A*算法
1.f(n) = g(n) + h(n)
其中f(n) 是节点n的估价函数,g(n)实在状态空间中从初始节点到n节点的实际代价,h(n)是从n到目 标节点最佳路径的估计代价。
2.
代码
3.
[翻译]A*寻路初探 GameDev.net
http://blog.vckbase.com/panic/archive/2005/03/20/3778.html
[翻译]A*分层寻路
http://blog.vckbase.com/panic/archive/2005/07/21/9906.html
Fixing Pathfinding Once and For All
http://www.ai-blog.net/archives/000152.html
A*(A星)算法(一)
http://hi.baidu.com/%BA%DA%B5%C4%B7%A2%D7%CF/blog/item/60e3483dce5bb8c29e3d62e0.html
初识A*算法
http://blog.csdn.net/zheng80037/archive/2007/06/04/1636953.aspx
[翻译]在A*寻路中使用二叉堆
http://blog.vckbase.com/panic/archive/2005/03/28/4144.html
二叉堆的模板代码--续“关于一道算法题《编写算法,从10亿个浮点数当中,选出其中最大的10000个》”
http://blog.vckbase.com/panic/archive/2006/06/19/20869.html
1.f(n) = g(n) + h(n)
其中f(n) 是节点n的估价函数,g(n)实在状态空间中从初始节点到n节点的实际代价,h(n)是从n到目 标节点最佳路径的估计代价。
2.
Best_First_Search()
{
Open = [起始节点]; Closed = [];
while ( Open表非空 )
{
从Open中取得一个节点X,并从OPEN表中删除。
if (X是目标节点)
{
求得路径PATH;返回路径PATH;
}
for (每一个X的子节点Y)
{
if( Y不在OPEN表和CLOSE表中 )
{
求Y的估价值;并将Y插入OPEN表中;//还没有排序
}
else
{
if( Y在OPEN表中 )
{
if( Y的估价值小于OPEN表的估价值 )
更新OPEN表中的估价值;
}
else //Y在CLOSE表中
{
if( Y的估价值小于CLOSE表的估价值 )
{
更新CLOSE表中的估价值;
从CLOSE表中移出节点,并放入OPEN表中;
}
}
}
}//end for
{
Open = [起始节点]; Closed = [];
while ( Open表非空 )
{
从Open中取得一个节点X,并从OPEN表中删除。
if (X是目标节点)
{
求得路径PATH;返回路径PATH;
}
for (每一个X的子节点Y)
{
if( Y不在OPEN表和CLOSE表中 )
{
求Y的估价值;并将Y插入OPEN表中;//还没有排序
}
else
{
if( Y在OPEN表中 )
{
if( Y的估价值小于OPEN表的估价值 )
更新OPEN表中的估价值;
}
else //Y在CLOSE表中
{
if( Y的估价值小于CLOSE表的估价值 )
{
更新CLOSE表中的估价值;
从CLOSE表中移出节点,并放入OPEN表中;
}
}
}
}//end for
将X节点插入CLOSE表中;
按照估价值将OPEN表中的节点排序;
}//end while
}//end func
按照估价值将OPEN表中的节点排序;
}//end while
}//end func
g
value can be lowered, and if so, you re-open it.
![](https://images.cnblogs.com/OutliningIndicators/ExpandedBlockStart.gif)
OPEN = priority queue containing START
CLOSED = empty set
while lowest rank in OPEN is not the GOAL:
current = remove lowest rank item from OPEN
add current to CLOSED
for neighbors of current:
cost = g(current) + movementcost(current, neighbor)
if neighbor in OPEN and cost less than g(neighbor):
remove neighbor from OPEN, because new path is better
if neighbor in CLOSED and cost less than g(neighbor): **
remove neighbor from CLOSED
if neighbor not in OPEN and neighbor not in CLOSED:
set g(neighbor) to cost
add neighbor to OPEN
set priority queue rank to g(neighbor) + h(neighbor)
set neighbor's parent to current
reconstruct reverse path from goal to start
by following parent pointers
CLOSED = empty set
while lowest rank in OPEN is not the GOAL:
current = remove lowest rank item from OPEN
add current to CLOSED
for neighbors of current:
cost = g(current) + movementcost(current, neighbor)
if neighbor in OPEN and cost less than g(neighbor):
remove neighbor from OPEN, because new path is better
if neighbor in CLOSED and cost less than g(neighbor): **
remove neighbor from CLOSED
if neighbor not in OPEN and neighbor not in CLOSED:
set g(neighbor) to cost
add neighbor to OPEN
set priority queue rank to g(neighbor) + h(neighbor)
set neighbor's parent to current
reconstruct reverse path from goal to start
by following parent pointers
(**) This should never happen if you have an monotone admissible heuristic. However in games we often have inadmissible heuristics.
