Code jam problem is the following:

You are given a complete undirected graph with N nodes and K "forbidden" edges. N <= 300, K <= 15. Find the number of Hamiltonian cycles in the graph that do not use any of the K "forbidden" edges.

Unfortunately the explanations of this here on stack and throughout the web are very insufficient. I can figure out HamCycles for a certain 'n' : (n-1)! / 2 .

And I can do the short set with dynamic programming.

But I don't get all the subset bologna, how to make it O^K? I'm in Python and have yet to decipher the C++ available. Eventually I'm sure I will take the time to learn C++ and then I will decipher it. But in the meantime, why can't someone explain this better somewhere on the web? They are always half explanations.

It might help if you point to the explanations that are lacking, but I'll try anyway...

The O(2^{k})-based solution uses the inclusion-exclusion principle. Given that there are ** k** forbidden edges, there are

For each subset, you calculate the number of cycles that include at least all the edges in that subset . If the number of cycles containing edges ** s** is

```
sum, for each subset s of S: f(s) * (-1)^|s|
```

where |** s**| is the number of elements in

Calculating ** f(s)** is not trivial -- at least I didn't find an easy way to do it. You might stop and ponder it before reading on.

To calculate ** f(s)**, start with the number of permutations of the nodes not involved with any

Now examine the edges in ** s** for chains. If there are any impossible combinations, such as a node involved with 3 edges or a subcycle within

Otherwise, for each chain increment ** m** by 1 and multiply

Similar Questions

(tl;dr at the bottom) Let me try to explain what I'm trying to accomplish: I have a two dimensional array, and I would like to display its contents a certain way. I want rows, and each row can displ

The following code finds the correct hamiltonian cycle for a knight in a chessboard when started on position 0 0 in a 10x10 or 8x8 chessboard but throws a NullPointerException when started anywhere el

i'm currently searching for a solution to save the mongodb cursor (after a find()) to access it between two http requests. My environment is JAVA Spring MVC and mongodb (Spring Data) so i have all of

I have implemented a BFS algorithm to detect cycles in a graph, this is the following code: void hasCycle(node *root,string start){ if(root->visted){ if(root->name == start) cout << Has

The for loop is working properly , but everything is happening in a single clock cycle. How I make it run a single iteration per cycle? `timescale 1ns/10ps module multiplier (clock,multiplier,multip

I have a vector of pairs representing hops between nodes which I would like to collapse when there are cycles (as in aggregate time between the hops in a cycle to display it as just one). So, for exam

I read from an wiki article (http://en.wikipedia.org/wiki/NAND_flash#Write_endurance) that says flash storage has a limit of read/write cycles (for NAND flash this limit is about 10K-100K). My questi

I can't find the link to the binaries for gcj for MinGW; it doesn't show up on the MinGW-get list, and I can't find the binaries on the site. Does it even exist? Where can I find it?

I found that SMLAxy consumes 1 cycle under ARM profiler ARM1176 (RVDS 4.0). [ARM1176] http://goo.gl/aS9N0t But SMLAxy consumes 2 cycles under Cortex-A9MPx1. [CortexA9] http://goo.gl/1kNAoA It confl

As there are some instructions that are being used in MIPS Architecture, which doesn't require all 5 cycles for its successful completion, like the store instruction doesn't need to use 5th stage. So

I need to make some sort of liblisp (in C11), and it will need to handle the basic functions, pretty much like what libobjc does for the Objective-C language. Edit I'm rewritting the question to somet

I am writing a program in c to find the time required to perform a task in terms of CPU cycles. I am avoiding the time conversion, Time in sec = 1/clock cycles as CPU frequency changes while low load

I am newbie with EF and trying to design my database using Code First. Following is my three Entities (I have not written all properties). I have an ode situation. The administrator is not allowed to

I know this is a fairly frequent question (tsp in general), but I've been stumped by it for awhile now. I'm looking to find the minimal distance hamiltonian path given a set of x,y coordinates. The st

I've been running some metrics on my Java project and apparently there are a lot of dependency cycles between packages. I didn't really know how to organize stuff into packages, so I just did what mad

I have a directed cyclic graph with more than one cycle in it and I need a way to detect (and list) each cycle present in the digraph. The graph can be seen here: http://img412.imageshack.us/img412/33

I have an undirected graph and what I would like to do is detect cycles that have three or more nodes in them. Is there a library in R that would do this? If not is there a simple algorithm that I cou

I read that on an SM with 8 SPs, each thread in a warp is mapped to each of the 8 SPs during the execution of one instruction. Hence, a warp is executed in 32/8 = 4 clock cycles. If so, then suppose

I'm trying to determine the cycles in a directed graph using Tarjan's algorithm, presented in his research paper Enumeration of the elementary circuits of a directed graph from Septermber 1972. I'm

I want to maintain a directed graph in hibernate/sql (ie: a simple many-to-many self association) that does not have cycles or diamonds. By no diamonds, I mean there is no more than one path from

