A*算法实现

1.A*基本流程图

2.扩展节点方法

3.A*最短路径条件

代码：

1.main.lua

require "Lib"

--create scene
local gameScene = cc.Scene:create()
gameScene:addChild(GameLayer:create())

2.Lib.lua

require "src/GameLayer"
require "src/Cube"
require "src/Constant"

3.Constant.lua

CubeSplit = 3
CellWidth = cc.Director:getInstance():getWinSize().width/10
CellHeight = cc.Director:getInstance():getWinSize().height/10
CubeWidth = CellWidth - CubeSplit --格子宽
CubeHeight = CellHeight - CubeSplit --格子高

4.Cube.lua

--地图方格
Cube = class("Cube", function ()
	return cc.Node:create()
end)

Cube.CUBE_TYPE_WALL = 1             --墙
Cube.CUBE_TYPE_START = 2            --起点格子
Cube.CUBE_TYPE_DESTANATION = 3      --目标地格子
Cube.CUBE_TYPE_AVIABLE = 4          --可以行走的格子

function Cube:create(row, col, type)
    local view = Cube:new()
    view:__init(row, col, type)
    return view
end

function Cube:__init(row, col, type)
    self.row = row
    self.col = col
    self.type = type

    self:addBgByType()
end

function Cube:addBgByType()
    local layerColor = nil
    local lblDesp = nil
    local fontSize = 15
    local color = {
        black = cc.c3b(0,0,0),
        red = cc.c3b(255,0,255),
        yellow = cc.c3b(255,255,0),
        white = cc.c3b(255,255,255),
        blue = cc.c3b(0,0,255),
        green = cc.c3b(0,255,127)
    }

    if self.type == Cube.CUBE_TYPE_WALL then
        layerColor = cc.LayerColor:create(color.blue, CubeWidth, CubeHeight)  --黑色
        lblDesp = cc.Label:createWithSystemFont("墙","Arial",fontSize)
    elseif self.type == Cube.CUBE_TYPE_START then
        layerColor = cc.LayerColor:create(color.red, CubeWidth, CubeHeight)   --紫红
        lblDesp = cc.Label:createWithSystemFont("起始点","Arial",fontSize)
    elseif self.type == Cube.CUBE_TYPE_DESTANATION then
        layerColor = cc.LayerColor:create(color.yellow, CubeWidth, CubeHeight) --黄
        lblDesp = cc.Label:createWithSystemFont("终点","Arial",fontSize)
    elseif self.type ==  Cube.CUBE_TYPE_AVIABLE then
        layerColor = cc.LayerColor:create(color.white, CubeWidth, CubeHeight)  --白
    else
        layerColor = cc.LayerColor:create(color.green, CubeWidth, CubeHeight)  --白
        layerColor:setOpacity(100)
    end

    layerColor:ignoreAnchorPointForPosition(false)
    self:addChild(layerColor)

    if lblDesp then
        lblDesp:setColor(cc.c3b(0,0,0))
        self:addChild(lblDesp)
    end
end

function Cube:getPositionByRowCol()
    return cc.p( CellWidth * (self.col-0.5), CellHeight * (self.row-0.5))
end

5.GameLayer.lua

GameLayer = class("GameLayer",function()
    return cc.Layer:create()
end)

function GameLayer:create()
    local view = GameLayer.new()
    view:__init()
    return view
end

function GameLayer:__init()
    self:addMap()
end

--是否出界
function GameLayer:checkIsInSide(cube)
    return cube.row >= 1 and cube.row <= 10 and cube.col >= 1 and cube.col <= 10 and not self:checkIsInSide(cube)
end

--判断2个格子是否一样
function GameLayer:isEqual(cube1, cube2)
    return cube1.row == cube2.row and cube1.col == cube2.col
end

--背景格子
function GameLayer:initBg()
    for row = 1, 10 do
        for col = 1, 10 do
            local cube = Cube:create(row, col, Cube.CUBE_TYPE_AVIABLE)
            cube:setPosition(cube:getPositionByRowCol())
            self:addChild(cube)
        end
    end
end

--是否可以行走
function GameLayer:checkIsCanGo(cube)

    if cube.row <= 0 or cube.row > 10  or cube.col <= 0 or cube.col > 10 then
        return false
    end

    for _, cubeTmp in ipairs(self.mapList) do
        if cube.row == cubeTmp.row and cube.col == cubeTmp.col and cubeTmp.type == Cube.CUBE_TYPE_WALL then
            return false
        end
    end
    return true
end

--开始点
function GameLayer:initStart()
    self.startCube = Cube:create(3, 4, Cube.CUBE_TYPE_START)
    self.startCube:setPosition(self.startCube:getPositionByRowCol())
    self:addChild(self.startCube)
    table.insert(self.mapList, self.startCube)
end

--结束点
function GameLayer:initDestination()
    self.desCube = Cube:create(3, 9, Cube.CUBE_TYPE_DESTANATION)
    self.desCube:setPosition(self.desCube:getPositionByRowCol())
    self:addChild(self.desCube)
    table.insert(self.mapList, self.desCube)
end

--墙
function GameLayer:initWall()
    math.randomseed(os.time())
    for i = 1, 60 do
        local row = math.random(1,10)
        local col = math.random(1,10)
        local cube = Cube:create(row, col, Cube.CUBE_TYPE_WALL)
        if not self:isEqual(cube, self.startCube) and not self:isEqual(cube, self.desCube) then
            cube:setPosition(cube:getPositionByRowCol())
            self:addChild(cube)
            table.insert(self.mapList, cube)
        end
    end
end

function GameLayer:clearMap()
    self:removeAllChildren()
    self.mapList = {}
end

