图论matlab代码整理
时间: 2023-12-27 09:05:13 浏览: 22
以下是一些常见的图论算法的Matlab代码示例:
1. 最短路径算法(Dijkstra)
```matlab
function [dist, prev] = dijkstra(A, s)
n = size(A, 1);
dist = Inf(1, n);
prev = zeros(1, n);
visited = zeros(1, n);
dist(s) = 0;
for i = 1:n-1
[~, u] = min(dist .* (1-visited));
visited(u) = 1;
for v = 1:n
if A(u, v) ~= 0 && visited(v) == 0
alt = dist(u) + A(u, v);
if alt < dist(v)
dist(v) = alt;
prev(v) = u;
end
end
end
end
end
```
2. 最小生成树算法(Prim)
```matlab
function [T, cost] = prim(A)
n = size(A, 1);
T = zeros(n, n);
visited = zeros(1, n);
visited(1) = 1;
cost = 0;
while sum(visited) < n
mincost = Inf;
u = 0;
v = 0;
for i = 1:n
if visited(i) == 1
for j = 1:n
if visited(j) == 0 && A(i, j) ~= 0 && A(i, j) < mincost
mincost = A(i, j);
u = i;
v = j;
end
end
end
end
T(u, v) = mincost;
T(v, u) = mincost;
visited(v) = 1;
cost = cost + mincost;
end
end
```
3. 拓扑排序算法
```matlab
function [order, flag] = topoSort(A)
n = size(A, 1);
indegree = sum(A, 1);
order = zeros(1, n);
flag = 1;
for i = 1:n
j = find(indegree == 0, 1);
if isempty(j)
flag = 0;
return;
end
order(i) = j;
indegree(j) = Inf;
for k = 1:n
if A(j, k) ~= 0
indegree(k) = indegree(k) - 1;
end
end
end
end
```
4. 最大流算法(Ford-Fulkerson)
```matlab
function maxflow = fordFulkerson(A, s, t)
n = size(A, 1);
flow = zeros(n, n);
while true
[P, F] = bfs(A, flow, s, t);
if isempty(P)
break;
end
for i = 1:length(P)-1
u = P(i);
v = P(i+1);
flow(u, v) = flow(u, v) + F;
flow(v, u) = flow(v, u) - F;
end
end
maxflow = sum(flow(s, :));
end
function [P, F] = bfs(A, flow, s, t)
n = size(A, 1);
P = zeros(1, n);
visited = zeros(1, n);
visited(s) = 1;
Q = [s];
F = Inf;
while ~isempty(Q)
u = Q(1);
Q = Q(2:end);
for v = 1:n
if visited(v) == 0 && A(u, v) - flow(u, v) > 0
visited(v) = 1;
P(v) = u;
Q = [Q v];
F = min(F, A(u, v) - flow(u, v));
if v == t
return;
end
end
end
end
P = [];
F = 0;
end
```
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