dijsktra算法代码matlab

以下是使用Matlab实现Dijkstra算法的示例代码：

function [distances, previous = dijkstra(adjacencyMatrix, source)
    numNodes = size(adjacencyMatrix, 1);
    distances = inf(1, numNodes);
    previous = zeros(1, numNodes);
    visited = false(1, numNodes);

    distances(source) = 0;

    for i = 1:numNodes
        currentNode = getNextNode(distances, visited);
        visited(currentNode) = true;

        neighbors = find(adjacencyMatrix(currentNode, :));
        for j = 1:length(neighbors)
            neighbor = neighbors(j);
            if ~visited(neighbor)
                distance = distances(currentNode) + adjacencyMatrix(currentNode, neighbor);
                if distance < distances(neighbor)
                    distances(neighbor) = distance;
                    previous(neighbor) = currentNode;
                end
            end
        end
    end
end

function nextNode = getNextNode(distances, visited)
    minDistance = inf;
    nextNode = -1;

    for i = 1:length(distances)
        if ~visited(i) && distances(i) <= minDistance
            minDistance = distances(i);
            nextNode = i;
        end
    end
end

使用示例：

% 定义邻接矩阵
adjacencyMatrix = [
    0 7 0 9 0 14;
    7 0 10 15 0 0;
    0 10 0 11 0 2;
    9 15 11 0 6 0;
    0 0 0 6 0 9;
    14 0 2 0 9 0
];

sourceNode = 1; % 源节点

 = dijkstra(adjacencyMatrix, sourceNode);

% 打印最短路径和距离
for i = 1:length(distances)
    if i ~= sourceNode
        path = getPath(previous, i);
        fprintf('从节点 %d 到节点 %d 的最短路径: %s，距离: %d\n', sourceNode, i, path, distances(i));
    end
end

function path = getPath(previous, node)
    path = "";
    while node ~= 0
        path = strcat(string(node), "->", path);
        node = previous(node);
    end
end

这段代码演示了如何使用Dijkstra算法找到从源节点到其他节点的最短路径及距离。首先，我们定义一个邻接矩阵来表示图的连接关系。然后，我们指定源节点，并调用`dijkstra`函数计算最短路径和距离。最后，我们通过遍历结果来打印出源节点到其他节点的最短路径和距离。

请注意，这只是一个简单的示例代码，适用于小规模的图。在实际应用中，可能需要对算法进行修改以处理更大规模的图或其他特殊情况。