dijkstra matlab编程

Dijkstra算法是一种最短路径算法，用于在带权图中找到从一个节点到另一个节点的最短路径。下面是一个使用Matlab实现Dijkstra算法的示例代码：

function [dist, path] = dijkstra(graph, start, goal)
% DIJKSTRA Calculates the shortest path in a graph using Dijkstra's algorithm
%   graph - a weighted adjacency matrix representing the graph
%   start - the index of the start node
%   goal - the index of the goal node
%   dist - a vector containing the minimum distance from the start node to each node in the graph
%   path - a vector containing the path from the start node to the goal node

n = size(graph, 1); % number of nodes in the graph
dist = Inf(1, n); % initialize distances to infinity
dist(start) = 0; % distance from start node to itself is 0
visited = false(1, n); % keep track of visited nodes
path = zeros(1, n); % initialize path

for i = 1:n-1 % loop through all nodes except the last one
    % select the unvisited node with the smallest distance
    [~, current] = min(dist .* ~visited);
    visited(current) = true; % mark node as visited
    
    % update distances and paths for adjacent nodes
    neighbors = find(graph(current, :));
    for j = 1:length(neighbors)
        neighbor = neighbors(j);
        if ~visited(neighbor)
            new_dist = dist(current) + graph(current, neighbor);
            if new_dist < dist(neighbor)
                dist(neighbor) = new_dist;
                path(neighbor) = current;
            end
        end
    end
end

% construct path from start to goal node
node = goal;
while node ~= start
    path(node) = path(node) + 1;
    node = path(node);
end
path = fliplr(path);

end

该代码使用了一个邻接矩阵来表示带权图，其中图中的每个节点都被表示为一个数字索引。在执行算法时，它从起始节点开始，通过遍历相邻节点来计算到每个节点的最短距离，并记录路径。最后，它构造了从起始节点到目标节点的最短路径。