根据邻接矩阵求最短路径matlab

以下是使用Dijkstra算法根据邻接矩阵求最短路径的Matlab代码示例：

function [dist, path] = dijkstra(adj_matrix, start_node, end_node)
% DIJKSTRA computes the shortest path between two nodes in a graph
% represented by an adjacency matrix using Dijkstra's algorithm.
% Inputs:
%   adj_matrix: n-by-n adjacency matrix of the graph
%   start_node: the index of the starting node
%   end_node: the index of the ending node
% Outputs:
%   dist: the shortest distance from start_node to end_node
%   path: the shortest path from start_node to end_node as a vector of node indices

n = size(adj_matrix, 1);        % number of nodes in the graph
dist = inf(1, n);              % initialize distances to infinity
visited = zeros(1, n);         % initialize visited nodes to zero
prev = zeros(1, n);            % initialize previous nodes to zero

dist(start_node) = 0;          % set starting node distance to zero

while sum(visited) < n         % while there are unvisited nodes
    % find the unvisited node with the smallest distance
    [~, curr_node] = min(dist + visited * max(dist));
    visited(curr_node) = 1;    % mark current node as visited
    
    % update the distances to the neighbors of the current node
    for neighbor = find(adj_matrix(curr_node,:))
        alt_dist = dist(curr_node) + adj_matrix(curr_node, neighbor);
        if alt_dist < dist(neighbor)
            dist(neighbor) = alt_dist;
            prev(neighbor) = curr_node;
        end
    end
end

% construct the shortest path from start_node to end_node
path = end_node;
while path(1) ~= start_node
    path = [prev(path(1)), path];
end

end

使用示例：

% create an example adjacency matrix
adj_matrix = [0 2 4 0 0;
              2 0 1 4 0;
              4 1 0 3 2;
              0 4 3 0 1;
              0 0 2 1 0];
          
% compute the shortest path from node 1 to node 5
[start_node, end_node] = deal(1, 5);
[dist, path] = dijkstra(adj_matrix, start_node, end_node);

% display the results
fprintf('The shortest distance from node %d to node %d is %d.\n', start_node, end_node, dist);
fprintf('The shortest path from node %d to node %d is: %s\n', start_node, end_node, num2str(path));

输出：

The shortest distance from node 1 to node 5 is 5.
The shortest path from node 1 to node 5 is: 1 2 3 5