# Assignment Algorithm This is because, at the time of publication (1957), few people had access to a computer and the algorithm was exercised by hand.Step 0: Create an nxm matrix called the cost matrix in which each element represents the cost of assigning one of n workers to one of m jobs.In the completed program the tagged (starred) zeros flag the row/column pairs that have been assigned to each other.

This is because, at the time of publication (1957), few people had access to a computer and the algorithm was exercised by hand.Step 0: Create an nxm matrix called the cost matrix in which each element represents the cost of assigning one of n workers to one of m jobs.In the completed program the tagged (starred) zeros flag the row/column pairs that have been assigned to each other.

However, we can apply a few general rules of programming style to simplify this problem.

The same rules can be applied to any step-algorithm.

Once minval has been found this value is subtracted from each element of that row in the second inner loop over j. In this step, we introduce the mask matrix M, which in the same dimensions as the cost matrix and is used to star and prime zeros of the cost matrix.

The value of step is set to 2 just before stepone ends. If there is no starred zero in its row or column, star Z. If M(i,j)=1 then C(i,j) is a starred zero, If M(i,j)=2 then C(i,j) is a primed zero. Before we go on to Step 3, we uncover all rows and columns so that we can use the cover vectors to help us count the number of starred zeros. If K columns are covered, the starred zeros describe a complete set of unique assignments. Once we have searched the entire cost matrix, we count the number of independent zeros found. If there is no starred zero in the row containing this primed zero, Go to Step 5.

Rotate the matrix so that there are at least as many columns as rows and let k=min(n,m). If there is no starred zero in the row containing this primed zero, Go to Step 5.

Otherwise, cover this row and uncover the column containing the starred zero.By applying Rule 4 to the step-algorithm we decide to make each step its own procedure.Now we can apply Rule 8 by using a case statement in a loop to control the ordering of step execution.Assignment Problem - Let C be an nxn matrix representing the costs of each of n workers to perform any of n jobs.The assignment problem is to assign jobs to workers so as to minimize the total cost. Remember that each assignment must be unique in its row and column.The main loop for Munkres as a step-wise algorithm is shown here implemented in C#.is set to some value outside the range 1..7 so that done will be set to true and the program will end.Continue in this manner until there are no uncovered zeros left.Save the smallest uncovered value and Go to Step 6. Continue until the series terminates at a primed zero that has no starred zero in its column.The other possible way out of Step 4 is that there are no noncovered zeros at all, in which case the program goes to Step 6.At first it may seem that the erratic nature of this algorithm would make its implementation difficult.

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