implement dijkstras algorithm in matlab

main.m
function [dist,prev] = dijkstra(adj,start)
%DIJKSTRA Calculates the shortest path in a graph using Dijkstra's algorithm
%   [dist,prev] = dijkstra(adj,start) returns an array of distances (dist)
%   and a corresponding array of previous vertices (prev) representing the
%   shortest path from the start vertex to every other vertex in the graph
%   represented by the adjacency matrix (adj).

n = size(adj,1); % Number of vertices
dist = inf(1,n); % Initialize distances to infinity
prev = zeros(1,n); % Initialize previous vertices to zero

dist(start) = 0; % Distance from start vertex to itself is zero
s = zeros(1,n); % Initialize set of visited vertices to empty

while sum(s) ~= n % While set of visited vertices is not equal to all vertices
    [~,u] = min(dist + inf*s); % Find unvisited vertex with minimum distance
    s(u) = 1; % Add vertex to set of visited vertices
    neighbors = find(adj(u,:) ~= 0); % Find neighbors of current vertex
    for v = neighbors
        alt = dist(u) + adj(u,v); % Calculate alternative distance
        if alt < dist(v)
            dist(v) = alt; % Update distance
            prev(v) = u; % Update previous vertex
        end
    end
end
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