I saw a solution to preventing block retain cycles here But I am having trouble wrapping my head around why or even how it works. In the example, a weak self reference is made and acted upon. I can se

Let G=(E,V) be a directed graph with non-negative edge costs. Let s be a vertex. I need to find an algorithm that finds for each vertex v, the shortest cycle that contains both s and v. The cycle may

there are lots of questions about this problem, but I couldn't solve my case. can some one please take a look at this: I have an Office table which has one-many relationship with Doctor and Secretary

When I run this segment of my program, the only loop to work is the last for loop involving the 'week' variable. cout << Enter Building: ; cin >> building; cout << \n; cout <

Instruments can visualize retain cycles under ARC in a graphically interesting way. I also remember that a few days ago I spotted the Cycles view in Instruments by accident. Now where I started usin

I've got some input files from my teacher wich we are supposed to test the program with. The task is to read from file, create a directed graph and print out the output. But if there is a cycle we are

I'm running an x86 processor, but I believe my question is pretty general. I'm curious about the theoretical difference in clock cycles consumed by a CMP + JE sequence versus a single MUL operation. I

I have a database table like following: column 1 | column 2 x | Y y | z z | x So basically x->y->z->x. Now I have to detect such entries in the DB. One solution could be take these entries

Reference counting alone does not collect cycles but there are additional techniques that can collect cycles as well. What is the simplest such technique? I'd like to compare the complexity of augment

I am writing a monitor for my Java backend and need to be able to monitor different things (memory, CPU, user activity, load, etc.) at different times. Most importantly is that I need to be able to co

Is there anywhere on the web where i can get an idea of what the various programming language syntax take in terms of processor (Core i7 and Core 2) cycles? At university i learnt the ARM assembly lan

I'm new to cocoa. I thought I could set the UITableViewCell background view to my own custom subclass in order to display a loading bar in the background of the cell, but it seems that calling setNeed

I had decided to try and compile minecraft into a native binary. For that I used the following (approximately, optimization may have differed): gcj -c -O2 -fjni -findirect-dispatch ./minecraft.jar &am

I am trying to implement an adjacency matrix in java that will produce an output for a Hamiltonian cycle, which can then be solved with different algorithms such as kruskurals, djikstras and the 2opt

I was implementing algorithms defined in this paper and I can't quite get the proposed way of removing false cycles from the results. Quote from the paper: The method will find non-existing cycles in

I not whether this is the sort of question to be asked on StackOverflow, but I'll ask it anyway. I am using GCJ (as part of MinGW) on Windows XP SP3 to compile a Java class to an EXE. The Java Class i

I'm having a bit of trouble getting my head around referencing self within a block, and not creating a retain cycle. Can you let me know if my understanding is correct: If I ever reference self within

I have many skeletonized images like this: How can i detect a cycle, a loop in the skeleton? Are there special functions that do this or should I implement it as a graph? In case there is only th

I've just read that some SqlExceptions thrown by Oracle jdbc drivers has reference to itself in cause field. IMHO an exception can cause itself about as easily as I can pull myself out of a swamp by

I'm still pretty new to Cocoa/Objective-C, so I hope I can explain my question. I created a Garbage Collected application in Xcode 4.2 I have my app delegate that creates an Authorize object (my class

I've been stock since yesterday with this problem. Unfurturenately/furturenately this problem makes only about 0.5% of the my super huge (for me, a c++ newbie) algorithm thus the need for a library of

First off here's my code layout: public partial class GUI : Form { public GUI() { InitializeComponent(); } private void GoButton_Click(object sender, EventArgs e) { backgroundWorker1.RunWorkerAsync();

I am implementing an algorithm which finds an optimal Hamiltonian path in a directed graph. I have implemented an algorithm which appears to work reasonably well, however I am not entirely sure if the

I have some different models that perform the same task, using different algorithms. I want to compare the performance of these models by measuring CPU cycles (I tried using System.Diagnostics.StopWat

I've read that the problem of finding whether a Hamiltonian path exists in a graph is NP-Complete, and since Dijkstra's Shortest Path Algorithm runs in Polynomial Time, it cannot be modified to find t

Will this lead to any sort of retain cycle? Is it safe to use? __block void (^myBlock)(int) = [^void (int i) { if (i == 0) return; NSLog(@%d, i); myBlock(i - 1); } copy]; myBlock(10); myBlock = nil;

I'm really new in MIPS and I have these questions which I found so many dissimil answers for them ... if someone can help, it would be great. Thanks How many clock cycles does this code take? #Macro I

I have a pic 16f886 and I want to know if you could explain how you get the answer of 250 instruction cycles

given n as number of nodes and edges as a list of edges can anyone tell me whats wrong with my code. It works on some instances but doesnt work for all of them for edgeindex in range(len(edges)): allt

How do you manage the various resources who have differing life cycles? For instance a project manager will be the busiest during the initiation phase of a project and then utilized at some level (usu