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本帖最后由 cluter 于 2011-04-24 00:49 編輯
忙了好久,總有有時間看內(nèi)核,最近研究下了LINUX內(nèi)核“頁面回收”時候采用的PST樹算法。
PST是 radix tree和heap tree的綜合體。而且LINUX的實現(xiàn)和傳統(tǒng)的算法還不一樣,甚是花了不少時間啊。廢話少說了,先上圖。
PST_CAT.JPG (4.29 MB, 下載次數(shù): 267)
下載附件
PST_CAT
2011-04-24 00:04 上傳
下面是插入操作:還是先上圖再帖代碼
PST_INSERT1.JPG (4.14 MB, 下載次數(shù): 151)
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PST_INSERT1
2011-04-24 00:08 上傳
PST_INSERT2.JPG (4.06 MB, 下載次數(shù): 145)
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PST_INSERT2
2011-04-24 00:13 上傳
struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,struct prio_tree_node *node)
{
獲取insert_node的radix和heap
get_index(root, node, &radix_index, &heap_index);
1 如果樹是空
2 要insert_node的heap大于root的maxindex,則要先"擴展"樹
if (prio_tree_empty(root) ||heap_index > prio_tree_maxindex(root->index_bits))
return prio_tree_expand(root, node, heap_index);
從root節(jié)點開始比較
cur = root->prio_tree_node;
獲取mask掩碼
mask = 1UL << (root->index_bits - 1);
while (mask) {
獲取cur_node的radix和heap
get_index(root, cur, &r_index, &h_index);
如果insert_node已經(jīng)存在,則直接返回當前node
if (r_index == radix_index && h_index == heap_index)
return cur;
1 cur_node->heap < insert_node->heap
2 cur_node->heap == insert_node->heap&&cur_node->radix > insert_node->radix,則交互兩個節(jié)點
if (h_index < heap_index ||(h_index == heap_index && r_index > radix_index))
{
struct prio_tree_node *tmp = node;
交換insert_node和cur_node
注意:insert_node已經(jīng)變成cur_node
node = prio_tree_replace(root, cur, node);
讓cur指針指向已經(jīng)插入的node節(jié)點
cur = tmp;
/* 交換radix和heap的值*/
index = r_index;
r_index = radix_index;
radix_index = index;
index = h_index;
h_index = heap_index;
heap_index = index;
}
獲取radix
if (size_flag)
index = heap_index - radix_index;
else
index = radix_index;
radix和mask&操作,決定insert_node插入left還是right
if (index & mask)
{
如果right==NULL則直接插入,否則繼續(xù)比較
if (prio_tree_right_empty(cur))
{
INIT_PRIO_TREE_NODE(node);
cur->right = node;
node->parent = cur;
return res;
} else
cur = cur->right;
}
else
{
如果left==NULL直接插入,否則繼續(xù)比較
if (prio_tree_left_empty(cur))
{
INIT_PRIO_TREE_NODE(node);
cur->left = node;
node->parent = cur;
return res;
} else
cur = cur->left;
}
mask移位,進行下一位的比較操作
mask >>= 1;
if (!mask) {
如果mask已經(jīng)到了最低位,則開始利用size進行比較
mask = 1UL << (BITS_PER_LONG - 1);
size_flag = 1;
}
}
/* Should not reach here */
BUG();
return NULL;
}
刪除操作:
PST_DEL.JPG (4.08 MB, 下載次數(shù): 131)
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PST_DEL
2011-04-24 00:15 上傳
//算法核心:刪除一個node,用其heap index比較大的child node來循環(huán)替代就OK了。
void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
{
struct prio_tree_node *cur;
unsigned long r_index, h_index_right, h_index_left;
cur = node;
//找到葉子結(jié)點,找到替換的路徑path
while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
if (!prio_tree_left_empty(cur))
get_index(root, cur->left, &r_index, &h_index_left);
else {
cur = cur->right;
continue;
}
if (!prio_tree_right_empty(cur))
get_index(root, cur->right, &r_index, &h_index_right);
else {
cur = cur->left;
continue;
}
/* both h_index_left and h_index_right cannot be 0 */
//找heap_index大的孩子結(jié)點
if (h_index_left >= h_index_right)
cur = cur->left;
else
cur = cur->right;
}
//如果當前結(jié)點是root,則重新初始化下root node
if (prio_tree_root(cur)) {
BUG_ON(root->prio_tree_node != cur);
__INIT_PRIO_TREE_ROOT(root, root->raw);
return;
}
//刪除當前結(jié)點
if (cur->parent->right == cur)
cur->parent->right = cur->parent;
else
cur->parent->left = cur->parent;
//循環(huán)向上替代parent結(jié)點
while (cur != node)
cur = prio_tree_replace(root, cur->parent, cur);
}
擴展操作:
PST_EXP1.JPG (3.98 MB, 下載次數(shù): 124)
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PST_EXP1
2011-04-24 00:16 上傳
PST_EXP2.JPG (3.88 MB, 下載次數(shù): 112)
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PST_EXP2
2011-04-24 00:12 上傳
static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,struct prio_tree_node *node, unsigned long max_heap_index)
{
struct prio_tree_node *first = NULL, *prev, *last = NULL;
首先擴展下index_bits,如果不進入while循環(huán),可直接把insert_node當做root節(jié)點。
if (max_heap_index > prio_tree_maxindex(root->index_bits))
root->index_bits++;
核心思想:
1 循環(huán)刪除原來的root_node,然后插入到insert_node的left左子樹上
2 如果原來的tree最后還是非空,則把整個樹插入到新的樹的left左子樹上
while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
root->index_bits++;
if (prio_tree_empty(root))
continue;
if (first == NULL) {
first = root->prio_tree_node;
prio_tree_remove(root, root->prio_tree_node);
INIT_PRIO_TREE_NODE(first);
last = first;
} else {
此時last=first,而first是樹第一個被刪除的root_node
prev = last;
先刪除root_node
last = root->prio_tree_node;
prio_tree_remove(root, root->prio_tree_node);
然后把root_node插入prev_node的左子樹上
INIT_PRIO_TREE_NODE(last);
prev->left = last;
last->parent = prev;
}
}
INIT_PRIO_TREE_NODE(node);
【first,last】是原先tree的被刪除的跟節(jié)點集合,并且以left指針相連
1 然后first掛在node的left子樹上
2 原來的tree掛在last的left子樹上
操作1
if (first) {
node->left = first;
first->parent = node;
} else
last = node;
操作2
如果此時樹還是非空的,則把樹的剩余部分掛在last的左子樹上
if (!prio_tree_empty(root)) {
last->left = root->prio_tree_node;
last->left->parent = last;
}
更新root節(jié)點
root->prio_tree_node = node;
return node;
}
圖和代碼稍微有點不一樣,就是 被刪除的跟節(jié)點先自己用LEFT指針 組合成LIST
然后在 NODE->LEFT=LIST.HEAD
LIST.HEAD->LEFT=remain_TREE |
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