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A star算法优化一
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A*算法 求最優解
算法一直維護兩個表: Open和Close
將起點S加入Open中
將所有S可到達的點（障礙物以及位于Close表中的點均看成不可達）加入到Open中。將起點從Open中刪去，并加入到Close中
①從Open中刪去F值最小的點Min，并將其加入到Close中
②將Min點所有可到達的點加入Open中，并設這些點的父節點為Min。若某點已經在Open中，則比較其F值，若新路徑F值較小，說明從Min走路更短，更新其父節點為Min；否則不更新此點
循環①②，直到Open中出現目的點E?
公式表示為： f(n)=g(n)+h(n),
其中 f(n) 是從初始狀態經由狀態n到目標狀態的代價估計，
g(n) 是在狀態空間中從初始狀態到狀態n的實際代價，
h(n) 是從狀態n到目標狀態的最佳路徑的估計代價。
通俗一點講:
g(n)代表你從起始點到下一點的實際距離（制定到下一點的距離的規則）
h(n)是自己設計的函數，可以是到目的地大致的距離
可將循環過程封裝成函數：
[cpp]?view plaincopy
????while?(isNotEnd())?{??????????Find_deleteMinFromOpen_AddToClose();??????????putReachableIntoOpen(close.back());??????}??
舉個栗子：
對于以下圖：5行15列
000000000000000
0000000x0000000
00s0000x0000e00
0000000x0000000
000000000000000
其中x為墻壁，s為起點，e為終點，建立合適的模型，調用A star算法，找到一條s到e的最短路徑。
取直走G值為10，斜走G值為14
這里H值設定為無視障礙到達終點所需的 步數*10
我們看開始的幾步：
000000000000000
0000000x0000000
00s0000x0000e00
0000000x0000000
000000000000000
灰色的點G=10，H=9*10 ,其F值最小，加入Close
000000000000000
0000000x0000000
00s0000x0000e00
0000000x0000000
000000000000000
灰色的點G=10+10，H=8*10 ,其F值最小，加入Close
000000000000000
0000000x0000000
00s0000x0000e00
0000000x0000000
000000000000000
灰色的點G=10+10+10，H=7*10 ,其F值最小，加入Close
000000000000000
0000000x0000000
00s0000x0000e00
0000000x0000000
000000000000000
灰色的點G=10+10+10+10，H=6*10 ,其F值最小，加入Close
以此循環，直到e在Open中，此時只需要沿著父節點往回走就可以到達起點了，這條路就是當前情況下最優的解
結果：
000000000000000
0000000x0000000
00s0000x0000e00
0000000x0000000
000000000000000
C++實現：
[cpp]?view plaincopy
#include#include#include#includeusing?namespace?std;??char?square[5][15]?=?{??????'0','0','0','0','0','0','0','0','0','0','0','0','0','0','0',??????'0','0','0','0','0','0','0','x','0','0','0','0','0','0','0',??????'0','0','s','0','0','0','0','x','0','0','0','0','e','0','0',??????'0','0','0','0','0','0','0','x','0','0','0','0','0','0','0',??????'0','0','0','0','0','0','0','0','0','0','0','0','0','0','0'??};????class?point?{????public:??????point(char?s)?{??????????v?=?s;??????????G?=?0;??????????H?=?0;??????????F?=?0;??????}??????pair?ParentPosi;??????pair?posi;??????char?v;??????int?F;??????int?G;??????int?H;??????int?UpdateF()?{??????????F?=?G?+?H;??????????return?F;??????}??????int?UpdateH()?{??????????int?x?=?posi.first?-?2;??????????int?y?=?posi.second?-?12;??????????x?*=?10;??????????y?*=?10;??????????if?(x?<?0)?{??????????????x?=?-x;??????????}??????????if?(y?<?0)?{??????????????y?=?-y;??????????}??????????H?=?x?+?y;??????????return?H;??????}??????void?setPosi(pair?x)?{??????????posi?=?x;??????}??????void?setParentPosi(pair?x)?{??????????ParentPosi=?x;??????}??????void?setG(int?g)?{??????????G?=?g;??????}??????void?setH(int?h)?{??????????H?=?h;??????}??????point?&operator?=?(point?&s)?{??????????(*this).v=(s).v;??????????(*this).ParentPosi?=?s.ParentPosi;??????????(*this).posi?=?s.posi;??????????(*this).F?=?s.F;??????????(*this).G?=?s.G;??????????(*this).H?=?s.H;??????????return?*this;??????}??};??vector?open;??vector?close;??point?squ[5][15]?=?{??????0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,??????0,0,0,0,0,0,0,'x',0,0,0,0,0,0,0,??????0,0,'s',0,0,0,0,'x',0,0,0,0,'e',0,0,??????0,0,0,0,0,0,0,'x',0,0,0,0,0,0,0,??????0,0,0,0,0,0,0,0,0,0,0,0,0,0,0??