# hungarian algorthim code

i need code in c# which implement the Hungarian algorithm

Hungarian algorithm
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Commented:
Is this a homework problem?

Can't directly answer homework problems, but I can provide tips and references...

http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=hungarianAlgorithm

-john

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Commented:
Found this on the net.  it was in java I converted it to C#.

I am not sure if it 100% correct but it should give you a good starting point.
``````using System;
using System.Collections.Generic;
using System.Text;

namespace ConsoleApplication2
{
public class Program
{
//**********************************//
//METHODS OF THE HUNGARIAN ALGORITHM//
//**********************************//

public static int[][] hgAlgorithm(int[][] array, String sumType)
{
int[][] cost = array;	//Create the cost matrix

if (sumType.ToLower().Equals("max"))	//Then array is weight array. Must change to cost.
{
int maxWeight = findLargest(cost);
for (int i=0; i<cost.Length; i++)		//Generate cost by subtracting.
{
for (int j=0; j<cost[i].Length; j++)
{
cost [i][j] = (maxWeight - cost [i][j]);
}
}
}
int maxCost = findLargest(cost);		//Find largest cost matrix element (needed for step 6).

for (int Array0 = 0; Array0 < cost.Length; Array0++)
{
int[] rowCover = new int[cost.Length];					//The row covering vector.
int[] colCover = new int[cost[0].Length];				//The column covering vector.
int[] zero_RC = new int[2];								//Position of last zero from Step 4.
int step = 1;
bool done = false;
while (done == false)	//main execution loop
{
switch (step)
{
case 1:
step = hg_step1(step, cost);
break;
case 2:
step = hg_step2(step, cost, mask, rowCover, colCover);
break;
case 3:
break;
case 4:
step = hg_step4(step, cost, mask, rowCover, colCover, zero_RC);
break;
case 5:
step = hg_step5(step, mask, rowCover, colCover, zero_RC);
break;
case 6:
step = hg_step6(step, cost, rowCover, colCover, maxCost);
break;
case 7:
done=true;
break;
}
}//end while

int[][] assignment = new int[array.Length][];
for (int Array0 = 0; Array0 < array.Length; Array0++)
{
assignment[Array0] = new int[2];
}
for (int i = 0; i < mask.Length; i++)
{
for (int j = 0; j < mask[i].Length; j++)
{
{
assignment[i][0] = i;
assignment[i][1] = j;
}
}
}

//If you want to return the min or max sum, in your own main method
//instead of the assignment array, then use the following code:
/*
int sum = 0;
for (int i=0; i<assignment.Length; i++)
{
sum = sum + array[assignment[i][0]][assignment[i][1]];
}
return sum;
*/
//Of course you must also change the header of the method to:
//public static int hgAlgorithm (int[][] array, String sumType)

return assignment;
}
public static int hg_step1(int step, int[][] cost)
{
//What STEP 1 does:
//For each row of the cost matrix, find the smallest element
//and subtract it from from every other element in its row.

int minval;

for (int i = 0; i < cost.Length; i++)
{
minval = cost[i][0];
for (int j = 0; j < cost[i].Length; j++)	//1st inner loop finds min val in row.
{
if (minval > cost[i][j])
{
minval = cost[i][j];
}
}
for (int j = 0; j < cost[i].Length; j++)	//2nd inner loop subtracts it.
{
cost[i][j] = cost[i][j] - minval;
}
}

step = 2;
return step;
}
public static int hg_step2(int step, int[][] cost, int[][] mask, int[] rowCover, int[] colCover)
{
//What STEP 2 does:
//Marks uncovered zeros as starred and covers their row and column.

for (int i = 0; i < cost.Length; i++)
{
for (int j = 0; j < cost[i].Length; j++)
{
if ((cost[i][j] == 0) && (colCover[j] == 0) && (rowCover[i] == 0))
{
colCover[j] = 1;
rowCover[i] = 1;
}
}
}

clearCovers(rowCover, colCover);	//Reset cover vectors.

step = 3;
return step;
}
public static int hg_step3(int step, int[][] mask, int[] colCover)
{
//What STEP 3 does:
//Cover columns of starred zeros. Check if all columns are covered.

for (int i = 0; i < mask.Length; i++)	//Cover columns of starred zeros.
{
for (int j = 0; j < mask[i].Length; j++)
{
{
colCover[j] = 1;
}
}
}

int count = 0;
for (int j = 0; j < colCover.Length; j++)	//Check if all columns are covered.
{
count = count + colCover[j];
}

