匈牙利算法MATLAB
时间: 2023-10-23 21:30:00 浏览: 50
匈牙利算法(也称为Kuhn-Munkres算法)是一种用于解决二分图最大权匹配问题的优化算法。在MATLAB中,可以使用以下代码实现匈牙利算法:
```matlab
function [matching, cost] = hungarianAlgorithm(costMatrix)
numWorkers = size(costMatrix, 1);
numTasks = size(costMatrix, 2);
% Step 1: Initialize labels and potential
labels = zeros(numWorkers, 1);
potential = zeros(numTasks, 1);
% Step 2: Augmenting path search
for worker = 1:numWorkers
% Step 3: Initialize the arrays used in finding augmenting path
visitedWorkers = false(numWorkers, 1);
visitedTasks = false(numTasks, 1);
predecessors = zeros(numWorkers, 1);
minSlackValues = inf(numTasks, 1);
minSlackWorkers = zeros(numTasks, 1);
augmentingPathFound = false;
% Step 4: Find augmenting path starting from current worker
workerIndex = worker;
while ~augmentingPathFound
visitedWorkers(workerIndex) = true;
minSlackValue = inf;
minSlackTaskIndex = -1;
% Step 5: Find minimum slack value and corresponding task index
for task = 1:numTasks
if ~visitedTasks(task)
slackValue = costMatrix(workerIndex, task) - labels(workerIndex) - potential(task);
if slackValue < minSlackValues(task)
minSlackValues(task) = slackValue;
minSlackWorkers(task) = workerIndex;
end
if minSlackValues(task) < minSlackValue
minSlackValue = minSlackValues(task);
minSlackTaskIndex = task;
end
end
end
% Step 6: Update labels and potential
for i = 1:numWorkers
if visitedWorkers(i)
labels(i) = labels(i) + minSlackValue;
end
end
for j = 1:numTasks
if visitedTasks(j)
potential(j) = potential(j) - minSlackValue;
else
minSlackValues(j) = minSlackValues(j) - minSlackValue;
end
end
% Step 7: Add edge to augmenting path
predecessors(minSlackTaskIndex) = minSlackWorkers(minSlackTaskIndex);
if sum(predecessors == 0) == 0
augmentingPathFound = true;
else
visitedTasks(minSlackTaskIndex) = true;
workerIndex = predecessors(minSlackTaskIndex);
end
end
% Step 8: Update matching and cost
for task = 1:numTasks
matching(worker, task) = costMatrix(worker, task) == labels(worker) + potential(task);
if matching(worker, task)
cost = cost + costMatrix(worker, task);
end
end
end
end
```
请注意,上述代码是用于求解最大权匹配问题的一种实现方式,其中`costMatrix`是一个二分图的邻接矩阵,`matching`是最大权匹配的结果,`cost`是最大权匹配的总权重。你可以根据自己的需求对代码进行调整和扩展。
希望这对你有帮助!如果还有其他问题,请随时提问。