*Let’s call this labeling feasible if it satisfies the following condition: .*

Discuss this article in the forums Are you familiar with the following situation?

You open the Div I Medium and don’t know how to approach it, while a lot of people in your room submitted it in less than 10 minutes.

(Example on the picture above, with root in W4)That’s all for the theory, now let’s look at the algorithm: First let’s have a look on the scheme of the Hungarian algorithm: Step 0. (See Picture 1)Picture 1Here are the global variables that will be used in the code:#define N 55 //max number of vertices in one part#define INF 100000000 //just infinityint cost[N][N]; //cost matrixint n, max_match; //n workers and n jobsint lx[N], ly[N]; //labels of X and Y partsint xy[N]; //xy[x] - vertex that is matched with x,int yx[N]; //yx[y] - vertex that is matched with ybool S[N], T[N]; //sets S and T in algorithmint slack[N]; //as in the algorithm descriptionint slackx[N]; //slackx[y] such a vertex, that// l(slackx[y]) l(y) - w(slackx[y],y) = slack[y]int prev[N]; //array for memorizing alternating paths It’s easy to see that next initial labeling will be feasible: And as an initial matching we’ll use an empty one. The code for initializing is quite easy, but I’ll paste it for completeness: The next three steps will be implemented in one function, which will correspond to a single iteration of the algorithm.

Find some initial feasible vertex labeling and some initial matching. If M is perfect, then it’s optimal, so problem is solved. (x – is a root of the alternating tree we’re going to build). When the algorithm halts, we will have a perfect matching, that's why we'll have n iterations of the algorithm and therefore (n 1) calls of the function.

be a spanning subgraph of G (in other words, it includes all vertices from G).

If G only those edges (x,y) which satisfy the following condition: , then it is an equality subgraph.

Then, after the contest, you find out in the editorial that this problem can be simply reduced to a classical one.

If yes, then this tutorial will surely be useful for you. We can also rephrase this problem in terms of graph theory.

Our goal is to complete all jobs minimizing total inputs, while assigning each worker to exactly one job and vice versa. Small example just to make things clearer: This problem is known as the assignment problem.

The assignment problem is a special case of the transportation problem, which in turn is a special case of the min-cost flow problem, so it can be solved using algorithms that solve the more general cases.

## Comments Steps To Solve Assignment Problem

## An Assignment Problem solved using the Hungarian Algorithm.

The Hungarian algorithm An example. We consider an example where four jobs J1, J2, J3, and J4 need to be executed by four workers W1, W2, W3, and W4, one job per worker. The matrix below shows the cost of assigning a certain worker to a certain job. The objective is to minimize the total cost of the assignment.…

## Assignment problem - Wikipedia

The assignment problem can be solved by. we arrive, after at most n steps, at a solution in which all variables.…

## Hungarian algorithm - Wikipedia

The Hungarian method is a combinatorial optimization algorithm that solves the assignment problem. time complexity, Liu, Shell. Solve any Assignment Problem online, provides a step by step explanation of the Hungarian Algorithm.…

## New Proposed Method for Solving Assignment Problem and.

In this paper we attempt to introduce a new proposed approach for solving assignment problem with algorithm and solution steps. We examine a numerical.…

## Assignment ProblemEasy Steps to solve -

Here is the video about assignment problem - Hungarian method on Operations research, In this video we discussed what is assignment problem and how to solve using Hungarian method with step by.…

## Steps to Solve Math Problems PrivateWriting

The ability to solve math problems not only boosts one’s abstract thinking, it is also a marketable skill in the workplace as many employers require that their employees have taken several math courses in college. Problem solving is a process of finding the solutions to difficult issues. Whether.…

## Hungarian Algorithm for Assignment Problem Set 1.

Brute force solution is to consider every possible assignment implies a. 0 1500 10 0 0 2000 500 Step 2 Subtract minimum of every column.…

## Hungarian Method Examples, Assignment Problem

Solution. This is a minimization example of assignment problem. We will use the. steps Step 1. Identify the minimum element in each row and subtract it from.…

## The Assignment Problem and the Hungarian Method

The Assignment Problem Suppose we have n resources to which we want to assign to n tasks on a one-to-one basis. Suppose also that we know the cost of assigning a given resource to a given task. We wish to ﬁnd an optimal assignment–one which minimizes total cost. 29…

## ES-3 Lesson 9. SOLUTION OF ASSIGNMENT PROBLEM

Although assignment problem can be solved either by using the techniques of. Step II Similarly subtract the minimum cost of each column of the cost matrix.…