};??bool?isInOpenList(pair?s)?{??????for?(int?i?=?0;i<open.size();i++)?{??????????if?(open[i].posi?==?s)?{??????????????return?true;??????????}??????}??????return?false;??}??bool?isInCloseList(pair?s)?{??????for?(int?i?=?0;i<close.size();i++)?{??????????if?(close[i].posi?==?s)?{??????????????return?true;??????????}??????}??????return?false;??}??void?putReachableIntoOpen(point?min)?{??????int?x?=?min.posi.first;??????int?y?=?min.posi.second;????????int?direc[8][2]?=?{??????????0,1,??????????1,1,??????????1,0,??????????1,-1,??????????0,-1,??????????-1,-1,??????????-1,0,??????????-1,1??????};??????for?(int?i?=?0;i?<?8;i++)?{??????????x?=?x?+?direc[i][0];??????????y?=?y?+?direc[i][1];??????????if?(isInOpenList(make_pair(x,?y))&&close.size()>0)?{??????????????int?tempi?=?0;??????????????for?(int?i?=?0;i?<?open.size();i++)?{??????????????????if?(open[i].posi?==?make_pair(x,?y))?{??????????????????????tempi?=?i;??????????????????}??????????????}??????????????if?(direc[i][0]?*?direc[i][1]?!=?0)?{??????????????????int?G_now?=?close.back().G?+?14;??????????????????if?(G_now?<?open[tempi].G)?{???????????????????????open[tempi].ParentPosi?=?make_pair(x,?y);??????????????????????squ[open[tempi].posi.first][open[tempi].posi.second].ParentPosi?=?make_pair(x,?y);??????????????????}??????????????}??????????????else?{??????????????????int?G_now?=?close.back().G?+?10;??????????????}??????????????continue;??????????}????????????????????if?((!isInOpenList(make_pair(x,?y)))?&&?(!isInCloseList(make_pair(x,y)))&&x?>=?0?&&?x?<?5?&&?square[x][y]?!=?'x')?{??????????????squ[x][y].setParentPosi(min.posi);??????????????open.push_back(squ[x][y]);??????????????if?(direc[i][0]?*?direc[i][1]?!=?0)?{??????????????????squ[x][y].setG(squ[x][y].G+14);??????????????}??????????????else?{??????????????????squ[x][y].setG(squ[x][y].G?+?10);??????????????}????????????????????????}??????????x?=?x?-?direc[i][0];??????????y?=?y?-?direc[i][1];??????}????????}??void?Find_deleteMinFromOpen_AddToClose()?{??????point?min_=?open[0];??????int?tempi?=?0;??????for?(int?i?=?0;i?<?open.size();i++)?{??????????if?(open[i].UpdateF()?<?min_.UpdateF())?{??????????????min_?=?open[i];??????????????tempi?=?i;??????????}??????}??????close.push_back(min_);??????std::vector::iterator?it=open.begin()+tempi;??????open.erase(it);????????????????????}??bool?isNotEnd()?{??????for?(int?i=0;i<open.size();i++)?{??????????if?(open[i].v?==?'e')?{??????????????open[i].ParentPosi=close.back().posi;??????????????return?false;??????????}??????}??????return?true;??}????void?findPath(pair?begin,pairend)?{????????????open.push_back(squ[2][2]);??????putReachableIntoOpen(squ[2][2]);??????int?tempi?=?0;??????for?(int?i?=?0;i?<?open.size();i++)?{??????????if?(open[i].v?==?'s')?{??????????????tempi?=?i;??????????}??????}??????std::vector::iterator?it?=?open.begin()+tempi;??????????????while?(isNotEnd())?{??????????Find_deleteMinFromOpen_AddToClose();??????????putReachableIntoOpen(close.back());??????}??}??void?print_path()?{??????for?(int?i?=?0;i?<?5;i++)?{??????????for?(int?j?=?0;j?<?15;j++)?{??????????????squ[i][j].posi?=?make_pair(i,?j);??
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