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Discover Accurate Answers to Frequently Asked Homework Questions

• How is blood in the feet returned to the heart against the force of gravity?
• Are muscles and glands part of the central nervous system, receptors, part of the peripheral nervous system, or effectors?
• What is the longest cranial nerve?
• What is the pH of carbon dioxide? What is the pH of carbon dioxide?
• What is the medical term for the eardrum?
• How do sweat glands protect the human body?
• What is an infarct of right and left parietal lobes of brain?
• What changes occur in a human body after death?
• Bones are part of which system?
• What is the purpose of the microvilli of the small intestine?
• What is the distance from earth to the planet pluto in meters?
• Do any other planet in our solar system have Iron metal, not necessarily in the core?
• What is the brightest planet seen from earth?
• How does red shift relate to the universe?
• Why do astronomers try to find the distance to stars using parallax?
• Is our solar system really a binary star system?
• Does the solar system change over time?
• How far is the sun from earth in light years?
• What causes day and night and different seasons?
• What is the parallax formula?
• How can meteorites be interplanetary arks?
• How does luminosity differ from the brightness of the same object as seen at the earth?
• How can solar flares affect communications on earth?
• Light from the sun travels through space to Earth's atmosphere. What will light waves do when they move from empty space into matter made up of different gases?
• How can parallax be used to determine distances?
• When can the zodiacal light be seen during the night?
• In which layer of the atmosphere are the ionized particles that cause the aurora borealis?
• What makes the speed of light exactly 299,792,458 metres per second?
• What is the temperature of betelgeuse?
• What is a magnetic field? How were they formed?
• What term defines a gene made up of two different alleles?
• How do stomata help conserve water?
• What is in atp that ADP also has?
• Why do materials diffuse across a membrane?
• How are angiosperms and gymnosperms related?
• How are the long DNA molecules found in eukaryotes packed into short chromosomes?
• Why is a species hard to define?
• What is the importance of matter cycles to an ecosystem?
• Are protists autotroph or heterotroph?
• What is the taxonomic classification of a horse?
• How many electrons are in an isotope of nitrogen with 8 neutrons?
• A given volume of a buffer solution contains #6.85 x 10^-3# mol of the weak acid HY and #2.98 x 10^-3# mol of the salt NaY. The pH of the buffer solution is 3.78. How do you calculate the value of #pKa# for the acid HY at this temperature?
• A sample of hydrogen gas is mixed with water vapor. The mixture has a total pressure of 745torr, and the water vapor has a partial pressure of 24 torr. What is the partial pressure of the hydrogen gas?
• For the reaction, #"2XO + O"_2 → "2XO"_2#, data obtained from measurement of the initial rate of reaction at varying concentrations are?
• How much calcium metal must be added to an excess of water to produce 3.7g of calcium hydroxide?
• What are the mole fractions of each component prepared by adding #5*g# of water to #95*g# of ethanol?
• What is the value of the equilibrium constant at 655 K for each of the following reactions?
• Calculate no. Of photons emitted by a 60 watt light bulb in 10 h if a bulb emitted least 6.62 A°?
• What is the atomic number of carbon?
• Why did Mendeleev have problems arranging the elements #Te# and #I#?
• Why do sedimentary rocks have layers?
• Does every rock go through the complete rock cycle, from igneous rock to sedimentary rock to metamorphic rock and back to igneous rock, each time around?
• What is the difference between lava and magma?
• What are the three factors that contribute the most to the formation of coastal currents?
• What are two recreational activities that can speed up weathering by exposing new rock surfaces?
• What is convection and how is it related to the mantle?
• How does the sun affect the solar system?
• What traps solar energy in the atmosphere?
• What is residence time and what are the average residence time for some of the major water reservoirs on earth?
• How do soils differ from sediments?
• What does the mining reclamation process look like?
• When did the world population reach 1 billion?
• Where is an elephant on the food pyramid?
• Is natural selection a law or theory?
• How does the rock cycle affect the atmosphere of the earth?
• What does the future of nuclear energy around the world look like?
• Do living organisms defy the second law of thermodynamics?
• What are some positive and negative impacts of agriculture?
• What are four examples of air pollutants?
• How can nuclear energy be improved?
• How is #NH_3 # acting in the reaction #H^++:NH_3 ->[H:NH_3]^+#according to the Lewis definition?
• What is ethyl alcohol used for?
• How can benzene be separated from thiophene chemically?
• Are aromatic amines less basic?