3.
void AstarPathfinder::FindPath(int sx, int sy, int dx, int dy)
{
NODE *Node, *BestNode;
int TileNumDest;
//得到目标位置,作判断用
TileNumDest = TileNum(sx, sy);
//生成Open和Closed表
OPEN=( NODE* )calloc(1,sizeof( NODE ));
CLOSED=( NODE* )calloc(1,sizeof( NODE ));
//生成起始节点,并放入Open表中
Node=( NODE* )calloc(1,sizeof( NODE ));
Node->g = 0;
//这是计算h值
Node->h = (dx-sx)*(dx-sx) + (dy-sy)*(dy-sy); //此处按道理应用开方
//这是计算f值,即估价值
Node->f = Node->g+Node->h;
Node->NodeNum = TileNum(dx, dy);
Node->x = dx;
Node->y = dy;
OPEN->NextNode=Node; // make Open List point to first node
for (;;)
{ //从Open表中取得一个估价值最好的节点
BestNode=ReturnBestNode();
//如果该节点是目标节点就退出
if (BestNode->NodeNum == TileNumDest) // if we've found the
//end, break and finish
break;
//否则生成子节点
GenerateSuccessors(BestNode,sx,sy);
}
PATH = BestNode;
}
void AstarPathfinder::GenerateSuccessors(NODE *BestNode,int dx,int dy)
{
int x, y;
//哦!依次生成八个方向的子节点,简单!
// Upper-Left
if ( FreeTile(x=BestNode->x-TILESIZE, y=BestNode->y-TILESIZE) )
GenerateSucc(BestNode,x,y,dx,dy);
// Upper
if ( FreeTile(x=BestNode->x, y=BestNode->y-TILESIZE) )
GenerateSucc(BestNode,x,y,dx,dy);
// Upper-Right
if ( FreeTile(x=BestNode->x+TILESIZE, y=BestNode->y-TILESIZE) )
GenerateSucc(BestNode,x,y,dx,dy);
// Right
if ( FreeTile(x=BestNode->x+TILESIZE, y=BestNode->y) )
GenerateSucc(BestNode,x,y,dx,dy);
// Lower-Right
if ( FreeTile(x=BestNode->x+TILESIZE, y=BestNode->y+TILESIZE) )
GenerateSucc(BestNode,x,y,dx,dy);
// Lower
if ( FreeTile(x=BestNode->x, y=BestNode->y+TILESIZE) )
GenerateSucc(BestNode,x,y,dx,dy);
// Lower-Left
if ( FreeTile(x=BestNode->x-TILESIZE, y=BestNode->y+TILESIZE) )
GenerateSucc(BestNode,x,y,dx,dy);
// Left
if ( FreeTile(x=BestNode->x-TILESIZE, y=BestNode->y) )
GenerateSucc(BestNode,x,y,dx,dy);
}
void AstarPathfinder::GenerateSucc(NODE *BestNode,int x,int y,int dx,int dy)
{
int g, TileNumS, c = 0;
NODE *Old, *Successor;
//计算子节点的g值
g = BestNode->g+1; //g(Successor)=g(BestNode)+cost of getting
//from BestNode to Successor
TileNumS = TileNum(x,y); // identification purposes
//子节点再Open表中吗?
if ( (Old=CheckOPEN(TileNumS)) != NULL ) // if equal to NULL then
//not in OPEN list, else it returns the Node in Old
{
//若在
for( c = 0; c < 8; c++)
if( BestNode->Child[c] == NULL ) // Add Old to the list of
// BestNode's Children (or Successors).
break;
BestNode->Child[c] = Old;
//比较Open表中的估价值和当前的估价值(只要比较g值就可以了)
if ( g < Old->g ) // if our new g value is < Old's then
//reset Old's parent to point to BestNode
{
//当前的估价值小就更新Open表中的估价值
Old->Parent = BestNode;
Old->g = g;
Old->f = g + Old->h;
}
}
else //在Closed表中吗?
