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• Continuous vs Discrete artificial neural networks

  - by gmatt

  I realize that this is probably a very niche question, but has anyone had experience with working with continuous neural networks? I'm specifically interested in what a continuous neural network may be useful for vs what you normally use discrete neural networks for.

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• help with matlab and Discrete Fourier transform

  - by user504363

  Hi all I have previous experience with Matlab, but the problem that I face some problems in apply a problem in (DSP : Digital signal processing) which is not my study field, but I must finish that problems in days to complete my project. all i want is help me with method and steps of solving this problem in matlab and then I can write the code with myself. the problem is about the signal x(t) = exp(-a*t); 1) what's the Discrete Fourier transform of the sampled signal with sample rate fs 2) if a=1 and fs =1 , plot the amplitude spectrum of sampled signal 3) fix the sampling frequency at fs = 1(hz) [what's it mean ?] and plot the magnitude of the Fourier Transform of the sampled signal at various values of a thanks

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• Discrete event simulation framework for .NET

  - by Kuba

  Does anyone have an experience with some discrete event simulation library that could be used in .NET (C#)? Despite the basic functionality for queing events and dispatching them, it would be fine to have some non-deterministic behavior (e.g. failures simulation). I have some tips and I am even considering to write my own, but first, I would like to collect some recomendations. Thanks. Additional info: i'm not looking explicitly for free product, however, the prize matters :) Just to precise the field i need to map, here is the example of a product: http://www.holushko.com/index.html

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• Rapid Planning: Next Generation MRP

  - by john.bermudez

  MRP has been a mainstay of manufacturing systems for 40 years. MRP evolved from simple inventory planning systems to become the heart of the MRPII systems which eventually became ERP. While the applications surrounding it have become broader, more sophisticated and web-based, MRP continues to operate in the loneliness of the Saturday night batch window quietly exploding bills of materials and logging exceptions for hours. During this same 40 years, manufacturing business processes have seen countless changes and improvements including JIT, TQM, Six Sigma, Flow Manufacturing, Lean Manufacturing and Supply Chain Management. Although much logic has been added to MRP to deal with new manufacturing processes, it has not been able to keep up with the real-time pace of today's supply chain. As a result, planners have devised ingenious ways to trick MRP to handle new processes but often need to dump the output into spreadsheets of their own design in the hope of wrestling thousands of exceptions to ground. Oracle's new Rapid Planning application is just what companies still running MRP have been waiting for! The newest member of the Value Chain Planning product line, Rapid Planning is designed to empower planners with comprehensive supply planning that runs online in minutes, not hours. It enables a planner simulate the incremental impact of a new order or re-run an entire plan in a separate sandbox. Rapid Planning does a complete multi-level bill of material explosion like MRP but plans orders considering material and capacity constraints. Considering material and capacity constraints in planning can help you quickly reduce inventory and improve on-time shipments. Rapid Planning is an APS application that leverages years of Oracle development experience and customer feedback. Rather than rely exclusively on black-box heuristics, Rapid Planning is designed to give planners the computing power to use their industry experience and business knowledge to improve MRP. For example, Rapid Planning has a powerful worksheet user interface with built-in query capability that allows the planner to locate the orders she is interested in and use a mass update function to make quick work of large changes. The planner can save these queries and unique user interface to personalize their planning environment. Most importantly, Rapid Planning is designed to do supply planning in today's dynamic supply chain environment. It can be used to supplement MRP or replace MRP entirely. It generates plans that provide order-by-order details with aggregate key performance indicators that enable planners to quickly assess the overall business impact of a plan. To find out more about how Rapid Planning can help improve your MRP, please contact me at [email protected] or your Oracle Account Manager.

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• Is it possible to install a discrete mobility card on a laptop without a graphics card already?

  - by JXPheonix

  To be specific: Can I: Install a discrete graphics card on a laptop that does not come with a discrete graphics card? Teach windows 8 to use the discrete card over the integrated graphics? To me this is the only downside of my laptop and I would not mind getting any graphics card as long as it is better than the integrated laptop card (an Intel 3000) The laptop if you need more information is an Asus U46E-BAL6.