if (count >= mask.Length)	//Should be cost.Length but ok, because mask has same dimensions.
{
step = 7;
}
else
{
step = 4;
}

return step;
}
public static int hg_step4(int step, int[][] cost, int[][] mask, int[] rowCover, int[] colCover, int[] zero_RC)
{
//What STEP 4 does:
//Find an uncovered zero in cost and prime it (if none go to step 6). Check for star in same row:
//if yes, cover the row and uncover the star's column. Repeat until no uncovered zeros are left
//and go to step 6. If not, save location of primed zero and go to step 5.

int[] row_col = new int[2];	//Holds row and col of uncovered zero.
bool done = false;
while (done == false)
{
row_col = findUncoveredZero(row_col, cost, rowCover, colCover);
if (row_col[0] == -1)
{
done = true;
step = 6;
}
else
{
mask[row_col[0]][row_col[1]] = 2;	//Prime the found uncovered zero.

bool starInRow = false;
for (int j = 0; j < mask[row_col[0]].Length; j++)
{
if (mask[row_col[0]][j] == 1)		//If there is a star in the same row...
{
starInRow = true;
row_col[1] = j;		//remember its column.
}
}

if (starInRow == true)
{
rowCover[row_col[0]] = 1;	//Cover the star's row.
colCover[row_col[1]] = 0;	//Uncover its column.
}
else
{
zero_RC[0] = row_col[0];	//Save row of primed zero.
zero_RC[1] = row_col[1];	//Save column of primed zero.
done = true;
step = 5;
}
}
}

return step;
}
public static int[] findUncoveredZero	//Aux 1 for hg_step4.
(int[] row_col, int[][] cost, int[] rowCover, int[] colCover)
{
row_col[0] = -1;	//Just a check value. Not a real index.
row_col[1] = 0;

int i = 0; bool done = false;
while (done == false)
{
int j = 0;
while (j < cost[i].Length)
{
if (cost[i][j] == 0 && rowCover[i] == 0 && colCover[j] == 0)
{
row_col[0] = i;
row_col[1] = j;
done = true;
}
j = j + 1;
}//end inner while
i = i + 1;
if (i >= cost.Length)
{
done = true;
}
}//end outer while

return row_col;
}
public static int hg_step5(int step, int[][] mask, int[] rowCover, int[] colCover, int[] zero_RC)
{
//What STEP 5 does:
//Construct series of alternating primes and stars. Start with prime from step 4.
//Take star in the same column. Next take prime in the same row as the star. Finish
//at a prime with no star in its column. Unstar all stars and star the primes of the
//series. Erasy any other primes. Reset covers. Go to step 3.

int count = 0;												//Counts rows of the path matrix.
{
path[Array0] = new int[2];
}	//Path matrix (stores row and col).
path[count][0] = zero_RC[0];								//Row of last prime.
path[count][1] = zero_RC[1];								//Column of last prime.

bool done = false;
while (done == false)
{
if (r>=0)
{
count = count+1;
path[count][0] = r;					//Row of starred zero.
path[count][1] = path[count-1][1];	//Column of starred zero.
}
else
{
done = true;
}

if (done == false)
{
count = count+1;
path[count][0] = path [count-1][0];	//Row of primed zero.
path[count][1] = c;					//Col of primed zero.
}
}//end while

clearCovers(rowCover, colCover);

step = 3;
return step;

}
public static int findStarInCol			//Aux 1 for hg_step5.
{
int r = -1;	//Again this is a check value.
for (int i = 0; i < mask.Length; i++)
{
{
r = i;
}
}

return r;
}
public static int findPrimeInRow		//Aux 2 for hg_step5.
{
int c = -1;
for (int j = 0; j < mask[row].Length; j++)
{
{
c = j;
}
}

return c;
}
public static void convertPath			//Aux 3 for hg_step5.
(int[][] mask, int[][] path, int count)
{
for (int i = 0; i <= count; i++)
{
{
}
else
{
}
}
}
public static void erasePrimes			//Aux 4 for hg_step5.
{
for (int i = 0; i < mask.Length; i++)
{
for (int j = 0; j < mask[i].Length; j++)
{
{
}
}
}
}
public static void clearCovers			//Aux 5 for hg_step5 (and not only).
(int[] rowCover, int[] colCover)
{
for (int i = 0; i < rowCover.Length; i++)
{
rowCover[i] = 0;
}
for (int j = 0; j < colCover.Length; j++)
{
colCover[j] = 0;
}
}
public static int hg_step6(int step, int[][] cost, int[] rowCover, int[] colCover, int maxCost)
{
//What STEP 6 does:
//Find smallest uncovered value in cost: a. Add it to every element of covered rows
//b. Subtract it from every element of uncovered columns. Go to step 4.

int minval = findSmallest(cost, rowCover, colCover, maxCost);

for (int i = 0; i < rowCover.Length; i++)
{
