@@ -1502,19 +1502,19 @@ The **Assignment Problem** aims to allocate *n* tasks to *n* agents (machines, w
15021502<br >
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15041504
1505- ## 1. { Hungarian Method] ( ) (Step by Step):
1505+ ## 1. [ Hungarian Method] ( ) (Step by Step):
15061506
15071507### [ ** Step 1] ( ) : Subtract Row Minimums**
15081508
1509- #### Subtract the minimum value in each row from all elements in that row.
1509+ ### Subtract the minimum value in each row from all elements in that row.
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15111511- Row 1 min: 2 → [ 0, 2, 1]
15121512- Row 2 min: 1 → [ 0, 2, 1]
15131513- Row 3 min: 2 → [ 3, 0, 2]
15141514
15151515<br >
15161516
1517- #### [ ** Matrix after row subtraction:** ] ( )
1517+ ## [ ** Matrix after row subtraction:** ] ( )
15181518
15191519| | M1 | M2 | M3 |
15201520| ---------| ----| ----| ----|
@@ -1525,7 +1525,38 @@ The **Assignment Problem** aims to allocate *n* tasks to *n* agents (machines, w
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15261526<br >
15271527
1528+ ### [ ** Step 2] ( ) : Subtract Column Minimums**
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1530+ ### Subtract the minimum value in each column from all elements in that column] ( ) .
1531+
1532+ - Col 1 min: 0 → [ 0, 0, 3]
1533+ - Col 2 min: 0 → [ 2, 2, 0]
1534+ - Col 3 min: 1 → [ 0, 0, 1]
1535+
1536+ <br >
1537+
1538+ ### [ ** Matrix after column subtraction:** ] ( )
1539+
1540+ | | M1 | M2 | M3 |
1541+ | ---------| ----| ----| ----|
1542+ | Task 1 | 0 | 2 | 0 |
1543+ | Task 2 | 0 | 2 | 0 |
1544+ | Task 3 | 3 | 0 | 1 |
1545+
1546+ <br >
1547+
1548+ ## [ ** Step 3] ( ) : Assignment (Cover Zeros)**
1549+
1550+ - Cover all zeros using the minimum number of lines (rows or columns).
1551+ - Assign tasks to machines where possible (one zero per row/column).
1552+
1553+ ** Optimal Assignment:**
1554+ - Task 1 → Machine 1 (cost 2)
1555+ - Task 2 → Machine 3 (cost 2)
1556+ - Task 3 → Machine 2 (cost 2)
1557+
1558+
1559+ ### *** Total Minimum Cost = [ 2 + 2 + 2 = 6*** ] ( )
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