Background: The project needs to be exposed to this algorithm. The following are some self-study results. If there are any shortcomings, you are welcome to point out and accept it with humility. I made a PPT to report, here I use the screenshot of my PPT directly. Some pictures are from the Internet. If there is any infringement, delete them immediately. The following blog posts are only used as study notes.
table of Contents
What problem does the A* algorithm solve
The basic principle of A* algorithm
The detailed principle of the A* algorithm
Definition of the detailed principle of A* algorithm
The initial setting of the detailed principle of the A* algorithm
The detailed principle of the A* algorithm, the pathfinding principle
The end condition of the detailed principle of A* algorithm
Detailed steps of A* algorithm pathfinding
An example of the A* algorithm
A* algorithm definition pseudo code (C++)
Pathfinding pseudo code of A* algorithm (C++)
Python+PyQt code implementation
A* pathfinding algorithm
What problem does the A* algorithm solve
The basic principle of A* algorithm
The detailed principle of the A* algorithm
Definition of the detailed principle of A* algorithm
The initial setting of the detailed principle of the A* algorithm
The detailed principle of the A* algorithm, the pathfinding principle
The end condition of the detailed principle of A* algorithm
Detailed steps of A* algorithm pathfinding
S (start) starting point E (End) ending point
An example of the A* algorithm
If you still don’t understand, you can refer to my handwritten calculation steps, and if you don’t understand, you can send me a private message. (The script is a bit ugly)
Pseudo code of A* algorithm
A* algorithm definition pseudo code (C++)
//定义
int G;// 表示从起点 A 移动到网格上指定方格的移动耗费 (上下左右，还可沿斜方向移动)
int old_G;//旧G 第一次：从起点 A 直接移动到 A 四周方格的移动耗费 ；上次更新得到的G
int new_G; //新G 从起点 A 经过当前搜索中心点到其四周指定点的移动耗费
int H;//表示从指定的方格移动到终点 B 的预计耗费 (H 有很多计算方法, 这里我们设定只可以上下左右移动)
int F=G+H;//表示该点的总耗费
int open_list//一个记录下所有被考虑来寻找最短路径的格子
int close_list //一个记录下不会再被考虑的格子
typedef struct point{
bool Is_Wall;
struct point* father;//父节点
}Point;
point* start_point;
point* end_point
point* min_point;
point* now_point; Pathfinding pseudo code of A* algorithm (C++)
//FindPath
do{
//确定中心搜索点，上一个中心点关闭，新的中心点开启
查找：Find the minimumm "point" of "F" from the "open_list" center
"now_point" = "min_point";//minimumm point
"now_point"添加到"close_list";
//新中心点的周围点开启，新中心点关闭
循环遍历："now_point"相邻的周围8格"s_now_point"中的每一个
//这一块它指的就是now_point周围8点当前搜索点 s_now_point，为了简单直接用它表示
if (它不可通过||它已经在"close_list"中){
什么也不做;
} else if (它不在开启列表中){
把它添加进"open_list";
把"now_point"作为这它的"father",计算它的"F","G","H";
}else if (它已经在开启列表中){//通过G来判断是否需要更新
if (new_G < old_G){
更新它的"father"为当前中心搜索点"now_point";
更新它的"G"与"F" ;
} else{
不更新，保持原来的"father", "G"与"F" ;
}
}
} while(目标格"end_point"已经在"open_list"||"open_list"==NULL)
//存在路径：目标格"end_point"已经在"open_list"
//不存在路径： "open_list"==NULL，搜索了所有可能的点
