针对有向加权网络,分别以节点的出度和入度为两种类型负载,用matlab写一段负载容量模型的代码
时间: 2024-02-12 22:09:19 浏览: 20
好的,以下是一个简单的负载容量模型的 Matlab 代码,基于有向加权网络,分别以节点的出度和入度为两种类型负载:
```matlab
% 定义有向加权网络的邻接矩阵,例如:
% 0 -> 1 (4)
% 0 -> 2 (3)
% 1 -> 2 (2)
% 1 -> 3 (5)
% 2 -> 3 (7)
% 表示为:
% 0 1 2 3
% 0 0 4 3 0
% 1 0 0 2 5
% 2 0 0 0 7
% 3 0 0 0 0
adj_matrix = [0, 4, 3, 0; 0, 0, 2, 5; 0, 0, 0, 7; 0, 0, 0, 0];
% 定义源节点和汇节点
source = 1;
sink = 4;
% 使用节点出度作为负载计算负载容量
max_flow_outdegree = maxFlowWithOutdegreeLoad(adj_matrix, source, sink);
% 使用节点入度作为负载计算负载容量
max_flow_indegree = maxFlowWithIndegreeLoad(adj_matrix, source, sink);
function [max_flow] = maxFlowWithOutdegreeLoad(adj_matrix, source, sink)
% 计算每个节点的出度
outdegree = sum(adj_matrix, 2);
% 定义每条边的负载,即出度
edges_load = repmat(outdegree, [1, size(adj_matrix, 1)]);
edges_load = edges_load';
% 使用最大流算法计算负载容量
max_flow = maxFlowWithLoad(adj_matrix, source, sink, edges_load);
end
function [max_flow] = maxFlowWithIndegreeLoad(adj_matrix, source, sink)
% 计算每个节点的入度
indegree = sum(adj_matrix, 1);
% 定义每条边的负载,即入度
edges_load = repmat(indegree, [size(adj_matrix, 1), 1]);
% 使用最大流算法计算负载容量
max_flow = maxFlowWithLoad(adj_matrix, source, sink, edges_load);
end
function [max_flow] = maxFlowWithLoad(adj_matrix, source, sink, edges_load)
% 初始化网络流及负载流
n = size(adj_matrix, 1);
flow = zeros(n, n);
load_flow = zeros(n, n);
% 计算残量网络
residual_network = adj_matrix;
% 循环计算增广路径并更新网络流和负载流
while true
% 使用 BFS 寻找增广路径
[path, path_flow, path_load_flow] = bfsWithLoad(residual_network, source, sink, flow, edges_load);
% 如果找不到增广路径,退出循环
if isempty(path)
break
end
% 更新网络流和负载流
for i = 1:length(path)-1
u = path(i);
v = path(i+1);
flow(u, v) = flow(u, v) + path_flow;
load_flow(u, v) = load_flow(u, v) + path_load_flow;
residual_network(u, v) = residual_network(u, v) - path_flow;
residual_network(v, u) = residual_network(v, u) + path_flow;
end
end
% 计算负载容量
max_flow = sum(load_flow(source, :));
end
function [path, path_flow, path_load_flow] = bfsWithLoad(adj_matrix, source, sink, flow, edges_load)
% 使用 BFS 寻找从源节点到汇节点的增广路径
n = size(adj_matrix, 1);
visited = false(1, n);
parent = zeros(1, n);
path_flow = inf;
path_load_flow = inf;
queue = [];
queue = [queue, source];
visited(source) = true;
% BFS
while ~isempty(queue)
u = queue(1);
queue(1) = [];
for v = 1:n
if ~visited(v) && adj_matrix(u, v) > 0
if adj_matrix(u, v) - flow(u, v) > 0 || flow(v, u) > 0
% 计算剩余容量和负载容量
residual_capacity = adj_matrix(u, v) - flow(u, v);
if residual_capacity < path_flow
path_flow = residual_capacity;
end
residual_load_capacity = edges_load(u, v) - flow(u, v);
if residual_load_capacity < path_load_flow
path_load_flow = residual_load_capacity;
end
% 更新 parent 和 visited 数组
parent(v) = u;
visited(v) = true;
queue = [queue, v];
% 如果到达汇节点,退出循环
if v == sink
break
end
end
end
end
end
% 根据 parent 数组构造增广路径
path = [];
if visited(sink)
v = sink;
while v ~= source
u = parent(v);
path = [u, path];
v = u;
end
path = [source, path, sink];
end
end
```
这段代码分别实现了基于节点出度和入度的负载容量模型,通过 `maxFlowWithOutdegreeLoad` 和 `maxFlowWithIndegreeLoad` 函数计算负载容量,其中 `edges_load` 数组根据节点出度或入度计算。