B樹的實現
今天我們就來實現以下B樹,B樹有什麼特點那?我們來列舉一下
- 每個非葉子節點中存放若干關鍵字數據,並且有若干指向兒子節點的指針。指針數目=關鍵字數目+1
- 根節點有最少1個,最多m-1個關鍵字,最少2個,最多m個子節點。
- 非根節點最少有m/2,最多m-1個關鍵字
- 每個節點中的關鍵字從左到右以非降序排列
- 每個關鍵字均不小於其左子節點的關鍵字,不大於其右子節點的所有關鍵字
- 每個葉子節點都具有相同的深度
B樹的節點的增加
我們還是通過1-25個數的增加,來探索一下,B樹的增加節點有什麼規律,並寫出代碼。
首先我們定義出來我們B樹的結構,如下:
#define DEGREE 3
typedef int KEY_VALUE;
typedef struct _BTREE_NODE
{
KEY_VALUE* keys;
struct _BTREE_NODE** Childrens;
int num;
int leaf;
}BTREE_NODE,*PBTREE_NODE;
typedef struct _BTREE
{
BTREE_NODE* root;
int t;
};
我們來看一下B樹1-20個數字的增加的圖片
1-5
6-10
11-15
16-20
我們首先需要創建一個根節點:
BTREE_NODE* btree_create_node(int t, int leaf) {
BTREE_NODE* node = (BTREE_NODE*)calloc(1, sizeof(BTREE_NODE));
if (node == NULL) assert(0);
node->leaf = leaf;
node->keys = (KEY_VALUE*)calloc(1, (2 * t - 1) * sizeof(KEY_VALUE));
node->Childrens = (BTREE_NODE**)calloc(1, (2 * t) * sizeof(BTREE_NODE*));
node->num = 0;
return node;
}
//創建根節點
void btree_create(BTREE*T,int t)
{
T->t = t;
PBTREE_NODE x = btree_create_node(t, 1);
T->root = x;
}
現在就寫一下我們插入的代碼
BTREE_NODE* btree_create_node(int t, int leaf) {
BTREE_NODE* node = (BTREE_NODE*)calloc(1, sizeof(BTREE_NODE));
if (node == NULL) assert(0);
node->leaf = leaf;
node->keys = (KEY_VALUE*)calloc(1, (2 * t - 1) * sizeof(KEY_VALUE));
node->Childrens = (BTREE_NODE**)calloc(1, (2 * t) * sizeof(BTREE_NODE*));
node->num = 0;
return node;
}
//節點分裂
void btree_split_child(BTREE* T,BTREE_NODE* x,int i)
{
int t = T->t;
BTREE_NODE* y = x->Childrens[i];
BTREE_NODE* z = btree_create_node(t, y->leaf);
z->num = t - 1;
int j = 0;
for (j=0;j<t-1;j++)
{
z->keys[j] = y->keys[j + t];
}
if (y->leaf==0)
{
for (j=0;j<t;j++)
{
z->Childrens[j] = y->Childrens[j + t];
}
}
y->num = t - 1;
for (j=x->num;j>=i+1;j--)
{
x->Childrens[j + 1] = x->Childrens[j];
}
x->Childrens[i + 1] = z;
for(j=x->num-1;j>=i;j--)
{
x->keys[j + 1] = x->keys[j];
}
x->keys[i] = y->keys[t - 1];
x->num += 1;
}
//創建節點
void btree_create(BTREE*T,int t)
{
T->t = t;
PBTREE_NODE x = btree_create_node(t, 1);
T->root = x;
}
void btree_insert_notfull(BTREE*T,BTREE_NODE *x,KEY_VALUE k)
{
//獲取節點數量,從0開始減1
int i = x->num-1;
//只有1個葉子節點
if (x->leaf==1)
{
while (i>=0&&x->keys[i]>k)
{
x->keys[i + 1] = x->keys[i];
i--;
}
//賦值
x->keys[i + 1] = k;
x->num += 1;
}else
{
//找到應該插入的葉子節點
while (i >= 0 && x->keys[i] > k) i--;
//是否已經滿了5個節點
if (x->Childrens[i+1]->num==((2*T->t))-1)
{
btree_split_child(T, x, i + 1);
if (k>x->keys[i+1])
{
i++;
}
}
btree_insert_notfull(T, x->Childrens[i + 1], k);
}
}
void btree_insert(BTREE *T ,KEY_VALUE key)
{
//獲取頭節點
BTREE_NODE* r = T->root;
//如果滿節點就要進行這裏的操作
if (r->num==2*T->t-1)
{
BTREE_NODE* node = btree_create_node(T->t, 0);
T->root = node;
node->Childrens[0] = r;
btree_split_child(T, node, 0);
int i = 0;
if (node->keys[0] < key) i++;
btree_insert_notfull(T, node->Childrens[i], key);
}
else
{
//如果沒有滿就要進行這裏的操作
btree_insert_notfull(T, r, key);
}
}
B樹節點的刪除
我們還是看一下是如何刪除的示意圖,然後再寫代碼。
這裏主要討論一下刪除的幾種情況,
B樹刪除的代碼
//釋放節點
void btree_destory_node(BTREE_NODE* node)
{
if (node == nullptr)
{
return;
}
free(node->Childrens);
free(node->keys);
free(node);
}
void btree_merge(BTREE* T, BTREE_NODE* node, int idx)
{
BTREE_NODE* left = node->Childrens[idx];
BTREE_NODE* right = node->Childrens[idx + 1];
int i = 0;
left->keys[T->t - 1] = node->keys[idx];
//開始數據的合併
for (i = 0; i < T->t - 1; i++)
{
left->keys[T->t + 1] = right->keys[i];
}
if (!left->leaf)