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• Simple in-place discrete fourier transform ( DFT )

  - by Adam

  I'm writing a very simple in-place DFT. I am using the formula shown here: http://en.wikipedia.org/wiki/Discrete_Fourier_transform#Definition along with Euler's formula to avoid having to use a complex number class just for this. So far I have this: private void fft(double[] data) { double[] real = new double[256]; double[] imag = new double[256]; double pi_div_128 = -1 * Math.PI / 128; for (int k = 0; k < 256; k++) { for (int n = 0; n < 256; n++) { real[k] += data[k] * Math.Cos(pi_div_128 * k * n); imag[k] += data[k] * Math.Sin(pi_div_128 * k * n); } data[k] = Math.Sqrt(real[k] * real[k] + imag[k] * imag[k]); } } But the Math.Cos and Math.Sin terms eventually go both positive and negative, so as I'm adding those terms multiplied with data[k], they cancel out and I just get some obscenely small value. I see how it is happening, but I can't make sense of how my code is perhaps mis-representing the mathematics. Any help is appreciated. FYI, I do have to write my own, I realize I can get off-the shelf FFT's.

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• Tangent of a parametric discrete curve

  - by gregseth

  I have a parametric curve, say two vectors of doubles where the parameter is the index, and I have to calculate the angle of the tangent to this curve at any given point (index). Any suggestion or link about how to do that? Thanks.

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• Matplotlib: plotting discrete values

  - by Arkapravo

  I am trying to plot the following ! from numpy import * from pylab import * import random for x in range(1,500): y = random.randint(1,25000) print(x,y) plot(x,y) show() However, I keep getting a blank graph (?). Just to make sure that the program logic is correct I added the code print(x,y), just the confirm that (x,y) pairs are being generated. (x,y) pairs are being generated, but there is no plot, I keep getting a blank graph. Any help ?

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• Discrete problem of probability theory [closed]

  - by calejero

  A jury consists of 12 persons each of which has, before the trial started, a probability of 0.4 to vote in favor of the defendant's innocence. During the trial, the lawyer has a probability of 0.6 to change the mind of each juror who was biased against the accused. How likely is the defendant to be acquitted if he needs 10 votes in favor?

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• How important is Discrete Mathematics for a Computer Scientist?

  - by mort

  As the title says, How important is Discrete Mathematics for a Computer Scientist? Background: I'm pursuing a Master's degree with a focus on fundamentals such as Algorithms, Complexity and Computability Theory and Programming Languages to get a good foundation for working in the field of Parallel Computing. Some more background: My university grants a lot of freedom in the choices of courses for my Master's degree. It's officially called "Software Engineering", but due to a the broad range of electives, a different focus is possible. Interestingly, none of the electives is a lecture in Math! I'm thinking about doing a course about Discrete Mathematics that would take half a semester to complete successfully, even if I can't use it for my degree. So with this question I'm trying to find out if the effort is justifiable.

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• Do any database "styles" use discrete files for their tables?

  - by Brad

  I've been talking to some people at work who believe some versions of a database store their data in discrete tables. That is to say you might open up a folder and see one file for each table in the database then several other supporting files. They do not have a lot of experience with databases but I have only been working with them for a little over a half year so I am not a canonical source of info either. I've been touting the benefits of SQL Server over Access (and before this, Access over Excel. Great strides have been made :) ). But, other people were of the impression that the/one of the the benefit(s) of using SQL Server over Access was that all the data was not consolidated down into one file. Yet, SQL Server packs everything into a single .mdf file (plus the log file). My question is, is there an RDBMS which holds it's data in multiple discrete files instead of one master file? And if the answer is yes, why do it one way over the other?

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• Simple encryption - Sum of Hashes in C

  - by Dogbert

  I am attempting to demonstrate a simple proof of concept with respect to a vulnerability in a piece of code in a game written in C. Let's say that we want to validate a character login. The login is handled by the user choosing n items, (let's just assume n=5 for now) from a graphical menu. The items are all medieval themed: eg: _______________________________ | | | | | Bow | Sword | Staff | |-----------|-----------|-------| | Shield | Potion | Gold | |___________|___________|_______| The user must click on each item, then choose a number for each item. The validation algorithm then does the following: Determines which items were selected Drops each string to lowercase (ie: Bow becomes bow, etc) Calculates a simple string hash for each string (ie: `bow = b=2, o=15, w=23, sum = (2+15+23=40) Multiplies the hash by the value the user selected for the corresponding item; This new value is called the key Sums together the keys for each of the selected items; this is the final validation hash IMPORTANT: The validator will accept this hash, along with non-zero multiples of it (ie: if the final hash equals 1111, then 2222, 3333, 8888, etc are also valid). So, for example, let's say I select: Bow (1) Sword (2) Staff (10) Shield (1) Potion (6) The algorithm drops each of these strings to lowercase, calculates their string hashes, multiplies that hash by the number selected for each string, then sums these keys together. eg: Final_Validation_Hash = 1*HASH(Bow) + 2*HASH(Sword) + 10*HASH(Staff) + 1*HASH(Shield) + 6*HASH(Potion) By application of Euler's Method, I plan to demonstrate that these hashes are not unique, and want to devise a simple application to prove it. in my case, for 5 items, I would essentially be trying to calculate: (B)(y) = (A_1)(x_1) + (A_2)(x_2) + (A_3)(x_3) + (A_4)(x_4) + (A_5)(x_5) Where: B is arbitrary A_j are the selected coefficients/values for each string/category x_j are the hash values for each string/category y is the final validation hash (eg: 1111 above) B,y,A_j,x_j are all discrete-valued, positive, and non-zero (ie: natural numbers) Can someone either assist me in solving this problem or point me to a similar example (ie: code, worked out equations, etc)? I just need to solve the final step (ie: (B)(Y) = ...). Thank you all in advance.