• What does "cis" isomer mean in cyclohexane ring?
• How do you draw geometric isomers?
• What amino acid has an aromatic ring in its side chain?
• How are SN1 and SN2 reactions different?
• How can I read a #C^13 NMR# spectrum?
• Why are there different Newman projections for one molecule in organic chemistry?
• If a worker pulls a 10kg bucket up a 25 m well, how much work has he or she done?
• If a projectile is shot at a velocity of #2 m/s# and an angle of #pi/6#, how far will the projectile travel before landing?
• The force applied against a moving object travelling on a linear path is given by #F(x)= sinx + 2 #. How much work would it take to move the object over #x in [ 0, (7 pi) / 8 ] #?
• A charge of #18 C# passes through a circuit every #4 s#. If the circuit can generate #24 W# of power, what is the circuit's resistance?
• A projectile is shot at an angle of #pi/8 # and a velocity of # 8 m/s#. How far away will the projectile land?
• What is the kinetic energy of a #8 kg# object moving at #5/4 m/s#?
• A ball with a mass of #350 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #9 (kg)/s^2# and was compressed by #7/4 m# when the ball was released. How high will the ball go?
• An electric toy car with a mass of #5 kg# is powered by a motor with a voltage of #12 V# and a current supply of #1 A#. How long will it take for the toy car to accelerate from rest to #3 m/s#?
• A projectile is shot from the ground at an angle of #pi/12 # and a speed of #8 /3 m/s#. Factoring in both horizontal and vertical movement, what will the projectile's distance from the starting point be when it reaches its maximum height?
• A model train with a mass of #4 kg# is moving along a track at #9 (cm)/s#. If the curvature of the track changes from a radius of #36 cm# to #24 cm#, by how much must the centripetal force applied by the tracks change?
• How do you simplify #\frac { 18x ^ { 4} y ^ { 3} } { 24x ^ { 2} y ^ { 3} }#?
• How do you factor # 2x^2 - 13x#?
• How do find the vertex and axis of symmetry, and intercepts for a quadratic equation #y=x^2-7x-28#?
• How do you find the c that makes the trinomial #x^2+22x+c# a perfect square?
• What is the vertex of # y= 4(x+2)^2-2x^2-4x+3#?
• How do you write the quadratic in vertex form given #y=x^2-5#?
• How do you factor completely #2x^3+10x^2+14x+70#?
• How do you solve using the completing the square method #x^2 + 2x = 7#?
• What is the axis of symmetry and vertex for the graph #y= -7x^2#?
• How do you write #y = x^2 - 9x - 10# into vertex form?
• What is the derivative of #f(x)=(x^2-4)ln(x^3/3-4x)#?
• How do you differentiate #cos(pi*x^2)#?
• What is the derivative of #y=sin(tan2x)#?
• What is the derivative of this function #arcsec(x^3)#?
• What is the derivative of this function #y=sin^-1(2x)#?
• What is the derivative of this function #sin^-1(x/4)#?
• How do you differentiate #(3+sin(x))/(3x+cos(x))#?
• How do you differentiate #f(x)= 1/ (lnx)# using the quotient rule?
• How do you find the derivative of #y=tan(3x)# ?
• How do you differentiate #g(y) =(60x^2+74)( 2x+2) # using the product rule?
• How can we find the area of irregular shapes?
• A triangle has corners at #(5 ,1 )#, #(2 ,9 )#, and #(4 ,3 )#. What is the area of the triangle's circumscribed circle?
• What is the trinomial that represents the area of a rectangular rug whose sides are (x+3) feet and (2x-1) feet?
• A triangle has corners at #(5 ,6 )#, #(4 ,3 )#, and #(2 ,2 )#. What is the area of the triangle's circumscribed circle?
• What is the area of the quadrilateral bounded by #y=5#; #x=1#; #y=1#; and #y=-2x+9#?
• How is the formula for the area of a parallelogram ABCD derived?
• Circle A has a center at #(2 ,5 )# and a radius of #2 #. Circle B has a center at #(4 ,-1 )# and a radius of #6 #. Do the circles overlap? If not, what is the smallest distance between them?
• An equilateral triangle is circumscribed inside a circle with a radius of 6. What is the area of the triangle?
• Two corners of an isosceles triangle are at #(5 ,8 )# and #(9 ,2 )#. If the triangle's area is #36 #, what are the lengths of the triangle's sides?
• How do you find the circumference of a circle with a diameter of 7.5 in?
• Jeanie has a 3/4 yard piece of ribbon. She needs one 3/8 yard piece and one 1/2 yard piece. Can she cut the piece of ribbon into the two smaller pieces? Why?
• How do you find the GCF of #25k, 35j#?
• How do you write 132/100 in a mixed number?
• How do you evaluate the power #2^3#?
• How do you simplify #(4^6)^2 #?
• How do you convert 3.2 tons to pounds?
• How do you solve #\frac { 5} { 8} + \frac { 3} { 2} ( 4- \frac { 1} { 4} ) - \frac { 1} { 8}#?
• Tiffany pays $40 for 160 minutes of talk time on her cell phone. How many minutes of talk time does she get per dollar?
• Jay made 8 of 10 free throws. Kim made 25 of 45. Who made free throws at the better rate?
• How do you convert the word phrase to symbols. "The product of twenty and eight, increased by ten?"
• How do you describe the end behavior for #f(x)=x^4-x^2-2#?
• How do you find vertical, horizontal and oblique asymptotes for #y = (4x^3 + x^2 + x + 5 )/( x^2 + 3x)#?
