Provide MATLAB representation for the following two graphs using adjacency matrices: Edges have uniform length 1. How to find in MATLAB a shortest path from Node 4 to Node 6 (in both graphs)?
Solution
Adjancy Matrix
function W = getAdjacencyMatrix(I)
[m, n] = size(I);
I_size = m*n;
V = repmat([ones(m-1,1); 0],n, 1);
V = V(1:end-1); % remove last zero
U = ones(m*(n-1), 1);
W = sparse(1:(I_size-1),   2:I_size, V, I_size, I_size)...
+ sparse(1:(I_size-m),(m+1):I_size, U, I_size, I_size);
W = W + W\';
Shorest Path
function D = dijkstra(G, pairs)
p = size(pairs, 1); % Number of pairs
v = size(G, 1); % Number of vertices
D = [];
for i = 1:v
for j = 1:v
if G(i,j) <= esp
G(i,j) = inf
end
end
end
for i = 1:p
dist = inf(1, v);
seen = ones(1, v);
not_seen = v;
dist(1, pairs(i,1)) = 0;
while not_seen > 0
[distance index] = min(dist .* seen);
if distance == inf
break;
end
if index == pairs(i,2)
break;
end
seen(index) = inf;
not_seen = not_seen - 1;
for n = 1:v
if seen(n) == 1
alt = distance + G(index, n);
if alt < dist(n)
dist(n) = alt;
end
end
end
end
D = [D ; dist(pairs(i,2))];
end
end
.
Find Shortest Paths in MATLAB Using Adjacency Matrices
1. Provide MATLAB representation for the following two graphs using adjacency matrices: Edges
have uniform length 1. How to find in MATLAB a shortest path from Node 4 to Node 6 (in both
graphs)?
Solution
Adjancy Matrix
function W = getAdjacencyMatrix(I)
[m, n] = size(I);
I_size = m*n;
V = repmat([ones(m-1,1); 0],n, 1);
V = V(1:end-1); % remove last zero
U = ones(m*(n-1), 1);
W = sparse(1:(I_size-1),   2:I_size, V, I_size, I_size)...
+ sparse(1:(I_size-m),(m+1):I_size, U, I_size, I_size);
W = W + W';
Shorest Path
function D = dijkstra(G, pairs)
p = size(pairs, 1); % Number of pairs
v = size(G, 1); % Number of vertices
D = [];
for i = 1:v
for j = 1:v
if G(i,j) <= esp
G(i,j) = inf
2. end
end
end
for i = 1:p
dist = inf(1, v);
seen = ones(1, v);
not_seen = v;
dist(1, pairs(i,1)) = 0;
while not_seen > 0
[distance index] = min(dist .* seen);
if distance == inf
break;
end
if index == pairs(i,2)
break;
end
seen(index) = inf;
not_seen = not_seen - 1;
for n = 1:v
if seen(n) == 1
alt = distance + G(index, n);
if alt < dist(n)
dist(n) = alt;
end
end
end
end
D = [D ; dist(pairs(i,2))];
end
end
![Provide MATLAB representation for the following two graphs using adjacency matrices: Edges
have uniform length 1. How to find in MATLAB a shortest path from Node 4 to Node 6 (in both
graphs)?
Solution
Adjancy Matrix
function W = getAdjacencyMatrix(I)
[m, n] = size(I);
I_size = m*n;
V = repmat([ones(m-1,1); 0],n, 1);
V = V(1:end-1); % remove last zero
U = ones(m*(n-1), 1);
W = sparse(1:(I_size-1),   2:I_size, V, I_size, I_size)...
+ sparse(1:(I_size-m),(m+1):I_size, U, I_size, I_size);
W = W + W';
Shorest Path
function D = dijkstra(G, pairs)
p = size(pairs, 1); % Number of pairs
v = size(G, 1); % Number of vertices
D = [];
for i = 1:v
for j = 1:v
if G(i,j) <= esp
G(i,j) = inf](https://image.slidesharecdn.com/providematlabrepresentationforthefollowingtwographsusingadjac-230208182312-8d59ca7c/85/Provide-MATLAB-representation-for-the-following-two-graphs-using-adjac-docx-1-320.jpg)
![end
end
end
for i = 1:p
dist = inf(1, v);
seen = ones(1, v);
not_seen = v;
dist(1, pairs(i,1)) = 0;
while not_seen > 0
[distance index] = min(dist .* seen);
if distance == inf
break;
end
if index == pairs(i,2)
break;
end
seen(index) = inf;
not_seen = not_seen - 1;
for n = 1:v
if seen(n) == 1
alt = distance + G(index, n);
if alt < dist(n)
dist(n) = alt;
end
end
end
end
D = [D ; dist(pairs(i,2))];
end
end](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)