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• Create a model that switches between two different states using Temporal Logic?

  - by NLed

  Im trying to design a model that can manage different requests for different water sources. Platform : MAC OSX, using latest Python with TuLip module installed. For example, Definitions : Two water sources : w1 and w2 3 different requests : r1,r2,and r3 - Specifications : Water 1 (w1) is preferred, but w2 will be used if w1 unavailable. Water 2 is only used if w1 is depleted. r1 has the maximum priority. If all entities request simultaneously, r1's supply must not fall below 50%. - The water sources are not discrete but rather continuous, this will increase the difficulty of creating the model. I can do a crude discretization for the water levels but I prefer finding a model for the continuous state first. So how do I start doing that ? Some of my thoughts : Create a matrix W where w1,w2 ? W Create a matrix R where r1,r2,r3 ? R or leave all variables singular without putting them in a matrix I'm not an expert in coding so that's why I need help. Not sure what is the best way to start tackling this problem. I am only interested in the model, or a code sample of how can this be put together. edit Now imagine I do a crude discretization of the water sources to have w1=[0...4] and w2=[0...4] for 0, 25, 50, 75,100 percent respectively. == means implies Usage of water sources : if w1[0]==w2[4] -- meaning if water source 1 has 0%, then use 100% of water source 2 etc if w1[1]==w2[3] if w1[2]==w2[2] if w1[3]==w2[1] if w1[4]==w2[0] r1=r2=r3=[0,1] -- 0 means request OFF and 1 means request ON Now what model can be designed that will give each request 100% water depending on the values of w1 and w2 (w1 and w2 values are uncontrollable so cannot define specific value, but 0...4 is used for simplicity )

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• Find the "largest" dense sub matrix in a large sparse matrix

  - by BCS

  Given a large sparse matrix (say 10k+ by 1M+) I need to find a subset, not necessarily continuous, of the rows and columns that form a dense matrix (all non-zero elements). I want this sub matrix to be as large as possible (not the largest sum, but the largest number of elements) within some aspect ratio constraints. Are there any known exact or aproxamate solutions to this problem? A quick scan on Google seems to give a lot of close-but-not-exactly results. What terms should I be looking for? edit: Just to clarify; the sub matrix need not be continuous. In fact the row and column order is completely arbitrary so adjacency is completely irrelevant. A thought based on Chad Okere's idea Order the rows from largest count to smallest count (not necessary but might help perf) Select two rows that have a "large" overlap Add all other rows that won't reduce the overlap Record that set Add whatever row reduces the overlap by the least Repeat at #3 until the result gets to small Start over at #2 with a different starting pair Continue until you decide the result is good enough

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• How would you solve this graph theory handshake problem in python?

  - by Zachary Burt

  I graduated college last year with a degree in Psychology, but I also took a lot of math for fun. I recently got the book "Introductory Graph Theory" by Gary Chartrand to brush up on my math and have some fun. Here is an exercise from the book that I'm finding particularly befuddling: Suppose you and your husband attended a party with three other married couples. Several handshakes took place. No one shook hands with himself (or herself) or with his (or her) spouse, and no one shook hands with the same person more than once. After all the handshaking was completed, suppose you asked each person, including your husband, how many hands he or she had shaken. Each person gave a different answer. a) How many hands did you shake? b) How many hands did your husband shake? Now, I've been reasoning about this for a while, and trying to draw sample graphs that could illustrate a solution, but I'm coming up empty-handed. My logic is this: there are 8 different vertices in the graph, and 7 of them have different degrees. The values for the degrees must therefore be 0, 1, 2, 3, 4, 5, 6, and x. The # of degrees for one married couple is (0, 6). Since all graphs have an even number of odd vertices, x must be either 5, 3, or 1. What's your solution to this problem? And, if you could solve it in python, how would you do it? (python is fun.) Cheers.