• How do you find all the asymptotes for function #y=(3x^2+2x-1)/(x^2-4 )#?
• How do you find the asymptotes for #f(x) = (x^2) / (x^2 + 1)#?
• How do you find #f(x)# and #g(x)# when #h(x)= (x+1)^2 -9(x+1)# and #h(x)= (fog)(x)#?
• How do you determine whether the graph of #y^2+3x=0# is symmetric with respect to the x axis, y axis or neither?
• How do you determine whether the graph of #y^2=(4x^2)/9-4# is symmetric with respect to the x axis, y axis, the line y=x or y=-x, or none of these?
• How do you find the inverse of #y=x^(2)-6x+4# and is it a function?
• How do you write a rule for the nth term of the arithmetic sequence and then find #a_10# for #d=5, a_5=33#?
• How do you solve #2^(x-1)=23#?
• A set of data contains 200 elements. How do you find the median of the data?
• What is the variance of a binomial distribution for which n = 75 and p = 0.20?
• Given 9 starting batters on a baseball team, how many batting orders are possible if the shortstop must bat first and the right fielder must bat fourth?
• What is the value of a? P(X≥a)=0.5
• Can someone help me answer this question?
• If you roll a die three times, how many different sequences are possible?
• What does an R-Squared value indicate about a linear regression?
• On a spinner, #P(3) = 2/5# and the #P(4) = 3/8#, what is the probability of getting 3 or 4?
• What is the z-score of sample X, if #n = 81, mu= 43, St. Dev. =90, and E[X] =57#?
• Suppose that the temperature is normally distributed with expectation 50℃ and variance 4℃.What is the probability that the temperature T will be between 48℃ and 53℃?What is the probability that T≥52℃?
• How can you verify #sinx/(sinx+cosx)=(cotx-1)/(cotx+1)# by only manipulating the left side?
• How do you identify the point (x,y) on the unit circle that corresponds to t=-11pi/4?
• How do you use the half angle formulas to simplify the expression #-sqrt((1-cos8x)/(1+cos8x))#?
• How do you solve this trigonometric equation?
• How do you write #2 +4i# in trigonometric form?
• A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 3, respectively. The angle between A and C is #(pi)/3# and the angle between B and C is # (pi)/4#. What is the area of the triangle?
• If #A = <5 ,2 ,8 >#, #B = <2 ,5 ,6 ># and #C=A-B#, what is the angle between A and C?
• How do you solve (2sinx+1)(sinx-1)=0?
• How do you prove # (cosA - cotA) / ( 1 - sinA) = - cotA#?
• How do you sketch y=2sinx when x is between 0 and 360?
• What is an intransitive complete verb?
• Is "Let's don't." grammatically correct?
• What is the difference between a metaphor and a symbol?
• What is the future tense of "lay"? I am using it in a line of a poem.
• Is "fur coat" a compound noun? For example, "First, its husky build and heavy fur coat allowed the Samoyed to sand changes in temperature."
• What are some examples of antithesis?
• What does this aphorism mean: "the doors of wisdom are never shut."? It is by Benjamin Franklin. What message was Franklin trying to send to the 18th century Americans when he wrote it?
• How can you rewrite the following sentence from the first-person perspective of someone in the sentence?: They bought a coat and gave it to the homeless man on the corner.
• I want to write a counterargument in an argumentative essay, but I have a hard time "un"-proving the point I bring up from the other side of the argument. Should I pick a new point?
• What is the collective noun for whales?
• Why did Lincoln need the support of the border states?
• What proposal was included in Secretary of the Treasury Alexander Hamilton's financial plans in the 1790s?
• When did the first American combat troops arrive in Vietnam?
• Which Great Awakening preacher warned people that God would punish them if they did not change their ways?
• What are the advantages to Marshall's "broad" interpretation of the Constitution? What are its disadvantages?
• What act of U.S. expansion was the direct result of Matthew Perry's naval journey to Japan?
• How does the baby boom illustrates a break from Depression Era American life?
• Do you agree with Susan B. Anthony that women should receive equal pay for equal work?
• Under President Ronald Reagan, the United States had the largest peacetime military buildup in history. How was this a challenge to the Soviet Union?
• What was the first act that the Parliament passed in an attempt to raise revenue by taxing the American colonists?
• What other nations joined Germany in forming the Axis Powers?
• Which group has dominated Russia's politics throughout most of its history?
• What kind of relationship did the Soviet Union have with the United States in 1945?
• What does this logo stand for?
• How and why did Africans come to Latin America?
• How did the the Zionist movement lead to the creation of the State of Israel?
• How would you describe USA and Italy's intentions behind the terms of the Treaty of Versailles?
• Bolivia is one of two landlocked countries in South America. What is the other country?
• What inventions sped up communication beginning in the late 19th century?
• How were early factories powered and who created the first factory?