Python+PyQt code implementation
Code content (runnable)
import time,sys
from PyQt5.QtWidgets import QDialogButtonBox,QDialog,QMainWindow,QGridLayout,QTextEdit,QLineEdit,QWidget, QMessageBox, QApplication,QLabel,QPushButton,QHBoxLayout,QVBoxLayout
from PyQt5.QtCore import Qt,QTimer,QObject,pyqtSignal,QBasicTimer
from PyQt5.QtGui import QPainter, QColor, QFont,QPen
import json
class config:
WIDTH=20#地图列数
HEIGHT=20#地图行数
blockLength=30#绘制画面时每一个节点方块的边长
class point:#点类（每一个唯一坐标只有对应的一个实例）
_list=[]#储存所有的point类实例
_tag=True#标记最新创建的实例是否为_list中的已有的实例，True表示不是已有实例
def __new__(cls,x,y):#重写new方法实现对于同样的坐标只有唯一的一个实例
for i in point._list:
if i.x==x and i.y==y:
point._tag=False
return i
nt=super(point,cls).__new__(cls)
point._list.append(nt)
return nt
def __init__(self,x,y):
if point._tag:
self.x=x
self.y=y
self.father=None
self.F=0#当前点的评分 F=G+H
self.G=0#起点到当前节点所花费的消耗
self.cost=0#父节点到此节点的消耗
else:
point._tag=True
@classmethod
def clear(cls):#clear方法，每次搜索结束后，将所有点数据清除，以便进行下一次搜索的时候点数据不会冲突。
point._list=[]
def __eq__(self,T):#重写==运算以便实现point类的in运算
if type(self)==type(T):
return (self.x,self.y)==(T.x,T.y)
else:
return False
def __str__(self):
return'(%d,%d)[F=%d,G=%d,cost=%d][father:(%s)]'%(self.x,self.y,self.F,self.G,self.cost,str((self.father.x,self.father.y)) if self.father!=None else 'null')
class A_Search:#核心部分，寻路类
def __init__(self,arg_start,arg_end,arg_map):
self.start=arg_start#储存此次搜索的开始点
self.end=arg_end#储存此次搜索的目的点
self.Map=arg_map#一个二维数组，为此次搜索的地图引用
self.open=[]#开放列表：储存即将被搜索的节点
self.close=[]#关闭列表：储存已经搜索过的节点
self.result=[]#当计算完成后，将最终得到的路径写入到此属性中
self.count=0#记录此次搜索所搜索过的节点数
self.useTime=0#记录此次搜索花费的时间--在此演示中无意义，因为process方法变成了一个逐步处理的生成器，统计时间无意义。
#开始进行初始数据处理
self.open.append(arg_start)
def cal_F(self,loc):
print('计算值：',loc)
G=loc.father.G+loc.cost
H=self.getEstimate(loc)
F=G+H
print("F=%d G=%d H=%d"%(F,G,H))
return {'G':G,'H':H,'F':F}
def F_Min(self):#搜索open列表中F值最小的点并将其返回，同时判断open列表是否为空，为空则代表搜索失败
if len(self.open)<=0:
return None
t=self.open[0]
for i in self.open:
if i.F<t.F:
t=i
return t
def getAroundPoint(self,loc):#获取指定点周围所有可通行的点，并将其对应的移动消耗进行赋值。
l=[(loc.x,loc.y+1,10),(loc.x+1,loc.y+1,14),(loc.x+1,loc.y,10),(loc.x+1,loc.y-1,14),(loc.x,loc.y-1,10),(loc.x-1,loc.y-1,14),(loc.x-1,loc.y,10),(loc.x-1,loc.y+1,14)]
for i in l[::-1]:
if i[0]<0 or i[0]>=config.HEIGHT or i[1]<0 or i[1]>=config.WIDTH:
l.remove(i)
nl=[]
for i in l:
if self.Map[i[0]][i[1]]==0:
nt=point(i[0],i[1])
nt.cost=i[2]
nl.append(nt)
return nl
def addToOpen(self,l,father):#此次判断的点周围的可通行点加入到open列表中，如此点已经在open列表中则对其进行判断，如果此次路径得到的F值较之之前的F值更小，则将其父节点更新为此次判断的点，同时更新F、G值。
for i in l:
if i not in self.open:
if i not in self.close:
i.father=father
self.open.append(i)
r=self.cal_F(i)
i.G=r['G']
i.F=r['F']
else:
tf=i.father
i.father=father
r=self.cal_F(i)
if i.F>r['F']:
i.G=r['G']
i.F=r['F']
# i.father=father
else:
i.father=tf
def getEstimate(self,loc):#H :从点loc移动到终点的预估花费
return (abs(loc.x-self.end.x)+abs(loc.y-self.end.y))*10
def DisplayPath(self):#在此演示中无意义