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• How would you solve this graph theory handshake problem in python?

  - by Zachary Burt

  I graduated college last year with a degree in Psychology, but I also took a lot of math for fun. I recently got the book "Introductory Graph Theory" by Gary Chartrand to brush up on my math and have some fun. Here is an exercise from the book that I'm finding particularly befuddling: Suppose you and your husband attended a party with three other married couples. Several handshakes took place. No one shook hands with himself (or herself) or with his (or her) spouse, and no one shook hands with the same person more than once. After all the handshaking was completed, suppose you asked each person, including your husband, how many hands he or she had shaken. Each person gave a different answer. a) How many hands did you shake? b) How many hands did your husband shake? Now, I've been reasoning about this for a while, and trying to draw sample graphs that could illustrate a solution, but I'm coming up empty-handed. My logic is this: there are 8 different vertices in the graph, and 7 of them have different degrees. The values for the degrees must therefore be 0, 1, 2, 3, 4, 5, 6, and x. The # of degrees for one married couple is (0, 6). Since all graphs have an even number of odd vertices, x must be either 5, 3, or 1. What's your solution to this problem? And, if you could solve it in python, how would you do it? (python is fun.) Cheers.

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• Python, dictionaries, and chi-square contingency table

  - by rohanbk

  I have a file which contains several lines in the following format (word, time that the word occurred in, and frequency of documents containing the given word within the given instance in time): #inputfile <word, time, frequency> apple, 1, 3 banana, 1, 2 apple, 2, 1 banana, 2, 4 orange, 3, 1 I have Python class below that I used to create 2-D dictionaries to store the above file using as the key, and frequency as the value: class Ddict(dict): ''' 2D dictionary class ''' def __init__(self, default=None): self.default = default def __getitem__(self, key): if not self.has_key(key): self[key] = self.default() return dict.__getitem__(self, key) wordtime=Ddict(dict) # Store each inputfile entry with a <word,time> key timeword=Ddict(dict) # Store each inputfile entry with a <time,word> key # Loop over every line of the inputfile for line in open('inputfile'): word,time,count=line.split(',') # If <word,time> already a key, increment count try: wordtime[word][time]+=count # Otherwise, create the key except KeyError: wordtime[word][time]=count # If <time,word> already a key, increment count try: timeword[time][word]+=count # Otherwise, create the key except KeyError: timeword[time][word]=count The question that I have pertains to calculating certain things while iterating over the entries in this 2D dictionary. For each word 'w' at each time 't', calculate: The number of documents with word 'w' within time 't'. (a) The number of documents without word 'w' within time 't'. (b) The number of documents with word 'w' outside time 't'. (c) The number of documents without word 'w' outside time 't'. (d) Each of the items above represents one of the cells of a chi-square contingency table for each word and time. Can all of these be calculated within a single loop or do they need to be done one at a time? Ideally, I would like the output to be what's below, where a,b,c,d are all the items calculated above: print "%s, %s, %s, %s" %(a,b,c,d)

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• Is it possible to implement bitwise operators using integer arithmetic?