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Yes, Question AI can provide versions of text that are longer or shorter based on your specific needs.

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QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

• The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
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How does smodin omni work.

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The Must-Have Math AI & Calculator for Students

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7 Most Effective Ways For How To Solve Assignment Problems

Here in this blog, CodeAvail experts will explain to you 7 most effective ways for how to solve assignment problems step by step in detail.

How To Solve Assignment Problems

Table of Contents

The most common question asked by many students is how to solve assignment problems. There are many students who are having a hard time with their assignments thats why they are looking for proper guidelines to solve those problems. The assignment is one of the most critical parts of the students’ academic journey, and one always states that I have a lot of assignments to do. Besides this, there is not a single student in the world who has never done any assignment in their academic life. But the students always want to find the best and most effective ways for how to solve assignment problems . In this blog, we have given all the necessary information to help you solve your assignment problems.

How To Solve Assignment Problems-Stepwise Guide

To solve assignment problems, you need to understand the question carefully first. Because if you don’t understand the question, you will not know the information you need to complete your assignments. Follow these steps to know How To Solve assignment Problems :

1) Proper Planning Is Required 

This is the first step when you start solving your assignment, you’ll most likely jump directly into the main thing. The primary thing you will do is pull out of your beg, at that point work your way through the remainder of your assignment. There’s a superior way. Know how much time you need to do an assignment. At that point list down all the various chores that you need to do. Check to what extent it will take you to finish every task to check whether you have to permit yourself additional time. Be practical. When your note down everything then the next step is to find the best place for work.

2) Collect All the required Data Before You Start  

This is the biggest problem of many students, they don’t really follow this step. Make sure you have all the required information to solve assignment problems. Don’t start your assignment without the proper information. Because after starting your assignment when you come back it may be hard to get once again and write with the same flow. It will just destroy your assignment writing flow. If you have planned efficiently, you should know what exactly you want to complete your assignment and set up everything in your study table you’ll require.

3) Set A Timetable For Certain Assignment

Set a proper timetable to achieve each part of your assignment based on how long you think each part of your assignment will take and how much time you have. Give yourself enough time to complete each part and do other nightly routines. Set a proper time and be honest with it. The less time you waste on checking your laptop or mobile, the more quickly you can complete your assignment. If you believe you can complete everything in a half-hour, set a timer and work honestly to complete it.

4) Stay Away From Distractions

You need a quiet place when you are working on your assignment problems. Problems like Maths assignment problems, Computer science problems needs a quiet place to complete. Keep your telephone away from you, stay away from your PC, and make your surroundings as peaceful as possible. Because to solve assignment problems it requires a lot of focus. Giving work your full focus will really make it simpler, in light of the fact that your brain won’t balance various tasks simultaneously. 

