ehtsham / munkres-algorithm Goto Github PK
View Code? Open in Web Editor NEWIn Python, Munkres Algorithm; the famous Linear Programming Algorithm, finds the matches between products and customers
Home Page: http://ehtshamml.blogspot.com/
In Python, Munkres Algorithm; the famous Linear Programming Algorithm, finds the matches between products and customers
Home Page: http://ehtshamml.blogspot.com/
In this document, I would explain the usage as well as underlying Assignment algorithm. Usage: python milo_challenge.py customersfile.txt productsfile.txt Please keep the customersfile.txt and productsfile.txt in the same folder as the code Assignment Algorithm: First of all, I create a matrix of dimension number of customers times number of products. Each cell in the matrix represents the suitability score calculated by the procedure described in the Challenge statement. Note that, it is possible that number of customers are more than number of products and vice versa. I deal with the situations by padding zeros as necessary to make a square matrix. The “customer to product” assignment problem is an example of the classic assignment problem in Linear Programming. There are various ways to solve the linear optimization problem like simplex method, Hungarian (Munkres) algorithm. I opted Hungarian Algorithm because of its cleaner flow and easy to understand steps. The Hungarian Algorithm I implemented consists of the following 6 steps: Step-1 For each row of the matrix, find the smallest element and subtract it from every element in its row. Go to Step 2. Step-2 From the matrix resulting from Step-1, find a zero. If there is no zero marked as 'starred' in the same row or column, mark that zero as 'starred'. Repeat for each element in the matrix. Go to Step-3. Step-3: Cover each column containing a 'starred' zero. If number of columns equal to number of columns in the matrix (assuming squared matrix) are covered, then the 'starred' zeros describe a complete set of unique assignments. In this case, algorithm has finished, hence Done. Otherwise, Go to Step 4. Step-4: Find a non-covered zero and mark it as 'primed'. 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. Continue in this manner until there are no uncovered zeros left. Save the smallest uncovered value and Go to Step 6. Step-5: Construct a series of alternating 'primed' and 'starred' zeros as follows: Let series[i][j] represent the location of uncovered 'primed' zero found in Step 4. Let series[k][j] denote the 'starred' zero in the column j(i-e in the same column as the last 'starred' zero), if there is any . Let series[k][l] denote the 'primed' zero in the row k (i-e in the row of last 'starred' zero). Continue until the you find a 'primed' zero that has no 'starred' zero in its column. Mark each 'starred' zero in the series as 'un-starred', 'star' each 'primed' zero of the series, erase all 'primed' and uncover every line in the matrix. Return to Step 3 Step-6: Add the value found in Step 4 to every element of each covered row, and subtract it from every element of each uncovered column. Return to Step 4 without altering any stars, primes, or covered lines.
A declarative, efficient, and flexible JavaScript library for building user interfaces.
🖖 Vue.js is a progressive, incrementally-adoptable JavaScript framework for building UI on the web.
TypeScript is a superset of JavaScript that compiles to clean JavaScript output.
An Open Source Machine Learning Framework for Everyone
The Web framework for perfectionists with deadlines.
A PHP framework for web artisans
Bring data to life with SVG, Canvas and HTML. 📊📈🎉
JavaScript (JS) is a lightweight interpreted programming language with first-class functions.
Some thing interesting about web. New door for the world.
A server is a program made to process requests and deliver data to clients.
Machine learning is a way of modeling and interpreting data that allows a piece of software to respond intelligently.
Some thing interesting about visualization, use data art
Some thing interesting about game, make everyone happy.
We are working to build community through open source technology. NB: members must have two-factor auth.
Open source projects and samples from Microsoft.
Google ❤️ Open Source for everyone.
Alibaba Open Source for everyone
Data-Driven Documents codes.
China tencent open source team.