  - by Statement

  Hello World! I am facing a rather peculiar problem. I am working on a compiler for an architecture that doesn't support bitwise operations. However, it handles signed 16 bit integer arithmetics and I was wondering if it would be possible to implement bitwise operations using only: Addition (c = a + b) Subtraction (c = a - b) Division (c = a / b) Multiplication (c = a * b) Modulus (c = a % b) Minimum (c = min(a, b)) Maximum (c = max(a, b)) Comparisons (c = (a < b), c = (a == b), c = (a <= b), et.c.) Jumps (goto, for, et.c.) The bitwise operations I want to be able to support are: Or (c = a | b) And (c = a & b) Xor (c = a ^ b) Left Shift (c = a << b) Right Shift (c = a b) (All integers are signed so this is a problem) Signed Shift (c = a b) One's Complement (a = ~b) (Already found a solution, see below) Normally the problem is the other way around; how to achieve arithmetic optimizations using bitwise hacks. However not in this case. Writable memory is very scarce on this architecture, hence the need for bitwise operations. The bitwise functions themselves should not use a lot of temporary variables. However, constant read-only data & instruction memory is abundant. A side note here also is that jumps and branches are not expensive and all data is readily cached. Jumps cost half the cycles as arithmetic (including load/store) instructions do. On other words, all of the above supported functions cost twice the cycles of a single jump. Some thoughts that might help: I figured out that you can do one's complement (negate bits) with the following code: // Bitwise one's complement b = ~a; // Arithmetic one's complement b = -1 - a; I also remember the old shift hack when dividing with a power of two so the bitwise shift can be expressed as: // Bitwise left shift b = a << 4; // Arithmetic left shift b = a * 16; // 2^4 = 16 // Signed right shift b = a >>> 4; // Arithmetic right shift b = a / 16; For the rest of the bitwise operations I am slightly clueless. I wish the architects of this architecture would have supplied bit-operations. I would also like to know if there is a fast/easy way of computing the power of two (for shift operations) without using a memory data table. A naive solution would be to jump into a field of multiplications: b = 1; switch (a) { case 15: b = b * 2; case 14: b = b * 2; // ... exploting fallthrough (instruction memory is magnitudes larger) case 2: b = b * 2; case 1: b = b * 2; } Or a Set & Jump approach: switch (a) { case 15: b = 32768; break; case 14: b = 16384; break; // ... exploiting the fact that a jump is faster than one additional mul // at the cost of doubling the instruction memory footprint. case 2: b = 4; break; case 1: b = 2; break; }

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• count of distinct acyclic paths from A[a,b] to A[c,d]?

  - by Sorush Rabiee

  I'm writing a sokoban solver for fun and practice, it uses a simple algorithm (something like BFS with a bit of difference). now i want to estimate its running time ( O and omega). but need to know how to calculate count of acyclic paths from a vertex to another in a network. actually I want an expression that calculates count of valid paths, between two vertices of a m*n matrix of vertices. a valid path: visits each vertex 0 or one times. have no circuits for example this is a valid path: but this is not: What is needed is a method to find count of all acyclic paths between the two vertices a and b. comments on solving methods and tricks are welcomed.

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• count of paths from A[a,b] to A[c,d] without duplicating?

  - by Sorush Rabiee

  I write a sokoban solver for fun and practice, it uses a simple algorithm (something like BFS). now i want to estimate its running time ( O and omega). but i need to know how to calculate count of paths from a vertex to another in a network. each path from a to b is a sequence of edges with no circuit. for example this is a correct path: http://www.imgplace.com/viewimg143/4789/501k.png but this is not: http://www.imgplace.com/viewimg143/6140/202.png

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• Counting problem: possible sudoko tables?

  - by Sorush Rabiee

  Hi, I'm working on a sudoko solver. my method is using a game tree and explore possible permutations for each set of digits by DFS Algorithm. in order to analyzing problem, i want to know what is the count of possible valid and invalid sudoko tables? - a 9*9 table that have 9 one, 9 two, ... , 9 nine. (this isn't exact duplicate by this question) my solution is: 1- First select 9 cells for 1s: (*) 2- and like (1) for other digits (each time, 9 cells will be deleted from remaining available cells): C(81-9,9) , C(81-9*2,9) .... = 3- finally multiply the result by 9! (permutation of 123456789 in (*)) this is not equal to accepted answer of this question but problems are equivalent. what did i do wrong?

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• finding ALL cycles in a huge sparse matrix

  - by Andy

  Hi there, First of all I'm quite a Java beginner, so I'm not sure if this is even possible! Basically I have a huge (3+million) data source of relational data (i.e. A is friends with B+C+D, B is friends with D+G+Z (but not A - i.e. unmutual) etc.) and I want to find every cycle within this (not necessarily connected) directed graph. I've found this thread (http://stackoverflow.com/questions/546655/finding-all-cycles-in-graph/549402#549402) which has pointed me to Donald Johnson's (elementary) cycle-finding algorithm which, superficially at least, looks like it'll do what I'm after (I'm going to try when I'm back at work on Tuesday - thought it wouldn't hurt to ask in the meanwhile!). I had a quick scan through the code of the Java implementation of Johnson's algorithm (in that thread) and it looks like a matrix of relations is the first step, so I guess my questions are: a) Is Java capable of handling a 3+million*3+million matrix? (was planning on representing A-friends-with-B by a binary sparse matrix) b) Do I need to find every connected subgraph as my first problem, or will cycle-finding algorithms handle disjoint data? c) Is this actually an appropriate solution for the problem? My understanding of "elementary" cycles is that in the graph below, rather than picking out A-B-C-D-E-F it'll pick out A-B-F, B-C-D etc. but that's not the end of the world given the task. E / \ D---F / \ / \ C---B---A d) If necessary, I can simplify the problem by enforcing mutuality in relations - i.e. A-friends-with-B <== B-friends-with-A, and if really necessary I can maybe cut down the data size, but realistically it is always going to be around the 1mil mark. z) Is this a P or NP task?! Am I biting off more than I can chew? Thanks all, any help appreciated! Andy

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• How can you transform a set of numbers into mostly whole ones?

