一、简介
A算法
A算法是一种典型的启发式搜索算法，建立在Dijkstra算法的基础之上，广泛应用于游戏地图、现实世界中，用来寻找两点之间的最短路径。A算法最主要的是维护了一个启发式估价函数，如式(1)所示。
f(n)=g(n)+h(n)(1)
其中，f(n)是算法在搜索到每个节点时，其对应的启发函数。它由两部分组成，第一部分g(n)是起始节点到当前节点实际的通行代价，第二部分h(n)是当前节点到终点的通行代价的估计值。算法每次在扩展时，都选取f(n)值最小的那个节点作为最优路径上的下一个节点。
在实际应用中，若以最短路程为优化目标，h(n)常取作当前点到终点的欧几里得距离(Euclidean Distance)或曼哈顿距离(Manhattan Distance)等。若令h(n)=0，表示没有利用任何当前节点与终点的信息，A算法就退化为非启发的Dijkstra算法，算法搜索空间随之变大，搜索时间变长。
A*算法步骤如下，算法维护两个集合：P表与Q表。P表存放那些已经搜索到、但还没加入最优路径树上的节点；Q表维护那些已加入最优路径树上的节点。
（1）P表、Q表置空，将起点S加入P表，其g值置0，父节点为空，路网中其他节点g值置为无穷大。
（2）若P表为空，则算法失败。否则选取P表中f值最小的那个节点，记为BT，将其加入Q表中。判断BT是否为终点T，若是，转到步骤（3）；否则根据路网拓扑属性和交通规则找到BT的每个邻接节点NT，进行下列步骤:
①计算NT的启发值
f(NT)=g(NT)+h(NT)(2)
g(NT)=g(BT)+cost(BT, NT)(3)
其中,cost(BT, NT)是BT到NT的通行代价。
②如果NT在P表中，且通过式(3)计算的g值比NT原先的g值小，则将NT的g值更新为式(3)结果，并将NT的父节点设为BT。
③如果NT在Q表中，且通过式(3)计算的g值比NT原先的g值小，则将NT的g值更新为式(3)结果，将NT的父节点设为BT，并将NT移出到P表中。
④若NT既不在P表，也不在Q表中，则将NT的父节点设为BT，并将NT移到P表中。
⑤转到步骤（2）继续执行。
（3）从终点T回溯，依次找到父节点，并加入优化路径中，直到起点S，即可得出优化路径。
二、源代码
function varargout = A_GUI(varargin)
% A_GUI MATLAB code for A_GUI.fig
% A_GUI, by itself, creates a new A_GUI or raises the existing
% singleton*.
%
% H = A_GUI returns the handle to a new A_GUI or the handle to
% the existing singleton*.
%
% A_GUI('CALLBACK',hObject,eventData,handles,...) calls the local
% function named CALLBACK in A_GUI.M with the given input arguments.
%
% A_GUI('Property','Value',...) creates a new A_GUI or raises the
% existing singleton*. Starting from the left, property value pairs are
% applied to the GUI before A_GUI_OpeningFcn gets called. An
% unrecognized property name or invalid value makes property application
% stop. All inputs are passed to A_GUI_OpeningFcn via varargin.
%
% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one
% instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES
% Edit the above text to modify the response to help A_GUI
% Last Modified by GUIDE v2.5 21-Oct-2018 17:10:48
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
'gui_Singleton', gui_Singleton, ...
'gui_OpeningFcn', @A_GUI_OpeningFcn, ...
'gui_OutputFcn', @A_GUI_OutputFcn, ...
'gui_LayoutFcn', [] , ...
'gui_Callback', []);
if nargin && ischar(varargin{
1})
gui_State.gui_Callback = str2func(varargin{
1});
end
if nargout
[varargout{
1:nargout}] = gui_mainfcn(gui_State, varargin{
:});
else
gui_mainfcn(gui_State, varargin{
:});
end
% End initialization code - DO NOT EDIT
% --- Executes just before A_GUI is made visible.
function A_GUI_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% varargin command line arguments to A_GUI (see VARARGIN)
% Choose default command line output for A_GUI
handles.output = hObject;
% Update handles structure
guidata(hObject, handles);
% UIWAIT makes A_GUI wait for user response (see UIRESUME)
% uiwait(handles.figure1);
% --- Outputs from this function are returned to the command line.
function varargout = A_GUI_OutputFcn(hObject, eventdata, handles)
% varargout cell array for returning output args (see VARARGOUT);
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Get default command line output from handles structure
varargout{
1} = handles.output;
% --- Executes on button press in pushbutton1.