Usually, students will attempt to perform multiple tasks, sitting in front of the TV or tuning in to the radio or proceeding to visit on Facebook or Instagram while additionally attempting to do assignments. It will be a lot more enjoyable to do those things after you are done completing your assignment.

5) Taking Breaks is Necessary

If your professor assigns you a lot of assignments to complete, then You want to work straight through hours and hours of assignment if you have a lot to do. But it would probably end up slowing you down and prolonging the whole session.

Get the work done in short periods. Go hard on an assignment, then take a short break to stretch and walk. To keep going, it will re-energize your mind and your body. This strategy will help you solve your assignment problems quickly and help you maintain your assignment’s quality. Try to do your assignment for 1 hour and then take a 10 minutes break.

6) Isolate Yourself

It is one of the best ways to do assignment problems. Because when we isolate ourselves from the outside world, we can do a better concentration on our assignment. The reason is, many outside elements distract our mind from our assignment. When we are going to do our assignment, we should isolate ourselves from our family, social media, and other social activities. 

7) Take Help From Online Service Providers

There are many Excel problems that are hard to solve at that time you can take help from online service providers. The reason for taking help from these online service providers because they have years of experience in their respective field. Plus if you need any help you can contact them because they are always available to deal with your problems. They are well aware of the guidelines provided by universities and colleges and know how to solve assignment problems .

Follow all the steps we mentioned above will help in solving your assignment problems. In this article, we have given all the required information that will help you find the answer on how to solve assignment problems . The assignment problems like Maths and Computer science required a lot of focus and proper time management. Time is everything if you manage your time effectively then you will not find any problem solving your assignment problems before the allotted time. Just put away the thing which you think can distract your mind. And give yourself a break after you complete every task because if you give your rain rest then it will be helpful for you to focus on your next task.

If you are facing a problem with completing your assignment or any other assignment, you can take help from us. Our Assignment providers have helped students across the world in completing their assignments on time, get good grades, and at the same time. There’s no doubt that many teachers are handing out assignments that are hard to complete on time. Some assignments can be about an unknown subject. But the truth is, often, the students need assignment help. It is your best decision when you have a lot of tasks to complete but still want to have free time.

As a result, Our computer science assignment help and programming assignment help experts are available for you to 24*7.

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• Branch and Bound Tutorial
• Backtracking Vs Branch-N-Bound
• 0/1 Knapsack
• 8 Puzzle Problem
• Job Assignment Problem
• N-Queen Problem
• Travelling Salesman Problem

Job Assignment Problem using Branch And Bound

Let there be N workers and N jobs. Any worker can be assigned to perform any job, incurring some cost that may vary depending on the work-job assignment. It is required to perform all jobs by assigning exactly one worker to each job and exactly one job to each agent in such a way that the total cost of the assignment is minimized.

Let us explore all approaches for this problem.

Solution 1: Brute Force  

We generate n! possible job assignments and for each such assignment, we compute its total cost and return the less expensive assignment. Since the solution is a permutation of the n jobs, its complexity is O(n!).

Solution 2: Hungarian Algorithm  

The optimal assignment can be found using the Hungarian algorithm. The Hungarian algorithm has worst case run-time complexity of O(n^3).

Solution 3: DFS/BFS on state space tree  

A state space tree is a N-ary tree with property that any path from root to leaf node holds one of many solutions to given problem. We can perform depth-first search on state space tree and but successive moves can take us away from the goal rather than bringing closer. The search of state space tree follows leftmost path from the root regardless of initial state. An answer node may never be found in this approach. We can also perform a Breadth-first search on state space tree. But no matter what the initial state is, the algorithm attempts the same sequence of moves like DFS.

Solution 4: Finding Optimal Solution using Branch and Bound  

The selection rule for the next node in BFS and DFS is “blind”. i.e. the selection rule does not give any preference to a node that has a very good chance of getting the search to an answer node quickly. The search for an optimal solution can often be speeded by using an “intelligent” ranking function, also called an approximate cost function to avoid searching in sub-trees that do not contain an optimal solution. It is similar to BFS-like search but with one major optimization. Instead of following FIFO order, we choose a live node with least cost. We may not get optimal solution by following node with least promising cost, but it will provide very good chance of getting the search to an answer node quickly.