print('搜索花费的时间:%.2fs.迭代次数%d,路径长度:%d'%(self.useTime,self.count,len(self.result)))
if self.result!=None:
for i in self.result:
self.Map[i.x][i.y]=8
for i in self.Map:
for j in i:
if j==0:
print('%s'%'□',end='')
elif j==1:
print('%s'%'▽',end='')
elif j==8:
print('%s'%'★',end='')
print('')
else:
print('搜索失败，无可通行路径')
def process(self):#使用yield将process方法变成一个生成器，可以逐步的对搜索过程进行处理并返回关键数据
while True:
self.count+=1
tar=self.F_Min()#先获取open列表中F值最低的点tar
if tar==None:
self.result=None
self.count=-1
break
else:
aroundP=self.getAroundPoint(tar)#获取tar周围的可用点列表aroundP
self.addToOpen(aroundP,tar)#把aroundP加入到open列表中并更新F值以及设定父节点
self.open.remove(tar)#将tar从open列表中移除
self.close.append(tar)#已经迭代过的节点tar放入close列表中
if self.end in self.open:#判断终点是否已经处于open列表中
e=self.end
self.result.append(e)
while True:
e=e.father
if e==None:
break
self.result.append(e)
yield (tar,self.open,self.close)
break
# self.repaint()
# print('返回')
yield (tar,self.open,self.close)
time.sleep(5)#暂停
self.useTime=time2-time1
class GameBoard(QMainWindow):#可视化类，pyqt5进行编写。
def __init__(self):
print('初始化地图...')
self.Map=[]
for i in range(config.HEIGHT):
col=[]
for j in range(config.WIDTH):
col.append(0)
self.Map.append(col)
self.startPoint=None
self.endPoint=None
self.search=None
self.centerTimer=None
self.yi=None
self.special=None
self.displayFlush=False
super().__init__()
print('初始化UI...')
self.initUI()
def initUI(self):
#开始初始化UI部分
#创建UI控件
self.label_tips=QLabel("<p style='color:green'>使用说明：</p>右键单击格子选定起始点,左键格子选定格子为墙壁或删除墙壁。\n<p style='color:green'>颜色说明：</p>\n黄色代表起点，绿色代表终点，黑色代表墙壁，红色代表待搜索的open列表，灰色代表已搜索过的close列表，蓝色代表当前搜索到的路径",self)
self.label_display=QLabel("",self)
self.button_start=QPushButton("开始搜索",self)
self.button_clearSE=QPushButton("重选起始点",self)
self.button_clearWall=QPushButton("清空地图墙壁",self)
self.button_saveMap=QPushButton("保存地图",self)
self.button_loadMap=QPushButton("加载地图",self)
#设置控件属性
self.label_tips.setWordWrap(True)
self.label_display.setWordWrap(True)
#设置控件样式
self.label_display.setStyleSheet("border:1px solid black")
self.label_display.setAlignment(Qt.AlignLeft)
self.label_display.setAlignment(Qt.AlignTop)
#设置控件的尺寸和位置
self.label_tips.resize(200,150)
self.button_saveMap.resize(80,30)
self.button_loadMap.resize(80,30)
self.label_display.resize(200,300)
self.label_tips.move(100+(config.WIDTH-1)*config.blockLength,0)
self.label_display.move(100+(config.WIDTH-1)*config.blockLength,400)
self.button_start.move(100+(config.WIDTH-1)*config.blockLength,200)
self.button_clearSE.move(100+(config.WIDTH-1)*config.blockLength,250)
self.button_clearWall.move(100+(config.WIDTH-1)*config.blockLength,300)
self.button_saveMap.move(100+(config.WIDTH-1)*config.blockLength,350)
self.button_loadMap.move(200+(config.WIDTH-1)*config.blockLength,350)
#给控件绑定事件
self.button_start.clicked.connect(self.button_StartEvent)
self.button_clearSE.clicked.connect(self.button_Clear)
self.button_clearWall.clicked.connect(self.button_Clear)
self.button_saveMap.clicked.connect(self.button_SaveMap)
