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For each row of the matrix, find the smallest element and subtract it from every element in its row.We try to assign tasks to agents such that each agent is doing only one task and the penalty incurred in each case is zero.Ĭore of the algorithm (assuming square matrix): We reduce our original weight matrix to contain zeros, by using the above theorem. If a number is added to or subtracted from all of the entries of any one row or column of a cost matrix, then an optimal assignment for the resulting cost matrix is also an optimal assignment for the original cost matrix. The Hungarian algorithm, aka Munkres assignment algorithm, utilizes the following theorem for polynomial runtime complexity ( worst case O(n 3)) and guaranteed optimality: Other Possible assignment: Cost = 9500 INR and this is the best of the 3! possible assignments.īrute force solution is to consider every possible assignment implies a complexity of Ω(n!). Find the number of islands | Set 1 (Using DFS).Travelling Salesman Problem | Set 1 (Naive and Dynamic Programming).
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Disjoint Set (Or Union-Find) | Set 1 (Detect Cycle in an Undirected Graph).Kruskal’s Minimum Spanning Tree Algorithm | Greedy Algo-2.
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