There are two approaches to calculate the cost function:  

• For each worker, we choose job with minimum cost from list of unassigned jobs (take minimum entry from each row).
• For each job, we choose a worker with lowest cost for that job from list of unassigned workers (take minimum entry from each column).

In this article, the first approach is followed.

Let’s take below example and try to calculate promising cost when Job 2 is assigned to worker A. 

Since Job 2 is assigned to worker A (marked in green), cost becomes 2 and Job 2 and worker A becomes unavailable (marked in red). 

Now we assign job 3 to worker B as it has minimum cost from list of unassigned jobs. Cost becomes 2 + 3 = 5 and Job 3 and worker B also becomes unavailable. 

Finally, job 1 gets assigned to worker C as it has minimum cost among unassigned jobs and job 4 gets assigned to worker D as it is only Job left. Total cost becomes 2 + 3 + 5 + 4 = 14. 

Below diagram shows complete search space diagram showing optimal solution path in green. 

Complete Algorithm:  

Below is the implementation of the above approach:

Time Complexity: O(M*N). This is because the algorithm uses a double for loop to iterate through the M x N matrix.  Auxiliary Space: O(M+N). This is because it uses two arrays of size M and N to track the applicants and jobs.

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The Assignment Problem, a NumPy function?

Since an assignment problem can be posed in the form of a single matrix, I am wondering if NumPy has a function to solve such a matrix. So far I have found none. Maybe one of you guys know if NumPy/SciPy has an assignment-problem-solve function?

Edit: In the meanwhile I have found a Python (not NumPy/SciPy) implementation at http://software.clapper.org/munkres/ . Still I suppose a NumPy/SciPy implementation could be much faster, right?

• optimization
• combinatorics

• What a shame it was not implemented with numpy. Not only might it be faster, but the algorithm must be much easier to express with numpy as well. –  u0b34a0f6ae Commented Sep 9, 2009 at 12:33

7 Answers 7

There is now a numpy implementation of the munkres algorithm in scikit-learn under sklearn/utils/linear_assignment_.py its only dependency is numpy. I tried it with some approximately 20x20 matrices, and it seems to be about 4 times as fast as the one linked to in the question. cProfiler shows 2.517 seconds vs 9.821 seconds for 100 iterations.

• 6 This will be included in scipy as scipy.optimize.linear_sum_assignment from version 0.18. –  joeln Commented Jan 14, 2016 at 3:41
• 1 The linear_assignment_ module is deprecated in 0.21 and will be removed from 0.23. Use scipy.optimize.linear_sum_assignment instead. –  min2bro Commented Dec 7, 2019 at 8:56

I was hoping that the newer scipy.optimize.linear_sum_assignment would be fastest, but (perhaps not surprisingly) the Cython library (which does not have pip support) is significantly faster, at least for my use case:

UPDATE: using munkres v1.1.2 and scipy v1.5.0 achieves the following results:

• I just tried the library for my case and got 25x speedup using the Cython version! –  Marcus V. Commented Apr 5, 2018 at 13:25
• I also tried the cython version and got a massive speedup. Just had to learn to install from source since it apparently lacks pip support –  kevinkayaks Commented Sep 12, 2018 at 23:43
• 2 The implementation of scipy.optimize.linear_sum_assignment has been revised and implemented from scratch in C++. The new implementation will be available in SciPy 1.4.0 and should provide substantial improvements in speed. –  fuglede Commented Jul 19, 2019 at 12:32
• Yes..Newer implementation of scipy.optimize.linear_sum_assignment is very fast. A 1000 x 1000 cost matrix takes 70ms to solve. –  Abhilash Awasthi Commented Jun 6, 2020 at 10:35

No, NumPy contains no such function. Combinatorial optimization is outside of NumPy's scope. It may be possible to do it with one of the optimizers in scipy.optimize but I have a feeling that the constraints may not be of the right form.

NetworkX probably also includes algorithms for assignment problems.

• 11 There is an implementation scipy.optimize.linear_sum_assignment from scipy version 0.18. –  joeln Commented Jan 14, 2016 at 3:41

Yet another fast implementation, as already hinted by @Matthew: scipy.optimize has a function called linear_sum_assignment . From the docs:

The method used is the Hungarian algorithm, also known as the Munkres or Kuhn-Munkres algorithm.

https://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.optimize.linear_sum_assignment.html

There is an implementation of the Munkres' algorithm as a python extension module which has numpy support. I've used it successfully on my old laptop. However, it does not work on my new machine - I assume there is a problem with "new" numpy versions (or 64bit arch).

