# Questions tagged [combinatorics]

Questions related to combinatorics and discrete mathematical structures

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### fast estimation of the amount of unique combinations

Let's say I have a set of two columns - Name, Surname. I have a list of possible values for Name -> Jacob, John Surname -> Mayerson, Kindle. I want to generate a set of unique combinations for ...
4k views

### Given n numbers How to find out a set of numbers whose sum equal to a certain given number

I am given an list of numbers and A number-s. I need to find out the collection(s) of numbers from the list of numbers whose sum corresponds to the given number s. ...
40 views

1 vote
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### The Hydra Game algorithm

I was recently introduced to the Hydra Game by the youtube channel Numberphile (https://www.youtube.com/watch?v=prURA1i8Qj4). In this video, they discuss many variants of the Hydra Game - cut off one ...
86 views

### The existence of a (nearly) quadratic time algorithm for 2-steps shortest path or smallest triangle

I am interested in two problems, which seem to be related, solving each will advance me in other possible directions. In both problems, $G=(V,E)$ is a positively-weighted undirected graph. Denote its ...
43 views

### Binary subset rank and unrank

Let there be "N" bits. We want to rank and unrank a specific subset of bit combinations based on the following criteria - ...
55 views

### Number of graphs that almost contain a $k$-clique

A (loop-free) graph almost contains a $k$-clique if it does not contain a $k$-clique, but adding an edge between any two different vertices that are not already connected by an edge would produce a $k$...
1 vote
29 views

### Minimum expected number of path to cut graph problem

I came up with a problem but was unable to show the hardness of the problem (NP/#P/P-hard). The problem is as follows. Given a directed graph $G=(V, E)$, each edge will have a confidence score $c$. ...
210 views

### Matching 2 sets of items by price

I'm trying to solve the following problem in the most efficient way I can find. I want to trade my items for someone elses items, every item have a price and a value. I want to maximize the value of ...
1 vote
145 views

71 views

### How to estimate the number of nodes in a trie based on a dictionary of words?

Say I want to build a trie out of 800,000 Sanskrit "base" words (in Devanagari script), with 20 prefixes and 2,000 possible suffixes. Each word is anywhere from 1-20 characters, and prefixes/...
17 views

### Finding all stable matchings in stable marriage problem [duplicate]

I need to find an algorithm for a modified version of the stable marriage problem. In particular, I need to find all possible stable matchings and not only one (unlike what the Gale-Shapley algorithm ...