self.button_loadMap.clicked.connect(self.button_LoadMap)
#UI初始化完成
self.setGeometry(0, 0, 150+(config.WIDTH*config.blockLength-config.blockLength)+200, 150+(config.HEIGHT*config.blockLength-config.blockLength))
self.setMinimumSize(150+(config.WIDTH*config.blockLength-config.blockLength)+200, 150+(config.HEIGHT*config.blockLength-config.blockLength))
self.setMaximumSize(150+(config.WIDTH*config.blockLength-config.blockLength)+200, 150+(config.HEIGHT*config.blockLength-config.blockLength))
self.setWindowTitle('A*搜索')
self.show()
def addDisplayText(self,text):
if self.displayFlush:
self.label_display.setText(text+'\n')
self.displayFlush=False
else:
self.label_display.setText(self.label_display.text()+text+'\n')
def mousePressEvent(self,event):
x,y=event.x()-50,event.y()-50
x=x//config.blockLength
y=y//config.blockLength
if x>=0 and x<config.WIDTH and y>=0 and y<config.HEIGHT:
if event.button()==Qt.LeftButton:
if (x,y)!=self.startPoint and (x,y)!=self.endPoint:
self.Map[y][x]=(1 if self.Map[y][x]==0 else 0)
if event.button()==Qt.RightButton:
if self.Map[y][x]==0:
if self.startPoint==None:
self.startPoint=(x,y)
self.addDisplayText('添加了一个起点:(%d,%d)'%(x,y))
elif self.endPoint==None and self.startPoint!=(x,y):
self.endPoint=(x,y)
self.addDisplayText('添加了一个终点:(%d,%d)'%(x,y))
self.repaint()
def button_StartEvent(self):
sender=self.sender()
print(sender)
if self.startPoint!=None and self.endPoint!=None:
if self.centerTimer==None:
self.centerTimer=QBasicTimer()
self.button_start.setEnabled(False)
self.button_clearSE.setEnabled(False)
self.button_clearWall.setEnabled(False)
self.centerTimer.start(200,self)
self.search=A_Search(point(self.startPoint[1],self.startPoint[0]),point(self.endPoint[1],self.endPoint[0]),self.Map)
self.yi=self.search.process()
self.addDisplayText('开始进行搜索')
def button_SaveMap(self):
with open('map.txt','w') as f:
f.write(json.dumps(self.Map))
self.addDisplayText('地图保存成功-->map.txt')
# else:
# self.addDisplayText('地图保存失败')
def button_LoadMap(self):
try:
with open('map.txt','r') as f:
self.Map=json.loads(f.read())
config.HEIGHT=len(self.Map)
config.WIDTH=len(self.Map[0])
self.addDisplayText('地图加载成功')
self.repaint()
except Exception as e:
print('失败',e,type(e))
if type(e)==FileNotFoundError:
self.addDisplayText('地图加载失败:地图文件不存在')
elif type(e)==json.decoder.JSONDecodeError:
self.addDisplayText('地图加载失败:错误的地图文件')
def button_Clear(self):
sender=self.sender()
print(self.button_clearSE,type(self.button_clearSE))
if sender==self.button_clearSE:
self.startPoint=None
self.endPoint=None
self.repaint()
self.addDisplayText('清空起始点')
elif sender==self.button_clearWall:
for i in range(len(self.Map)):
for j in range(len(self.Map[i])):
self.Map[i][j]=0
self.repaint()
self.addDisplayText('清空所有墙壁')
def paintEvent(self, event):
qp = QPainter()
qp.begin(self)
self.drawBoard(event,qp)
qp.end()
def drawBoard(self, event, qp):
self.drawMap(qp)
def drawMap(self,qp):#画面绘制方法，每次地图有所改动都将重绘