As of version 2.4 (released 2019-10-16), NetworkX solves the problem through nx.algorithms.bipartite.minimum_weight_full_matching . At the time of writing, the implementation uses SciPy's scipy.optimize.linear_sum_assignment under the hood, so expect the same performance characteristics.

In addition to the solver in scipy.optimize.linear_sum_assignment already mentioned in some of the other answers, SciPy (as of 1.6.0) also comes with a sparsity-friendly solver in scipy.sparse.csgraph.min_weight_full_bipartite_matching .

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#1 Excel tutorial on the net

• Assignment Problem

Formulate the Model | Trial and Error | Solve the Model

Use the solver in Excel to find the assignment of persons to tasks that minimizes the total cost.

Formulate the Model

The model we are going to solve looks as follows in Excel.

1. To formulate this assignment problem , answer the following three questions.

a. What are the decisions to be made? For this problem, we need Excel to find out which person to assign to which task (Yes=1, No=0). For example, if we assign Person 1 to Task 1, cell C10 equals 1. If not, cell C10 equals 0.

b. What are the constraints on these decisions? Each person can only do one task (Supply=1). Each task only needs one person (Demand=1).

c. What is the overall measure of performance for these decisions? The overall measure of performance is the total cost of the assignment, so the objective is to minimize this quantity.

2. To make the model easier to understand, create the following named ranges .

3. Insert the following functions.

Explanation: The SUM functions calculate the number of tasks assigned to a person and the number of persons assigned to a task. Total Cost equals the sumproduct of Cost and Assignment.

Trial and Error

With this formulation, it becomes easy to analyze any trial solution.

For example, if we assign Person 1 to Task 1, Person 2 to task 2 and Person 3 to Task 3, Tasks Assigned equals Supply and Persons Assigned equals Demand. This solution has a total cost of 147.

It is not necessary to use trial and error. We shall describe next how the Excel Solver can be used to quickly find the optimal solution.

Solve the Model

To find the optimal solution, execute the following steps.

1. On the Data tab, in the Analyze group, click Solver.

Note: can't find the Solver button? Click here to load the Solver add-in .

Enter the solver parameters (read on). The result should be consistent with the picture below.

You have the choice of typing the range names or clicking on the cells in the spreadsheet.

2. Enter TotalCost for the Objective.

3. Click Min.

4. Enter Assignment for the Changing Variable Cells.

5. Click Add to enter the following constraint.

Note: binary variables are either 0 or 1.

6. Click Add to enter the following constraint.

7. Click Add to enter the following constraint.

8. Check 'Make Unconstrained Variables Non-Negative' and select 'Simplex LP'.

9. Finally, click Solve.

The optimal solution:

Conclusion: it is optimal to assign Person 1 to task 2, Person 2 to Task 3 and Person 3 to Task 1. This solution gives the minimum cost of 129. All constraints are satisfied.

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One of the most well-known combinatorial optimization problems is the assignment problem . Here's an example: suppose a group of workers needs to perform a set of tasks, and for each worker and task, there is a cost for assigning the worker to the task. The problem is to assign each worker to at most one task, with no two workers performing the same task, while minimizing the total cost.

You can visualize this problem by the graph below, in which there are four workers and four tasks. The edges represent all possible ways to assign workers to tasks. The labels on the edges are the costs of assigning workers to tasks.

An assignment corresponds to a subset of the edges, in which each worker has at most one edge leading out, and no two workers have edges leading to the same task. One possible assignment is shown below.

The total cost of the assignment is 70 + 55 + 95 + 45 = 265 .

The next section shows how solve an assignment problem, using both the MIP solver and the CP-SAT solver.

Other tools for solving assignment problems

OR-Tools also provides a couple of other tools for solving assignment problems, which can be faster than the MIP or CP solvers:

• Linear sum assignment solver
• Minimum cost flow solver

However, these tools can only solve simple types of assignment problems. So for general solvers that can handle a wide variety of problems (and are fast enough for most applications), we recommend the MIP and CP-SAT solvers.

Except as otherwise noted, the content of this page is licensed under the Creative Commons Attribution 4.0 License , and code samples are licensed under the Apache 2.0 License . For details, see the Google Developers Site Policies . Java is a registered trademark of Oracle and/or its affiliates.

Last updated 2024-08-28 UTC.