for (int j = 0; j < colCover.Length; j++)
{
if (rowCover[i] == 1)
{
cost[i][j] = cost[i][j] + minval;
}
if (colCover[j] == 0)
{
cost[i][j] = cost[i][j] - minval;
}
}
}

step = 4;
return step;
}
public static int findSmallest		//Aux 1 for hg_step6.
(int[][] cost, int[] rowCover, int[] colCover, int maxCost)
{
int minval = maxCost;				//There cannot be a larger cost than this.
for (int i = 0; i < cost.Length; i++)		//Now find the smallest uncovered value.
{
for (int j = 0; j < cost[i].Length; j++)
{
if (rowCover[i] == 0 && colCover[j] == 0 && (minval > cost[i][j]))
{
minval = cost[i][j];
}
}
}

return minval;
}

//***********//
//MAIN METHOD//
//***********//

public static void Main(String[] args)
{
//Below enter "max" or "min" to find maximum sum or minimum sum assignment.
String sumType = "max";

//Hard-coded example.
//int[][] array =
//{
//		{1, 2, 3},
//		{2, 4, 6},
//		{3, 6, 9}
//};

//<UNCOMMENT> BELOW AND COMMENT BLOCK ABOVE TO USE A RANDOMLY GENERATED MATRIX

Console.WriteLine("How many rows for the matrix? ");

Console.WriteLine("How many columns for the matrix? ");
int[][] array = new int[numOfRows][];
for (int Array0 = 0; Array0 < numOfRows; Array0++)
{
array[Array0] = new int[numOfCols];
}
generateRandomArray(array, "random");	//All elements within [0,1].
//</UNCOMMENT>

if (array.Length > array[0].Length)
{
Console.Write("Array transposed (because rows>columns).\n");	//Cols must be >= Rows.
array = transpose(array);
}

//<COMMENT> TO AVOID PRINTING THE MATRIX FOR WHICH THE ASSIGNMENT IS CALCULATED

Console.Write("The matrix is:");
for (int i=0; i<array.Length; i++)
{
for (int j=0; j<array[i].Length; j++)
{ Console.Write("{0}\t", array[i][j]); }
Console.Write("");
}
Console.Write("");
//</COMMENT>*/

long startTime = DateTime.Now.Ticks;
int[][] assignment = new int[array.Length][];
for (int Array0 = 0; Array0 < array.Length; Array0++)
{
assignment[Array0] = new int[2];
}
assignment = hgAlgorithm(array, sumType);	//Call Hungarian algorithm.
long endTime = DateTime.Now.Ticks;

Console.Write("\n\nThe winning assignment (" + sumType + " sum) is:\n");
int sum = 0;
for (int i=0; i<assignment.Length; i++)
{
//<COMMENT> to avoid printing the elements that make up the assignment

Console.Write("array({0},{1}) = {2}\n", (assignment[i][0]+1), (assignment[i][1]+1),
array[assignment[i][0]][assignment[i][1]]);
sum = sum + array[assignment[i][0]][assignment[i][1]];
//</COMMENT>
}

Console.Write("\nThe {0} is: {1}\n", sumType, sum);
Console.Write("Time elapsed:");
Console.Write((endTime - startTime) / 1000000000.0);

}

//*******************************************//
//*******************************************//

public static void generateRandomArray	//Generates random 2-D array.
(int[][] array, String randomMethod)
{
Random generator = new Random(1);
for (int i = 0; i < array.Length; i++)
{
for (int j = 0; j < array[i].Length; j++)
{
array[i][j] = generator.Next();
}
}
}
public static int findLargest		//Finds the largest element in a positive array.
(int[][] array)
//works for arrays where all values are >= 0.
{
int largest = 0;
for (int i = 0; i < array.Length; i++)
{
for (int j = 0; j < array[i].Length; j++)
{
if (array[i][j] > largest)
{
largest = array[i][j];
}
}
}
Console.Write("\n\nLargest Value {0}: ", largest);
return largest;
}
public static int[][] transpose		//Transposes a int[][] array.
(int[][] array)
{
int[][] transposedArray = new int[array[0].Length][];
for (int Array0 = 0; Array0 < array[0].Length; Array0++)
{
transposedArray[Array0] = new int[array.Length];
}
for (int i=0; i<transposedArray.Length; i++)
{
for (int j=0; j<transposedArray[i].Length; j++)
{transposedArray[i][j] = array[j][i];}
}
return transposedArray;
}
public static int[][] copyOf			//Copies all elements of an array to a new array.
(int[][] original)
{
int[][] copy = new int[original.Length][];
for (int Array0 = 0; Array0 < original.Length; Array0++)
{
copy[Array0] = new int[original[0].Length];
}
for (int i=0; i<original.Length; i++)
{
//Need to do it this way, otherwise it copies only memory location
Array.Copy(original[i], 0, copy[i], 0, original[i].Length);

}

return copy;
}

}

}
``````
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