test

calculateDistanceMatrix.m

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+function adjacencyMatrix = calculateDistanceMatrix(positions)
+    % 计算任意两个城市之间的直线距离，返回加权邻接矩阵
+    % 输入：positions - 包含城市坐标的矩阵 (n行3列)
+    % 输出：adjacencyMatrix - n×n的加权邻接矩阵
+    
+    % 获取城市数量
+    numCities = size(positions, 1);
+    
+    % 初始化邻接矩阵
+    adjacencyMatrix = zeros(numCities, numCities);
+    
+    % 计算每对城市之间的欧几里得距离
+    for i = 1:numCities
+        for j = 1:numCities
+            if i ~= j
+                % 计算欧几里得距离
+                dx = positions(i, 2) - positions(j, 2);
+                dy = positions(i, 3) - positions(j, 3);
+                adjacencyMatrix(i, j) = sqrt(dx^2 + dy^2);
+            end
+        end
+    end
+end

calculateTourDistance.m

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+function [route, totalDistance] = calculateTourDistance(adjacencyMatrix, startCity)
+    % 计算从指定城市出发，遍历所有城市一次后返回起点的路径距离
+    % 输入：adjacencyMatrix - 城市间距离的邻接矩阵
+    %      startCity - 起始城市的编号
+    % 输出：route - 遍历路径
+    %      totalDistance - 总路径长度
+    
+    numCities = size(adjacencyMatrix, 1);
+    
+    % 创建除起始城市外的城市列表
+    otherCities = setdiff(1:numCities, startCity);
+    
+    % 随机排列其他城市（这里不要求最优路径）
+    otherCities = otherCities(randperm(length(otherCities)));
+    
+    % 创建完整路径
+    route = [startCity, otherCities, startCity];
+    
+    % 计算总路径距离
+    totalDistance = 0;
+    for i = 1:length(route)-1
+        totalDistance = totalDistance + adjacencyMatrix(route(i), route(i+1));
+    end
+end

main.m

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+% 加载数据
+load('postion_att48.mat');
+% 假设加载的变量名为positions，如果实际变量名不同，请相应调整
+
+% 计算城市间距离矩阵
+distMatrix = calculateDistanceMatrix(postion);
+
+% 输出距离矩阵
+disp('城市间距离矩阵:');
+disp(distMatrix);
+
+% 选择起始城市（这里选择城市1）
+startCity = 1;
+
+% 生成遍历路径并计算总距离
+[route, totalDistance] = calculateTourDistance(distMatrix, startCity);
+
+% 输出总距离
+fprintf('从城市%d出发的遍历路径总距离: %.2f\n', startCity, totalDistance);
+
+% 绘制遍历路径
+plotTour(postion, route);

plotTour.m

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+function plotTour(positions, route)
+    % 绘制遍历路径的示意图
+    % 输入：positions - 包含城市坐标的矩阵
+    %      route - 遍历路径
+    
+    % 创建新图形窗口
+    figure;
+    
+    % 绘制所有城市点
+    plot(positions(:, 2), positions(:, 3), 'o', 'MarkerSize', 8, 'MarkerFaceColor', 'blue');
+    hold on;
+    
+    % 绘制路径连线
+    for i = 1:length(route)-1
+        current = route(i);
+        next = route(i+1);
+        
+        % 绘制从当前城市到下一个城市的线
+        line([positions(current, 2), positions(next, 2)], ...
+             [positions(current, 3), positions(next, 3)], ...
+             'Color', 'red', 'LineWidth', 1.5);
+    end
+    
+    % 标记起点和终点（相同城市）
+    plot(positions(route(1), 2), positions(route(1), 3), 'gs', 'MarkerSize', 12, 'MarkerFaceColor', 'green');
+    
+    % 添加城市标签
+    for i = 1:size(positions, 1)
+        text(positions(i, 2), positions(i, 3), num2str(i), ...
+             'HorizontalAlignment', 'left', 'VerticalAlignment', 'bottom');
+    end
+    
+    % 添加图例和标题
+    xlabel('X坐标');
+    ylabel('Y坐标');
+    title('城市遍历路径');
+    grid on;
+    legend('城市', '路径', '起点/终点');
+    hold off;
+end