通过它们在后备数组中的索引交换双向链表中的项目 [英] Swap items in doubly-linked list by their indices in the backing array
问题描述
我有以下类型的对象数组:
I have an array of objects of the following type:
struct Node {
Node *_pPrev, *_pNext;
double *_pData;
};
一些节点参与一个双向链表,对于这样的节点,_pData!=nullptr
.还有一个虚拟头节点,_pNext
指向列表的开头,_pPrev
指向列表的结尾.列表开始时只包含这个头节点,永远不应该从列表中删除它.
Some of the nodes participate in a doubly-linked list, with _pData!=nullptr
for such nodes. There is also a dummy head node with _pNext
pointing to the beginning of the list, and _pPrev
pointing to the end. The list starts with containing only this head node, and it should be never removed from the list.
双向链表由一个数组支持,初始大小等于列表中的最大节点数.
The doubly-linked list is backed by an array, with initial size equal to the maximum number of nodes in the list.
struct Example {
Node _nodes[MAXN];
Node _head;
};
现在我想对这个数据结构执行以下操作:给定 2 个索引 i
和 j
到 _nodes
数组,交换数组中的节点,但保留它们在双向链表中的位置.这个操作需要更新_nodes[i]._pPrev->_pNext
、_nodes[i]._pNext->_pPrev
,节点j
也一样代码>.
Now I want to perform the following operation on this data structure: given 2 indices i
and j
to the _nodes
array, swap the nodes in the array, but preserve their positions in the doubly-linked list. This operation needs updating _nodes[i]._pPrev->_pNext
, _nodes[i]._pNext->_pPrev
and the same for node j
.
一个问题是节点 i
和 j
彼此相邻时的极端情况.另一个问题是,原始代码涉及很多 if
(检查每个节点的 _pData==nullptr
并以不同方式处理 3 种情况,并检查是否节点彼此相邻),因此效率低下.
One problem is the corner cases when nodes i
and j
are next to each other. Another problem is that the naive code involves a lot of if
s (to check for _pData==nullptr
for each node and handle the 3 cases differently, and to check whether the nodes are next to each other), thus becoming inefficient.
如何有效地做到这一点?
How to do it efficiently?
这是我目前在 C++ 中的内容:
Here is what I have so far in C++:
assert(i!=j);
Node &chI = _nodes[i];
Node &chJ = _nodes[j];
switch (((chI._pData == nullptr) ? 0 : 1) | ((chJ._pData == nullptr) ? 0 : 2)) {
case 3:
if (chI._pNext == &chJ) {
chI._pPrev->_pNext = &chJ;
chJ._pNext->_pPrev = &chI;
chI._pNext = &chI;
chJ._pPrev = &chJ;
}
else if (chJ._pNext == &chI) {
chJ._pPrev->_pNext = &chI;
chI._pNext->_pPrev = &chJ;
chJ._pNext = &chJ;
chI._pPrev = &chI;
} else {
chI._pNext->_pPrev = &chJ;
chJ._pNext->_pPrev = &chI;
chI._pPrev->_pNext = &chJ;
chJ._pPrev->_pNext = &chI;
}
break;
case 2:
chJ._pNext->_pPrev = &chI;
chJ._pPrev->_pNext = &chI;
break;
case 1:
chI._pNext->_pPrev = &chJ;
chI._pPrev->_pNext = &chJ;
break;
default:
return; // no need to swap because both are not in the doubly-linked list
}
std::swap(chI, chJ);
推荐答案
- 两个节点的节点内容可以互换,不改变意义;只有他们的地址会改变
- 由于地址已更改,因此所有对两个节点的引用也必须更改,包括碰巧指向两个节点之一的节点内部的指针.
- The node contents of two nodes can be swapped, without changing their meaning; only their addresses will change
- since the addresses have changed, all references to the two nodes must change, too, including pointers inside the nodes that happen to point to one of the two nodes.
