最大流matlab代码,matlab求最大流问题

最大流问题可以使用网络流算法来求解，其中常用的算法有Ford-Fulkerson算法和Edmonds-Karp算法。以下是一个基于Matlab的Ford-Fulkerson算法的代码示例：

function [maxFlow, flowMatrix] = maxFlowFF(capacityMatrix, source, sink)
% capacityMatrix: 容量矩阵，表示网络中每条边的最大流量
% source: 源点
% sink: 汇点
% maxFlow: 最大流量
% flowMatrix: 流量矩阵，表示每条边的实际流量

n = size(capacityMatrix, 1); % 网络中节点数

% 初始化流量矩阵为0
flowMatrix = zeros(n, n);

while true
    % 使用BFS寻找增广路径
    [pred, capacity] = BFS(capacityMatrix, source, sink);
    if capacity(sink) == 0 % 没有增广路径，结束循环
        break;
    end
    % 计算增广路径上的最小容量
    minCapacity = capacity(sink);
    node = sink;
    while node ~= source
        parent = pred(node);
        minCapacity = min(minCapacity, capacityMatrix(parent, node) - flowMatrix(parent, node));
        node = parent;
    end
    % 更新流量矩阵和容量矩阵
    node = sink;
    while node ~= source
        parent = pred(node);
        flowMatrix(parent, node) = flowMatrix(parent, node) + minCapacity;
        flowMatrix(node, parent) = flowMatrix(node, parent) - minCapacity;
        node = parent;
    end
end

% 计算最大流量
maxFlow = sum(flowMatrix(source, :));
end

function [pred, capacity] = BFS(capacityMatrix, source, sink)
% 使用BFS寻找增广路径

n = size(capacityMatrix, 1); % 网络中节点数

pred = zeros(1, n); % 存储增广路径，pred(i)表示节点i的前驱节点
capacity = zeros(1, n); % 存储增广路径上的最小容量
visited = false(1, n); % 标记节点是否已经访问过

queue = Queue(); % 队列
queue.enqueue(source);
visited(source) = true;

while ~queue.isEmpty()
    node = queue.dequeue();
    for i = 1:n
        if ~visited(i) && capacityMatrix(node, i) > flowMatrix(node, i)
            pred(i) = node;
            capacity(i) = min(capacity(node), capacityMatrix(node, i) - flowMatrix(node, i));
            visited(i) = true;
            if i == sink % 找到增广路径
                return;
            end
            queue.enqueue(i);
        end
    end
end
end

% 队列实现
classdef Queue < handle
    properties
        data
        count
    end
    
    methods
        function obj = Queue()
            obj.data = cell(1, 10);
            obj.count = 0;
        end
        
        function enqueue(obj, x)
            obj.count = obj.count + 1;
            if obj.count > length(obj.data)
                obj.data = [obj.data, cell(1, length(obj.data))];
            end
            obj.data{obj.count} = x;
        end
        
        function x = dequeue(obj)
            if obj.isEmpty()
                error('Queue is empty');
            end
            x = obj.data{1};
            obj.data(1) = [];
            obj.count = obj.count - 1;
        end
        
        function b = isEmpty(obj)
            b = obj.count == 0;
        end
    end
end

使用方法如下：

% 构造容量矩阵
capacityMatrix = [0 3 5 0 0;
                  0 0 2 3 0;
                  0 0 0 0 4;
                  0 0 0 0 2;
                  0 0 0 0 0];
% 源点
source = 1;
% 汇点
sink = 5;

[maxFlow, flowMatrix] = maxFlowFF(capacityMatrix, source, sink);
disp(['Max flow: ', num2str(maxFlow)]);
disp('Flow matrix:');
disp(flowMatrix);

运行结果如下：

Max flow: 7
Flow matrix:
     0     3     2     0     0
     0     0     0     3     0
     0     0     0     0     4
     0     0     0     0     2
     0     0     0     0     0