  - by Alice

  Small amount of background: I am working on a converter that bridges between a map maker (Tiled) that outputs in XML, and an engine (Angel2D) that inputs lua tables. Most of this is straight forward However, Tiled outputs in pixel offsets (integers of absolute values), while Angel2D inputs OpenGL units (floats of relative values); a conversion factor between these two is needed (for example, 32px = 1gu). Since OpenGL units are abstract, and the camera can zoom in or out if the objects are too small or big, the actual conversion factor isn't important; I could use a random number, and the user would merely have to zoom in or out. But it would be best if the conversion factor was selected such that most numbers outputted were small and whole (or fractions of small whole numbers), because that makes it easier to work with (and the whole point of the OpenGL units is that they are easy to work with). How would I find such a conversion factor reliably? My first attempt was to use the smallest number given; this resulted in no fractions below 1, but often lead to lots of decimal places where the factors didn't line up. Then I tried the mode of the sequence, which lead to the largest number of 1's possible, but often lead to very long floats for background images. My current approach gets the GCD of the whole sequence, which, when it works, works great, but can easily be thrown off course by a single bad apple. Note that while I could easily just pass the numbers I am given along, or pick some fixed factor, or use one of the conversions I specified above, I am looking for a method to reliably scale this list of integers to small, whole numbers or simple fractions, because this would most likely be unsurprising to the end user; this is not a one off conversion. The end users tend to use 1.0 as their "base" for manipulations (because it's simple and obvious), so it would make more sense for the sizes of entities to cluster around this.

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• Resource placement (optimal strategy)

  - by blackened

  I know that this is not exactly the right place to ask this question, but maybe a wise guy comes across and has the solution. I'm trying to write a computer game and I need an algorithm to solve this question: The game is played between 2 players. Each side has 1.000 dollars. There are three "boxes" and each player writes down the amount of money he is going to place into those boxes. Then these amounts are compared. Whoever placed more money in a box scores 1 point (if draw half point each). Whoever scores more points wins his opponents 1.000 dollars. Example game: Player A: [500, 500, 0] Player B: [333, 333, 334] Player A wins because he won Box A and Box B (but lost Box C). Question: What is the optimal strategy to place the money? I have more questions to ask (algorithm related, not math related) but I need to know the answer to this one first. Update (1): After some more research I've learned that these type of problems/games are called Colonel Blotto Games. I did my best and found few (highly technical) documents on the subject. Cutting it short, the problem I have (as described above) is called simple Blotto Game (only three battlefields with symmetric resources). The difficult ones are the ones with, say, 10+ battle fields with non-symmetric resources. All the documents I've read say that the simple Blotto game is easy to solve. The thing is, none of them actually say what that "easy" solution is.

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• Finding a Eulerian Tour

  - by user590903

  I am trying to solve a problem on Udacity described as follows: # Find Eulerian Tour # # Write a function that takes in a graph # represented as a list of tuples # and return a list of nodes that # you would follow on an Eulerian Tour # # For example, if the input graph was # [(1, 2), (2, 3), (3, 1)] # A possible Eulerian tour would be [1, 2, 3, 1] I came up with the following solution, which, while not as elegant as some of the recursive algorithms, does seem to work within my test case. def find_eulerian_tour(graph): tour = [] start_vertex = graph[0][0] tour.append(start_vertex) while len(graph) > 0: current_vertex = tour[len(tour) - 1] for edge in graph: if current_vertex in edge: if edge[0] == current_vertex: current_vertex = edge[1] else: current_vertex = edge[0] graph.remove(edge) tour.append(current_vertex) break return tour graph = [(1, 2), (2, 3), (3, 1)] print find_eulerian_tour(graph) >> [1, 2, 3, 1] However, when submitting this, I get rejected by the grader. I am doing something wrong? I can't see any errors.

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