dijkstra MATLAB

Dijkstra's algorithm is a popular algorithm used to find the shortest path between two vertices in a graph with non-negative edge weights. Here is an implementation of Dijkstra's algorithm in MATLAB:

function [dist, prev] = dijkstra(graph, start)
% graph is an adjacency matrix representing the graph
% start is the starting vertex

n = size(graph, 1);
dist = inf(1, n);
prev = zeros(1, n);
visited = zeros(1, n);

dist(start) = 0;

for i = 1:n
    u = find(visited == 0 & dist == min(dist));
    u = u(1);
    visited(u) = 1;
    for v = 1:n
        if graph(u, v) ~= 0
            alt = dist(u) + graph(u, v);
            if alt < dist(v)
                dist(v) = alt;
                prev(v) = u;
            end
        end
    end
end

The function takes as input an adjacency matrix `graph` representing the graph and the starting vertex `start`. The output is two vectors, `dist` and `prev`, where `dist(i)` is the shortest distance from `start` to vertex `i`, and `prev(i)` is the previous vertex on the shortest path from `start` to vertex `i`.

The algorithm works by initializing all distances to infinity except for the starting vertex, which is set to 0. It then repeatedly selects the unvisited vertex with the smallest distance, marks it as visited, and updates the distances of its neighbors if a shorter path is found. The `prev` vector is updated accordingly to keep track of the shortest path.

Note that this implementation assumes that the graph is connected and has non-negative edge weights. It also does not handle disconnected graphs or graphs with negative edge weights.