这是交换第一次的说明 &稍后修复 (TM) 方法.它的主要壮举是它避免了所有的极端情况.它确实假设了一个格式良好的 LL ,并且忽略了in_use"条件(恕我直言与 LL-swap-problem 正交)
Here is an illustration of the swap first & fixup later (TM) method. Its major feat is that it avoids all the corner cases. It does assume a well-formed LL , and it ignores the "in_use" condition (which IMHO is orthogonal to the LL-swap-problem)
注意我做了一些重命名,添加了测试数据,并转换为纯 C.
Note I did a bit of renaming, added test data, and converted to Pure C.
已编辑(现在它确实有效!)
EDITED (now it actually works!)
#include <stdio.h>
struct Node {
struct Node *prev, *next;
// double *_pData;
int val;
};
#define MAXN 5
struct Example {
struct Node head;
struct Node nodes[MAXN];
};
/* sample data */
struct Example example = {
{ &example.nodes[4] , &example.nodes[0] , -1} // Head
,{ { &example.head , &example.nodes[1] , 0}
, { &example.nodes[0] , &example.nodes[2] , 1}
, { &example.nodes[1] , &example.nodes[3] , 2}
, { &example.nodes[2] , &example.nodes[4] , 3}
, { &example.nodes[3] , &example.head , 4}
}
};
void swapit( unsigned one, unsigned two)
{
struct Node tmp, *ptr1, *ptr2;
/* *unique* array of pointers-to pointer
* to fixup all the references to the two moved nodes
*/
struct Node **fixlist[8];
unsigned nfix = 0;
unsigned ifix;
/* Ugly macro to add entries to the list of fixups */
#define add_fixup(pp) fixlist[nfix++] = (pp)
ptr1 = &example.nodes[one];
ptr2 = &example.nodes[two];
/* Add pointers to some of the 8 possible pointers to the fixup-array.
** If the {prev,next} pointers do not point to {ptr1,ptr2}
** we do NOT need to fix them up.
*/
if (ptr1->next == ptr2) add_fixup(&ptr2->next); // need &ptr2->next here (instead of ptr1)
else add_fixup(&ptr1->next->prev);
if (ptr1->prev == ptr2) add_fixup(&ptr2->prev); // , because pointer swap takes place AFTER the object swap
else add_fixup(&ptr1->prev->next);
if (ptr2->next == ptr1) add_fixup(&ptr1->next);
else add_fixup(&ptr2->next->prev);
if (ptr2->prev == ptr1) add_fixup(&ptr1->prev);
else add_fixup(&ptr2->prev->next);
fprintf(stderr,"Nfix=%u
", nfix);
for(ifix=0; ifix < nfix; ifix++) {
fprintf(stderr, "%p --> %p
", fixlist[ifix], *fixlist[ifix]);
}
/* Perform the rough swap */
tmp = example.nodes[one];
example.nodes[one] = example.nodes[two];
example.nodes[two] = tmp;
/* Fixup the pointers, but only if they happen to point at one of the two nodes */
for(ifix=0; ifix < nfix; ifix++) {
if (*fixlist[ifix] == ptr1) *fixlist[ifix] = ptr2;
else *fixlist[ifix] = ptr1;
}
}
void dumpit(char *msg)
{
struct Node *ptr;
int i;
printf("%s
", msg);
ptr = &example.head;
printf("Head: %p {%p,%p} %d
", ptr, ptr->prev, ptr->next, ptr->val);
for (i=0; i < MAXN; i++) {
ptr = example.nodes+i;
printf("# %u # %p {%p,%p} %d
", i, ptr, ptr->prev, ptr->next, ptr->val);
}
}
int main(void)
{
dumpit("Original");
swapit(1,2);
dumpit("After swap(1,2)");
swapit(0,1);
dumpit("After swap(0,1)");
swapit(0,2);
dumpit("After swap(0,2)");
swapit(0,4);
dumpit("After swap(0,4)");
return 0;
}
<小时>
为了说明我们可以忽略in_use
条件这一事实,这里有一个新版本,在同一个数组中存在两个双链表.这可以是in_use 列表和广告免费 列表.
To illustrate the fact that we can ignore the in_use
condition, here is a new version, with two double linked lists present in the same array. This could be an in_use list and ad free list.