{
if ( (Old=CheckCLOSED(TileNumS)) != NULL ) // if equal to NULL then
// not in OPEN list, else it returns the Node in Old
{
//若在
for( c = 0; c< 8; c++)
if ( BestNode->Child[c] == NULL ) // Add Old to the list of
//BestNode's Children (or Successors).
break;
BestNode->Child[c] = Old;
//比较Closed表中的估价值和当前的估价值(只要比较g值就可以了)
if ( g < Old->g ) // if our new g value is < Old's then
// reset Old's parent to point to BestNode
{
//当前的估价值小就更新Closed表中的估价值
Old->Parent = BestNode;
Old->g = g;
Old->f = g + Old->h;
//再依次更新Old的所有子节点的估价值
PropagateDown(Old); // Since we changed the g value of
//Old,we need to propagate this new
//value downwards, i.e.
// do a Depth-First traversal of the tree!
}
}
else//不在Open表中也不在Close表中
{
//生成新的节点
Successor = ( NODE* )calloc(1,sizeof( NODE ));
Successor->Parent = BestNode;
Successor->g = g;
Successor->h = (x-dx)*(x-dx) + (y-dy)*(y-dy); // should do
// sqrt(), but since we don't really
Successor->f = g+Successor->h; // care about the distance but
//just which branch looks
Successor->x = x; // better this should suffice.
// Anyayz it's faster.
Successor->y = y;
Successor->NodeNum = TileNumS;
//再插入Open表中,同时排序。
Insert(Successor); // Insert Successor on OPEN list wrt f
for( c =0; c < 8; c++)
if ( BestNode->Child[c] == NULL ) // Add Old to the
// list of BestNode's Children (or Successors).
break;
BestNode->Child[c] = Successor;
}
}
}
{
NODE *Node, *BestNode;
int TileNumDest;
//得到目标位置,作判断用
TileNumDest = TileNum(sx, sy);
//生成Open和Closed表
OPEN=( NODE* )calloc(1,sizeof( NODE ));
CLOSED=( NODE* )calloc(1,sizeof( NODE ));
//生成起始节点,并放入Open表中
Node=( NODE* )calloc(1,sizeof( NODE ));
Node->g = 0;
//这是计算h值
Node->h = (dx-sx)*(dx-sx) + (dy-sy)*(dy-sy); //此处按道理应用开方
//这是计算f值,即估价值
Node->f = Node->g+Node->h;
Node->NodeNum = TileNum(dx, dy);
Node->x = dx;
Node->y = dy;
OPEN->NextNode=Node; // make Open List point to first node
for (;;)
{ //从Open表中取得一个估价值最好的节点
BestNode=ReturnBestNode();
//如果该节点是目标节点就退出
if (BestNode->NodeNum == TileNumDest) // if we've found the
//end, break and finish
break;
//否则生成子节点
GenerateSuccessors(BestNode,sx,sy);
}
PATH = BestNode;
}
void AstarPathfinder::GenerateSuccessors(NODE *BestNode,int dx,int dy)
{
int x, y;
//哦!依次生成八个方向的子节点,简单!
// Upper-Left
if ( FreeTile(x=BestNode->x-TILESIZE, y=BestNode->y-TILESIZE) )
GenerateSucc(BestNode,x,y,dx,dy);
// Upper
if ( FreeTile(x=BestNode->x, y=BestNode->y-TILESIZE) )
GenerateSucc(BestNode,x,y,dx,dy);
// Upper-Right
if ( FreeTile(x=BestNode->x+TILESIZE, y=BestNode->y-TILESIZE) )
GenerateSucc(BestNode,x,y,dx,dy);
// Right
if ( FreeTile(x=BestNode->x+TILESIZE, y=BestNode->y) )
GenerateSucc(BestNode,x,y,dx,dy);
// Lower-Right
if ( FreeTile(x=BestNode->x+TILESIZE, y=BestNode->y+TILESIZE) )
GenerateSucc(BestNode,x,y,dx,dy);
// Lower
if ( FreeTile(x=BestNode->x, y=BestNode->y+TILESIZE) )
GenerateSucc(BestNode,x,y,dx,dy);
// Lower-Left
if ( FreeTile(x=BestNode->x-TILESIZE, y=BestNode->y+TILESIZE) )
GenerateSucc(BestNode,x,y,dx,dy);
// Left
if ( FreeTile(x=BestNode->x-TILESIZE, y=BestNode->y) )
GenerateSucc(BestNode,x,y,dx,dy);
}
void AstarPathfinder::GenerateSucc(NODE *BestNode,int x,int y,int dx,int dy)
{
int g, TileNumS, c = 0;
NODE *Old, *Successor;
//计算子节点的g值
g = BestNode->g+1; //g(Successor)=g(BestNode)+cost of getting
//from BestNode to Successor
TileNumS = TileNum(x,y); // identification purposes
//子节点再Open表中吗?