--480 * 320
--格子大小  48 * 32
function GameLayer:addMap()
    self:clearMap()
    self:initBg()
    self:initStart()
    self:initDestination()
    self:initWall()
    self:findAStarPath()
end

function GameLayer:tableInclude(cubeList, cube)
    local isResult = false
    for i = 1, #cubeList do
        if self:isEqual(cube, cubeList[i]) then
            isResult = true
            break
        end
    end
    return isResult
end

function GameLayer:tableRemove(cubeList, cube)
    for i = 1, #cubeList do
        if self:isEqual(cube, cubeList[i]) then
            table.remove(cubeList, i)
            break
        end
    end
end

function GameLayer:findValueInTable(cubeList, cube)
    for i = 1, #cubeList do
        if self:isEqual(cube, cubeList[i]) then
            return cubeList[i]
        end
    end
end

function GameLayer:findAStarPath()
    --以左下角为起点，顺时针转一圈
    local dirList = {
        {-1,-1},{-1,0},{-1,1},{0,1},{1,1},{1,0},{1,-1},{0,-1}
    }
    self.openList = {}
    self.closeList = {}

    table.insert(self.openList, self.startCube)
    self.startCube.g = 0
    self.startCube.h = self:getManhattonDis(self.startCube)
    self.startCube.f = self.startCube.g + self.startCube.h

    while true do
    	if #self.openList == 0 then
    	   print("Fail, not find !!!")
    	   break
    	else
            local firstCubeInOpenList = self.openList[1]
            table.remove(self.openList, 1)
            table.insert(self.closeList, firstCubeInOpenList)
    	    if self:isEqual(firstCubeInOpenList, self.desCube) then
    	       self.desCube.parent = firstCubeInOpenList
    	       print("Success, find !!!")
               self:printPath()
    	       break
    	    else
    	       for i = 1, 8 do
    	           local dir = dirList[i]
                   local tmpCube = Cube:create(firstCubeInOpenList.row + dir[1], firstCubeInOpenList.col + dir[2], self.startCube.type)
                   if not self:checkIsCanGo(tmpCube) then

                   elseif not self:tableInclude(self.openList, tmpCube) and not self:tableInclude(self.closeList, tmpCube) then
                       self:getOrGetAndSetCubeFGH(firstCubeInOpenList, tmpCube, i)
                       table.insert(self.openList, tmpCube)
                   elseif self:tableInclude(self.openList, tmpCube) then
                        local newFTmp = self:getOrGetAndSetCubeFGH(firstCubeInOpenList, tmpCube, i, true)
                        if newFTmp < self:findValueInTable(self.openList, tmpCube).f then
                            self:getOrGetAndSetCubeFGH(firstCubeInOpenList, tmpCube, i)
                        end
                   elseif self:tableInclude(self.closeList, tmpCube) then
                        local newFTmp = self:getOrGetAndSetCubeFGH(firstCubeInOpenList, tmpCube, i, true)
                        if newFTmp < self:findValueInTable(self.closeList, tmpCube).f then
                            self:tableRemove(self.closeList, tmpCube)
                            table.insert(self.openList, tmpCube)
                            self:getOrGetAndSetCubeFGH(firstCubeInOpenList, tmpCube, i)
                        end
                   end
    	       end
    	    end

    	    --按照f值升序排列openList
    	    local sortFunction = function(cube1, cube2)
    	       return cube1.f < cube2.f
    	    end
            table.sort(self.openList, sortFunction)
--            self:printOpenList(self.openList)
    	end
    end
end

--打印开放列表
function GameLayer:printOpenList(openList)
    print("==========================================")
    for i = 1, #openList do
        local cube = openList[i]
        print("row:"..cube.row.."   col:"..cube.col.."  f:"..cube.f.."  g:"..cube.g.."  h:"..cube.h)
    end
end

--回溯打印路径
function GameLayer:printPath()
    local parentCube = self.desCube

    local resultPath = {}
    while parentCube.parent ~= nil do
        parentCube  = parentCube.parent
        local row = parentCube.row
        local col = parentCube.col

        local cube = Cube:create(row, col)
        cube:setPosition(cube:getPositionByRowCol())
        self:addChild(cube)
    end
end

--1.isOnlyGetFValue 为true: 只返回curCube的可能设置的临时f值
--2.isOnlyGetFValue为nil或false: 设置curCubed的f,g,h并且返回节点的f值
function GameLayer:getOrGetAndSetCubeFGH(srcCube, curCube, i, isOnlyGetFValue)
    if isOnlyGetFValue then
        local g
        if i == 1 or i == 3 or i == 5 or i == 7 then
            g = srcCube.g + 14
        else
            g = srcCube.g + 10
        end
        local h = self:getManhattonDis(curCube)
        local f = g + h
        return f
    else
        if i == 1 or i == 3 or i == 5 or i == 7 then
            curCube.g =  srcCube.g + 14
        else
            curCube.g =  srcCube.g + 10
        end
        curCube.h = self:getManhattonDis(curCube)
        curCube.f = curCube.g + curCube.h
        curCube.parent = srcCube
        return curCube.f
    end
end

--得到一个节点的曼哈顿距离
function GameLayer:getManhattonDis(cube)
    local value = math.abs(self.desCube.row - cube.row) + math.abs( self.desCube.col - cube.col)
    return value*10
end

return GameLayer

具体代码详见我github工程:

https://git.oschina.net/jianan/AStar/tree/master

截图实例:

说明：在随机生成的墙壁中，给定开始点和结束点，浅绿色部分为A*算法计算出来的最短路径。

1.

2.

3.

总结：当估价函数h选定后，就可以让A*是最优算法，在此处采用的是曼哈顿距离！

其它A*入门视频：

http://m.blog.csdn.net/article/details?id=17187239

http://www.jiangzhongyou.net/forum-40-1.html