匈牙利算法指派问题matlab代码
时间: 2023-08-26 09:05:17 浏览: 55
Sure, here is an example of the Hungarian algorithm implemented in MATLAB:
```matlab
function [assignments, cost] = hungarianAlgorithm(costMatrix)
% Step 1: Subtract the smallest value from each row
costMatrix = bsxfun(@minus, costMatrix, min(costMatrix,[],2));
% Step 2: Subtract the smallest value from each column
costMatrix = bsxfun(@minus, costMatrix, min(costMatrix,[],1));
% Step 3: Assign initial zeros
assignments = zeros(size(costMatrix));
% Step 4: Assign zeros recursively
while true
[rowCovered, colCovered, numCovered] = coverZeros(assignments);
if numCovered == size(costMatrix,1)
break; % All zeros are covered
else
[costMatrix, assignments] = findAssignments(costMatrix, assignments, rowCovered, colCovered);
end
end
% Step 5: Calculate the final assignment cost
indices = find(assignments == 1);
cost = sum(costMatrix(indices));
end
function [rowCovered, colCovered, numCovered] = coverZeros(assignments)
rowCovered = any(assignments == 1, 2);
colCovered = any(assignments == 1, 1);
numCovered = sum(rowCovered) + sum(colCovered);
end
function [costMatrix, assignments] = findAssignments(costMatrix, assignments, rowCovered, colCovered)
while true
% Find a zero that is not covered
[rowZero, colZero] = find(costMatrix == 0 & ~rowCovered & ~colCovered, 1);
if isempty(rowZero) || isempty(colZero)
[costMatrix, assignments] = updateCostMatrix(costMatrix, assignments, rowCovered, colCovered);
break;
else
rowCovered(rowZero) = true;
colCovered(colZero) = true;
assignments(rowZero, colZero) = 1;
% Find a starred zero in the same row
colStarred = find(assignments(rowZero, :) == 1, 1);
if isempty(colStarred)
% No starred zero in the same row
[costMatrix, assignments] = updateCostMatrix(costMatrix, assignments, rowCovered, colCovered);
break;
else
% Cover the column of the starred zero and uncover the row of the starred zero
colCovered(colStarred) = false;
end
end
end
end
function [costMatrix, assignments] = updateCostMatrix(costMatrix, assignments, rowCovered, colCovered)
% Find the smallest uncovered value
uncoveredValues = costMatrix(~rowCovered, ~colCovered);
if ~isempty(uncoveredValues)
minUncoveredValue = min(uncoveredValues(:));
% Subtract the smallest uncovered value from uncovered rows
costMatrix(~rowCovered, ~colCovered) = costMatrix(~rowCovered, ~colCovered) - minUncoveredValue;
% Add the smallest uncovered value to covered columns
costMatrix(rowCovered, colCovered) = costMatrix(rowCovered, colCovered) + minUncoveredValue;
end
% Reset the covered assignments
assignments(rowCovered, :) = 0;
assignments(:, colCovered) = 0;
end
```
You can use this code by passing your cost matrix to the `hungarianAlgorithm` function. It will return the assignments and the minimum cost.
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