Element {
	if p := e.next; e.list != nil && p != &e.list.root {
		return p
	}
	return nil
}

// Prev returns the previous list element or nil.
func (e *Element) Prev() *Element {
	if p := e.prev; e.list != nil && p != &e.list.root {
		return p
	}
	return nil
}

// List represents a doubly linked list.
// The zero value for List is an empty list ready to use.
type List struct {
	root Element // sentinel list element, only &root, root.prev, and root.next are used
	len  int     // current list length excluding (this) sentinel element
}

它是一個特殊迴圈雙向連結串列. 特殊在 Element::list 指向頭節點. 

隨著我們對 list 記憶體佈局理解後, 後面的業務程式碼實現起來就很一般了. 例如這裡

// PushBackList inserts a copy of an other list at the back of list l.
// The lists l and other may be the same. They must not be nil.
func (l *List) PushBackList(other *List) {
	l.lazyInit()
	for i, e := other.Len(), other.Front(); i > 0; i, e = i-1, e.Next() {
		l.insertValue(e.Value, l.root.prev)
	}
}

其實可以實現的更貼合 list 庫總體的風格, 效能還更好

// PushBackList inserts a copy of an other list at the back of list l.
// The lists l and other may be the same. They must not be nil.
func (l *List) PushBackList(other *List) {
	l.lazyInit()
	for e := other.Front(); e != nil; e = e.Next() {
		l.insertValue(e.Value, l.root.prev)
	}
}

是不是發現上層程式碼理解起來心智負擔不大. 不過 go 中 slice list map 都不是執行緒安全的.

特殊場景需要自行加鎖. 這裡不過多扯. 以後有機會會詳細分析 Go 中鎖原始碼實現. 最後通過

上面 list 包真實現一個 LRU Cache

package cache

import (
	"container/list"
	"sync"
)

// entry 儲存實體內容
type entry struct {
	key   interface{}
	value interface{}
}

// Cache LRU 快取實現
type Cache struct {
	// x 保證 LRU 訪問安全
	m sync.Mutex

	// max 表示快取容量的最大值, 0 表示無限快取
	max uint

	// list 迴圈雙向連結串列
	list *list.List

	// pond 快取的池子
	pond map[interface{}]*list.Element
}

// New 新建一個 LRU 快取物件
func New(max uint) *Cache {
	return &Cache{
		max:  max,
		list: list.New(),
		pond: make(map[interface{}]*list.Element),
	}
}

// remove 通過 *list.Element 刪除
func (c *Cache) remove(e *list.Element) {
	n, ok := c.list.Remove(e).(*entry)
	if ok {
		delete(c.pond, n.key)
	}
}

// Set 新增快取
func (c *Cache) Set(key, value interface{}) {
	c.m.Lock()
	defer c.m.Unlock()

	if e, ok := c.pond[key]; ok {
		if value == nil {
			// Set key nil <=> Remove key
			c.remove(e)
		} else {
			e.Value = value
			c.list.MoveToFront(e)
		}
		return
	}

	// 如果是首次新增
	c.pond[key] = c.list.PushFront(&entry{key, value})

	// 如果超出池子快取開始清理
	if c.max != 0 && uint(c.list.Len()) > c.max {
		c.remove(c.list.Back())
	}
}

// Get 獲取快取
func (c *Cache) Get(key interface{}) (interface{}, bool) {
	c.m.Lock()
	defer c.m.Unlock()

	if e, ok := c.pond[key]; ok {
		c.list.MoveToFront(e)
		return e.Value.(*entry).value, true
	}
	return nil, false
}

用起來很容易

	c := cache.New(1)
	c.Set("123", "123")
	c.Set("234", "234")
	fmt.Println(c.Get("123"))
	fmt.Println(c.Get("234"))

是不是離開了 C, 整個世界也很簡單. 沒啥設計模式, 有的是效能還可以, 也能用.

希望能幫到有心人 ~

後記 - 那個開啟的大門

你曾是少年 - https://music.163.com/#/song?id=426027293

每個男人心裡都有一塊淨土, 只不過生活所逼硬生生的, 藏在心底最深處 . ... ..