function pushbutton1_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% set up color map for display 生成彩色地图
global cmap;
global map;
global n_r;
global n_c;
global state;
cmap = [1 1 1; ...% 1 -白色-无障碍
0 0 0; ...% 2 -黑色-有障碍
0 0.8 0; ...% 3 -绿色-已搜索
0 0.4 0; ...% 4 -粉色-正在搜索
0 1 1; ...% 5 -浅蓝色-起始点
1 1 0; ...% 6 -黄色-目标点
0 0 1]; % 7 -蓝色-最终路径
colormap(cmap);
%生成随机地图
map = zeros(n_r,n_c);
randmap = rand(n_r,n_c);
for i = 2:(sub2ind(size(randmap),n_r,n_c)-1)
if (randmap(i) >= 0.75)
map(i) = 2;
end
end
map(1, 1) = 5; % start_coords 起点坐标
map(n_r, n_c) = 6; % dest_coords 终点坐标
image(1.5,1.5,map);
grid on;
axis image;
set(handles.text5,'string','随机地图生成完毕');
% --- Executes on button press in pushbutton2.
function pushbutton2_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
%搜索最佳路径
global n_r;
global n_c;
global cmap;
global map;
global state;
nrows = n_r;
ncols = n_c;
start_node = sub2ind(size(map), 1, 1);
%sub2ind()函数将矩阵中的某个元素的线性序号计算出来
%线性索引号例子：2*2矩阵[1 3;中，1是第一个，5是第二个
% 5 7] ，3是第三个，7是第四个
%（matlab是列优先，不是我们通常习惯的行优先）
dest_node = sub2ind(size(map), n_r, n_c);
% Initialize distance array 初始化距离数组
distanceFromStart = Inf(nrows,ncols);
distanceFromStart(start_node) = 0 ;
[X, Y] = meshgrid (1:ncols, 1:nrows);
H = abs(Y - n_r) + abs(X - n_c);
f = Inf(nrows,ncols);
f(start_node) = H(start_node);
% For each grid cell this array holds the index of its parent 对于每个网格单元，该数组都保存其父单元的索引
parent = zeros(nrows,ncols);
% Main Loop
while true
% Draw current map
map(start_node) = 5;
map(dest_node) = 6;
image(1.5, 1.5, map);
grid on; %网格
axis image; %显示坐标
drawnow; %刷新屏幕
% Find the node with the minimum distance 找到距离最短的节点
% [min_dist, current] = min(distanceFromStart(:));
[~, current] = min(f(:)); [min_dist, ~] = min(distanceFromStart(:));
if ((current == dest_node) || isinf(min_dist)) %TF = isinf(A) 返回一个和A尺寸一样的数组， 如果A中某个元素是inf (无穷)， 则对应TF中元素是1， 否则TF中对应元素是0。
break;
end;
%搜索中心的索引坐标：current,
%搜索中心与起始点的路程：min_dist
% 这两个值后面会用。
map(current) = 3;
% distanceFromStart(current) = Inf;
f(current) = Inf;
[i, j] = ind2sub(size(distanceFromStart), current); %索引号变为坐标
neighbor = [i-1,j;
i+1,j;
i,j+1;
i,j-1];
outRangetest = (neighbor(:,1)<1) + (neighbor(:,1)>nrows)+(neighbor(:,2)<1) + (neighbor(:,2)>ncols);
locate = find(outRangetest>0); %返回outRangetest中大于0的元素的相对应的线性索引值。
neighbor(locate,:)=[];
neighborIndex = sub2ind(size(map),neighbor(:,1),neighbor(:,2));
for i=1:length(neighborIndex)
if (map(neighborIndex(i))~=2) && (map(neighborIndex(i))~=3 && map(neighborIndex(i))~= 5)
map(neighborIndex(i)) = 4;
if (distanceFromStart(neighborIndex(i))>= min_dist + 1 )
distanceFromStart(neighborIndex(i)) = min_dist+1;
parent(neighborIndex(i)) = current;
f(neighborIndex(i)) = H(neighborIndex(i));
% pause(0.02);
end
end
end
end
% %%
if (isinf(distanceFromStart(dest_node)))
%route = [];
disp('路径搜索失败');
set(handles.text5,'string','路径搜索失败');
else
%提取路线坐标
set(handles.text5,'string','路径搜索成功');
route = [dest_node];
while (parent(route(1)) ~= 0)
route(1);
parent(route(1))
route = [parent(route(1)), route] ;
end
三、运行结果
四、备注
完整代码或者代写添加QQ 912100926