# Questions tagged [combinatorics]

Questions related to combinatorics and discrete mathematical structures

529 questions
Filter by
Sorted by
Tagged with
309 views

### Count number of pairs of elements whose product is a perfect square

Given two arrays whose elements lie between $[1,10^5]$ and the size of arrays is $[1,10^5]$, how can we find the total number of pairs of elements from these arrays such that their product is a ...
66 views
+50

### Selection over combinatorics that satisfies a distribution

I'm having an exciting problem that I could not manage to find an optimized solution. I actually have no idea if the problem is already known or not. Here is the problem : Consider a list of M ...
23 views

### What is a good method for modelling combinatorial tree (sport competition results)?

Probably newbie question here, please point me out to relevant theories/tutorials if needed : let say I want to evaluate the probabilities of the final rankings for a sport competition the ...
25 views

### Sliding Puzzle w/ multiple solutions

I am trying to write an algorithm which produces a solution to a modified n by n sliding puzzle (assuming that an end state is reachable from the given start state). The change is as follows: tiles ...
19 views

### Find an algorithm to fully consume items with criteria and produce minimal result

So here are the prerequisites: There are items to be consumed. Consider an item is just an object with a bunch of properties (e.g. size, weight), and there are tens or hundreds of properties. Items ...
22 views

### Counting number of binary trees with given node values and root

I came across following problem: Find number of binary trees possible with 2 as roots. Nodes={1,2,3,4,5} There was no solution given. I knew number of binary trees for given preorder is given by ...
60 views

### Generation of all k-combinations of a set in max-differing order

I'm looking for an algorithm that generates all k-combinations of a set, such that each successive combination generated differs as much as possible (or in practice, a lot) from all previous ...
512 views

### Showing that the number of primitive-recursion programs for each function is countably-infinite

Problem Statement Prove that if a function $f$ is primitive recursive, then there are countably infinite number of primitive recursive definitions of $f$ Yes, this is a homework question. My ...
Consider a string of characters $a, b, c$ only. Such a string is called good if the number of $a$'s + number of $b$'s is equal to the number of $c$'s. Given an integer $n$, find the number of strings ...