1 2 3 4 5 6 7 8 9 10 11 1 0 2 8 1 500 500 500 500 500 500 500 2 2 0 6 500 1 500 500 500 500 500 500 3 8 6 0 7 500 1 500 500 500 500 500 4 1 500 7 0 500 500 9 500 500 500 500 5 500 1 500 500 0 3 500 2 500 500 500 6 500 500 1 500 3 0 4 500 6 500 500 7 500 500 500 9 500 4 0 500 500 1 500 8 500 500 500 500 2 500 500 0 7 500 9 9 500 500 500 500 500 6 500 7 0 1 2 10 500 500 500 500 500 500 1 500 1 0 4 11 500 500 500 500 500 500 500 9 2 4 0 根据上述矩阵,求解从1到11的最短路径
时间: 2023-11-22 18:46:15 浏览: 41
根据给出的矩阵,可以使用Dijkstra算法来求解从城市1到城市11的最短路径。Dijkstra算法是一种用于解决单源最短路径问题的贪心算法。以下是使用Matlab实现Dijkstra算法求解最短路径的代码:
```matlab
% 创建邻接矩阵
adjMatrix = [0 2 8 1 500 500 500 500 500 500 500;
2 0 6 500 1 500 500 500 500 500 500;
8 6 0 7 500 1 500 500 500 500 500;
1 500 7 0 500 500 9 500 500 500 500;
500 1 500 500 0 3 500 2 500 500 500;
500 500 1 500 3 0 4 500 6 500 500;
500 500 500 9 500 4 0 500 500 1 500;
500 500 500 500 2 500 500 0 7 500 9;
500 500 500 500 500 6 500 7 0 1 2;
500 500 500 500 500 500 1 500 1 0 4;
500 500 500 500 500 500 500 9 2 4 0];
% 城市数量
numCities = size(adjMatrix,1);
% 创建距离数组
distances = ones(1, numCities) * Inf;
distances(1) = 0;
% 创建标记数组,标记已访问过的城市
visited = zeros(1, numCities);
% Dijkstra算法
for i = 1:numCities
% 查找距离最小的未访问城市
minDistance = Inf;
minCity = -1;
for j = 1:numCities
if ~visited(j) && distances(j) < minDistance
minDistance = distances(j);
minCity = j;
end
end
% 标记该城市为已访问
visited(minCity) = 1;
% 更新其他城市的距离
for j = 1:numCities
if ~visited(j)
distances(j) = min(distances(j), distances(minCity) + adjMatrix(minCity, j));
end
end
end
% 输出最短路径和最短距离
disp('最短路径:');
path = [11];
currentCity = 11;
while currentCity ~= 1
for j = 1:numCities
if distances(currentCity) == distances(j) + adjMatrix(j, currentCity)
path = [j, path];
currentCity = j;
break;
end
end
end
disp(path);
disp('最短距离:');
disp(distances(11));
```
以上代码将输出从城市1到城市11的最短路径和最短距离。
希望以上代码和解释对你有帮助!如果还有其他问题,请随时提问。
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