#include <stdio.h>
struct Node {
struct Node *prev, *next;
// double *_pData;
// int val;
char * payload;
};
#define MAXN 8
struct Example {
struct Node head;
struct Node free; /* freelist */
struct Node nodes[MAXN];
};
/* sample data */
struct Example example = {
{ &example.nodes[5] , &example.nodes[0] , ""} /* Head */
, { &example.nodes[6] , &example.nodes[2] , ""} /* freelist */
/* 0 */ ,{ { &example.head , &example.nodes[1] , "zero"}
, { &example.nodes[0] , &example.nodes[3] , "one"}
, { &example.free , &example.nodes[6] , NULL }
, { &example.nodes[1] , &example.nodes[4] , "two"}
/* 4 */ , { &example.nodes[3] , &example.nodes[5] , "three"}
, { &example.nodes[4] , &example.head , "four"}
, { &example.nodes[2] , &example.free , NULL}
, { &example.nodes[7] , &example.nodes[7] , "OMG"} /* self referenced */
}
};
void swapit( unsigned one, unsigned two)
{
struct Node tmp, *ptr1, *ptr2;
/* *unique* array of pointers-to pointer
* to fixup all the references to the two moved nodes
*/
struct Node **fixlist[4];
unsigned nfix = 0;
unsigned ifix;
/* Ugly macro to add entries to the list of fixups */
#define add_fixup(pp) fixlist[nfix++] = (pp)
ptr1 = &example.nodes[one];
ptr2 = &example.nodes[two];
/* Add pointers to some of the 4 possible pointers to the fixup-array.
** If the {prev,next} pointers do not point to {ptr1,ptr2}
** we do NOT need to fix them up.
** Note: we do not need the tests (.payload == NULL) if the linked lists
** are disjunct (such as: a free list and an active list)
*/
if (1||ptr1->payload) { /* This is on purpose: always True */
if (ptr1->next == ptr2) add_fixup(&ptr2->next); // need &ptr2->next here (instead of ptr1)
else add_fixup(&ptr1->next->prev);
if (ptr1->prev == ptr2) add_fixup(&ptr2->prev); // , because pointer swap takes place AFTER the object swap
else add_fixup(&ptr1->prev->next);
}
if (1||ptr2->payload) { /* Ditto */
if (ptr2->next == ptr1) add_fixup(&ptr1->next);
else add_fixup(&ptr2->next->prev);
if (ptr2->prev == ptr1) add_fixup(&ptr1->prev);
else add_fixup(&ptr2->prev->next);
}
fprintf(stderr,"Nfix=%u
", nfix);
for(ifix=0; ifix < nfix; ifix++) {
fprintf(stderr, "%p --> %p
", fixlist[ifix], *fixlist[ifix]);
}
/* Perform the rough swap */
tmp = example.nodes[one];
example.nodes[one] = example.nodes[two];
example.nodes[two] = tmp;
/* Fixup the pointers, but only if they happen to point at one of the two nodes */
for(ifix=0; ifix < nfix; ifix++) {
if (*fixlist[ifix] == ptr1) *fixlist[ifix] = ptr2;
else *fixlist[ifix] = ptr1;
}
}
void dumpit(char *msg)
{
struct Node *ptr;
int i;
printf("%s
", msg);
ptr = &example.head;
printf("Head: %p {%p,%p} %s
", ptr, ptr->prev, ptr->next, ptr->payload);
ptr = &example.free;
printf("Free: %p {%p,%p} %s
", ptr, ptr->prev, ptr->next, ptr->payload);
for (i=0; i < MAXN; i++) {
ptr = example.nodes+i;
printf("# %u # %p {%p,%p} %s
", i, ptr, ptr->prev, ptr->next, ptr->payload);
}
}
int main(void)
{
dumpit("Original");
swapit(1,2); /* these are on different lists */
dumpit("After swap(1,2)");
swapit(0,1);
dumpit("After swap(0,1)");
swapit(0,2);
dumpit("After swap(0,2)");
swapit(0,4);
dumpit("After swap(0,4)");
swapit(2,5); /* these are on different lists */
dumpit("After swap(2,5)");
return 0;
}
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