{
for (i = 0; i < T->t; i++)
{
left->Childrens[T->t + 1] = right->Childrens[i];
}
}
left->num += T->t;
//合併完成摧毀節點
btree_destory_node(right);
//node
for (i = idx + 1; i < node->num; i++)
{
node->keys[i - 1] = node->keys[i];
node->Childrens[i] = node->Childrens[i + 1];
}
node->Childrens[i + 1] = NULL;
node->num -= 1;
if (node->num == 0)
{
T->root = left;
btree_destory_node(node);
}
}
void btree_delete_key(BTREE* T, BTREE_NODE* node, KEY_VALUE key)
{
//如果是空節點,直接返回
if (node == nullptr)
{
return;
}
int idx = 0, i;
//獲取key所在的位置
while (idx<node->num && key>node->keys[idx])
{
idx++;
}
if (idx < node->num && key == node->keys[idx])
{
if (node->leaf)
{
//如果是葉子節點,直接刪除
for (i = idx; i < node->num - 1; i++)
{
node->keys[i] = node->keys[i + 1];
}
node->keys[node->num - 1] = 0;
node->num--;
//如果是根節點的情況
if (node->num == 0)
{
free(node);
T->root = nullptr;
}
return;
}//直接刪除
else if (node->Childrens[idx]->num >= T->t)
{
BTREE_NODE* left = node->Childrens[idx];
node->keys[idx] = left->keys[left->num - 1];
btree_delete_key(T, left, left->keys[left->num - 1]);
}//直接刪除
else if (node->Childrens[idx + 1]->num >= T->t)
{
BTREE_NODE* right = node->Childrens[idx + 1];
node->keys[idx] = right->keys[0];
btree_delete_key(T, right, right->keys[0]);
}
else {
//如果都不是,說明是左右孩子節點都是T-1個關鍵字
btree_merge(T, node, idx);
btree_delete_key(T, node->Childrens[idx], key);
}
}
else
{
BTREE_NODE* child = node->Childrens[idx];
if (child == NULL)
{
printf("Can\'t del key=%d\n", key);
return;
}//子節點的數目剛好等於2
if (child->num == T->t - 1)
{
BTREE_NODE* left = nullptr;
BTREE_NODE* right = nullptr;
if (idx - 1 >= 0)
{
left = node->Childrens[idx - 1];
}
if (idx + 1 <= node->num)
{
right = node->Childrens[idx + 1];
}
//如果左右節點任何一個都可以借用節點
if ((left && left->num >= T->t) || (right && right->num >= T->t))
{
int richR = 0;
if (right)
{
richR = 1;
}
if (left && right)
{
richR = (right->num > left->num) ? 1 : 0;
}
//從右借用節點
if (right && right->num >= T->t && richR)
{
child->keys[child->num] = node->keys[idx];
child->Childrens[child->num + 1] = right->Childrens[0];
child->num++;
node->keys[idx] = right->keys[0];
//調整右邊的節點
for (i = 0; i < right->num - 1; i++)
{
right->keys[i] = right->keys[i + 1];
right->Childrens[i] = right->Childrens[i + 1];
}
right->keys[right->num - 1] = 0;
right->Childrens[right->num - 1] = right->Childrens[right->num];
right->Childrens[right->num] = NULL;
right->num--;
}
else
{
//從左借節點
for (i = child->num; i > 0; i--)
{
child->keys[i] = child->keys[i - 1];
child->Childrens[i + 1] = child->Childrens[i];
}
child->Childrens[1] = child->Childrens[0];
child->Childrens[0] = left->Childrens[left->num];
child->keys[0] = node->keys[idx - 1];
child->num++;
node->keys[idx - 1] = left->keys[left->num - 1];
left->keys[left->num - 1] = 0;
left->Childrens[left->num] = NULL;
left->num--;
}
}
else if ((!left) || (left->num == T->t - 1) && (!right) || (right->num == T->t - 1))
{
if (left&&left->num==T->t-1)
{
btree_merge(T, node, idx - 1);
child = left;
}else if(right&&right->num==T->t-1)
{
btree_merge(T, node, idx);
}
}
btree_delete_key(T, child, key);
}
}
}
int btree_delete(BTREE* T, KEY_VALUE key)
{
if (!T->root)
{
return -1;
}
btree_delete_key(T, T->root, key);
return 0;
}
推薦一個零聲學院免費教程,個人覺得老師講得不錯,
分享給大家:[Linux,Nginx,ZeroMQ,MySQL,Redis,
fastdfs,MongoDB,ZK,流媒體,CDN,P2P,K8S,Docker,
TCP/IP,協程,DPDK等技術內容,點擊立即學習:
服務器
音視頻
dpdk
Linux內核