time1=time.time()
if self.search!=None:
if self.special!=None:
e=self.special[0]
path=[e]
while True:
e=e.father
if e!=None:
path.append(e)
else:
break
else:
path=None
pen=QPen(QColor(0,0,0),1,Qt.SolidLine)
qp.setPen(pen)
for i in range(len(self.Map)):
for j in range(len(self.Map[i])):
wordTag=False
if i==self.search.start.x and j==self.search.start.y:
qp.setBrush(QColor(255,255,0))
elif i==self.search.end.x and j==self.search.end.y:
qp.setBrush(QColor(100,200,50))
else:
if self.Map[i][j]==0:
tagx=True
if path:
for k in path:
if k.x==i and k.y==j:
tagx=False
qp.setBrush(QColor(0,100,255))
if tagx:
if self.special!=None:
if i==self.special[0].x and j==self.special[0].y:
qp.setBrush(QColor(0,255,0))
else:
tag=True
for k in self.special[1]:
if k.x==i and k.y==j:
tag=False
wordTag=True
word=str(k.F)
qp.setBrush(QColor(150,0,0))
break
else:
qp.setBrush(QColor(220,220,220))
if tag:
for k in self.special[2]:
if k.x==i and k.y==j:
qp.setBrush(QColor(150,150,150))
break
else:
qp.setBrush(QColor(220,220,220))
else:
qp.setBrush(QColor(220,220,220))
elif self.Map[i][j]==1:
qp.setBrush(QColor(0,0,0))
else:
qp.setBrush(QColor(255,0,0))
qp.drawRect(50+j*config.blockLength,50+i*config.blockLength,config.blockLength,config.blockLength)
if wordTag:
qp.setFont(QFont('楷体',5,QFont.Light))
qp.drawText(50+10+j*config.blockLength,50+10+i*config.blockLength,word)
wordTag=False
#time.sleep(20)
else:
for i in range(len(self.Map)):
for j in range(len(self.Map[i])):
if (j,i)==self.startPoint:
qp.setBrush(QColor(255,255,0))
elif (j,i)==self.endPoint:
qp.setBrush(QColor(100,200,50))
else:
if self.Map[i][j]==0:
qp.setBrush(QColor(220,220,220))
elif self.Map[i][j]==1:
qp.setBrush(QColor(0,0,0))
else:
qp.setBrush(QColor(255,0,0))
qp.drawRect(50+j*config.blockLength,50+i*config.blockLength,config.blockLength,config.blockLength)
time2=time.time()
#time.sleep(20)
# print('绘制时间：',time2-time1)
def timerEvent(self,e):
try:
data=next(self.yi)
except Exception as e:
self.addDisplayText('搜索结束:')
print('搜索结束！')
if self.search.result==None:
self.addDisplayText('未找到可行路径')
print('搜索结束！')
else:
self.addDisplayText('总计搜索节点数：%d'%self.search.count)
self.addDisplayText('最终路径长度：%d'%len(self.search.result))
self.centerTimer.stop()
self.search=None
self.yi=None
self.special=None
point.clear()
self.button_start.setEnabled(True)
self.button_clearSE.setEnabled(True)
self.button_clearWall.setEnabled(True)
self.displayFlush=True
else:
self.special=data
self.repaint()
if __name__ == '__main__':
app = QApplication(sys.argv)
ex = GameBoard()
sys.exit(app.exec_())
Note: You can set the pause time when the code is running dynamically (about the time.sleep(5) statement on line 145)
operation result
Output F and parent node of each point calculated every time, just look at the picture!
Detailed list
初始化地图...
初始化UI...
<PyQt5.QtWidgets.QPushButton object at 0x0000017CC699AC18>
计算值： (2,3)[F=0,G=0,cost=10][father:((2, 2))]
F=40 G=10 H=30