if ( (Old=CheckOPEN(TileNumS)) != NULL ) // if equal to NULL then
//not in OPEN list, else it returns the Node in Old
{
//若在
for( c = 0; c < 8; c++)
if( BestNode->Child[c] == NULL ) // Add Old to the list of
// BestNode's Children (or Successors).
break;
BestNode->Child[c] = Old;
//比较Open表中的估价值和当前的估价值(只要比较g值就可以了)
if ( g < Old->g ) // if our new g value is < Old's then
//reset Old's parent to point to BestNode
{
//当前的估价值小就更新Open表中的估价值
Old->Parent = BestNode;
Old->g = g;
Old->f = g + Old->h;
}
}
else //在Closed表中吗?
{
if ( (Old=CheckCLOSED(TileNumS)) != NULL ) // if equal to NULL then
// not in OPEN list, else it returns the Node in Old
{
//若在
for( c = 0; c< 8; c++)
if ( BestNode->Child[c] == NULL ) // Add Old to the list of
//BestNode's Children (or Successors).
break;
BestNode->Child[c] = Old;
//比较Closed表中的估价值和当前的估价值(只要比较g值就可以了)
if ( g < Old->g ) // if our new g value is < Old's then
// reset Old's parent to point to BestNode
{
//当前的估价值小就更新Closed表中的估价值
Old->Parent = BestNode;
Old->g = g;
Old->f = g + Old->h;
//再依次更新Old的所有子节点的估价值
PropagateDown(Old); // Since we changed the g value of
//Old,we need to propagate this new
//value downwards, i.e.
// do a Depth-First traversal of the tree!
}
}
else//不在Open表中也不在Close表中
{
//生成新的节点
Successor = ( NODE* )calloc(1,sizeof( NODE ));
Successor->Parent = BestNode;
Successor->g = g;
Successor->h = (x-dx)*(x-dx) + (y-dy)*(y-dy); // should do
// sqrt(), but since we don't really
Successor->f = g+Successor->h; // care about the distance but
//just which branch looks
Successor->x = x; // better this should suffice.
// Anyayz it's faster.
Successor->y = y;
Successor->NodeNum = TileNumS;
//再插入Open表中,同时排序。
Insert(Successor); // Insert Successor on OPEN list wrt f
for( c =0; c < 8; c++)
if ( BestNode->Child[c] == NULL ) // Add Old to the
// list of BestNode's Children (or Successors).
break;
BestNode->Child[c] = Successor;
}
}
}
[翻译]A*寻路初探 GameDev.net
http://blog.vckbase.com/panic/archive/2005/03/20/3778.html
[翻译]A*分层寻路
http://blog.vckbase.com/panic/archive/2005/07/21/9906.html
Fixing Pathfinding Once and For All
http://www.ai-blog.net/archives/000152.html
A*(A星)算法(一)
http://hi.baidu.com/%BA%DA%B5%C4%B7%A2%D7%CF/blog/item/60e3483dce5bb8c29e3d62e0.html
初识A*算法
http://blog.csdn.net/zheng80037/archive/2007/06/04/1636953.aspx
[翻译]在A*寻路中使用二叉堆
http://blog.vckbase.com/panic/archive/2005/03/28/4144.html
二叉堆的模板代码--续“关于一道算法题《编写算法,从10亿个浮点数当中,选出其中最大的10000个》”
http://blog.vckbase.com/panic/archive/2006/06/19/20869.html