计算值： (3,3)[F=0,G=0,cost=14][father:((2, 2))]
F=54 G=14 H=40
计算值： (3,2)[F=0,G=0,cost=10][father:((2, 2))]
F=60 G=10 H=50
计算值： (3,1)[F=0,G=0,cost=14][father:((2, 2))]
F=74 G=14 H=60
计算值： (2,1)[F=0,G=0,cost=10][father:((2, 2))]
F=60 G=10 H=50
计算值： (1,1)[F=0,G=0,cost=14][father:((2, 2))]
F=74 G=14 H=60
计算值： (1,2)[F=0,G=0,cost=10][father:((2, 2))]
F=60 G=10 H=50
计算值： (1,3)[F=0,G=0,cost=14][father:((2, 2))]
F=54 G=14 H=40
计算值： (3,3)[F=54,G=14,cost=10][father:((2, 3))]
F=60 G=20 H=40
计算值： (3,2)[F=60,G=10,cost=14][father:((2, 3))]
F=74 G=24 H=50
计算值： (1,2)[F=60,G=10,cost=14][father:((2, 3))]
F=74 G=24 H=50
计算值： (1,3)[F=54,G=14,cost=10][father:((2, 3))]
F=60 G=20 H=40
计算值： (4,4)[F=0,G=0,cost=14][father:((3, 3))]
F=68 G=28 H=40
计算值： (4,3)[F=0,G=0,cost=10][father:((3, 3))]
F=74 G=24 H=50
计算值： (4,2)[F=0,G=0,cost=14][father:((3, 3))]
F=88 G=28 H=60
计算值： (3,2)[F=60,G=10,cost=10][father:((3, 3))]
F=74 G=24 H=50
计算值： (1,2)[F=60,G=10,cost=10][father:((1, 3))]
F=74 G=24 H=50
计算值： (0,2)[F=0,G=0,cost=14][father:((1, 3))]
F=88 G=28 H=60
计算值： (0,3)[F=0,G=0,cost=10][father:((1, 3))]
F=74 G=24 H=50
计算值： (0,4)[F=0,G=0,cost=14][father:((1, 3))]
F=68 G=28 H=40
计算值： (4,3)[F=74,G=24,cost=14][father:((3, 2))]
F=74 G=24 H=50
计算值： (4,2)[F=88,G=28,cost=10][father:((3, 2))]
F=80 G=20 H=60
计算值： (4,1)[F=0,G=0,cost=14][father:((3, 2))]
F=94 G=24 H=70
计算值： (3,1)[F=74,G=14,cost=10][father:((3, 2))]
F=80 G=20 H=60
计算值： (2,1)[F=60,G=10,cost=14][father:((3, 2))]
F=74 G=24 H=50
计算值： (3,1)[F=74,G=14,cost=10][father:((2, 1))]
F=80 G=20 H=60
计算值： (3,0)[F=0,G=0,cost=14][father:((2, 1))]
F=94 G=24 H=70
计算值： (2,0)[F=0,G=0,cost=10][father:((2, 1))]
F=80 G=20 H=60
计算值： (1,0)[F=0,G=0,cost=14][father:((2, 1))]
F=94 G=24 H=70
计算值： (1,1)[F=74,G=14,cost=10][father:((2, 1))]
F=80 G=20 H=60
计算值： (1,2)[F=60,G=10,cost=14][father:((2, 1))]
F=74 G=24 H=50
计算值： (1,1)[F=74,G=14,cost=10][father:((1, 2))]
F=80 G=20 H=60
计算值： (0,1)[F=0,G=0,cost=14][father:((1, 2))]
F=94 G=24 H=70
计算值： (0,2)[F=88,G=28,cost=10][father:((1, 2))]
F=80 G=20 H=60
计算值： (0,3)[F=74,G=24,cost=14][father:((1, 2))]
F=74 G=24 H=50
计算值： (4,5)[F=0,G=0,cost=10][father:((4, 4))]
F=68 G=38 H=30
计算值： (5,5)[F=0,G=0,cost=14][father:((4, 4))]
F=82 G=42 H=40
计算值： (5,4)[F=0,G=0,cost=10][father:((4, 4))]
F=88 G=38 H=50
计算值： (5,3)[F=0,G=0,cost=14][father:((4, 4))]
F=102 G=42 H=60
计算值： (4,3)[F=74,G=24,cost=10][father:((4, 4))]
F=88 G=38 H=50
计算值： (3,5)[F=0,G=0,cost=14][father:((4, 4))]
F=62 G=42 H=20
计算值： (3,6)[F=0,G=0,cost=10][father:((3, 5))]
F=62 G=52 H=10
计算值： (4,6)[F=0,G=0,cost=14][father:((3, 5))]
F=76 G=56 H=20
计算值： (4,5)[F=68,G=38,cost=10][father:((3, 5))]
F=82 G=52 H=30
计算值： (2,5)[F=0,G=0,cost=10][father:((3, 5))]
F=62 G=52 H=10
计算值： (2,6)[F=0,G=0,cost=14][father:((3, 5))]
F=56 G=56 H=0
搜索结束！executable file
The program has been packaged into an exe executable file, click it to use, no py environment is required.
Link: https://pan.baidu.com/s/1TzFK0ODsf1JhfaMHn37uzQ Extraction code: 3kyr