# Questions tagged [counting]

The term Counting in Computer Science is usually used to refer to counting objects in certain arrangements or with certain properties.

197 questions
Filter by
Sorted by
Tagged with
18 views

1 vote
41 views

1 vote
166 views

### Counting independent sets

I know the Independent set problem is NP-complete. But could there be a more efficient way to count the exact number of different independent sets in an arbitrary, given graph?
51 views

### BSTs with repeating keys

The problem is to count number of unique binary search trees with keys $a_1,a_2,...,a_n$, given that some of the keys are not unique. For example, $a$ could be 2, 1, 1, 4, 3, 4. We could try an ...
654 views

### Count number of non-contiguous occurrences in string

Given strings $S,T$ such that $n=|T|>|S|$ , I'd like an algorithm to count number of occurrences of $S$ in $T$ (as a subsequence), not necessarily contiguous. Example: if $T=aababc, S=abc$, the ...
97 views

### how to count all pairs such that w^x=y^z, where 1<=w,x,y,x<=n and 1<=n<=1000000

how to count all pairs such that w^x=y^z, where 1<=w,x,y,x<=n and 1<=n<=1000000 for example for n=3, there is 15 solutions 1^1=1^1 1^1=1^2 1^1=1^3 1^2=1^1 1^2=1^2 1^2=1^3 1^3=1^1 1^3=1^2 1^...
58 views

### Let F be a function defined for all nonnegative integers by the following recursive definition

Let F be a function defined for all nonnegative integers by the following recursive definition. F(0) = 0, F(1)= 1 F(n + 2) = 2F(n) + F(n +1), n>0 Compute the first six values of F; that is, write ...
144 views

### Why solving #2SAT in polynomial time implies P = NP?

The wikipedia article for #P states that if we have a polynomial-time algorithm for a #P-complete problem, P = NP is true. As #2SAT is #P-complete, this would mean that providing a polynomial-time ...
40 views

51 views

### Efficiently count distinct in large range

I have a pubsub channel where an event is fired every time a user logs in, and I want to be able to query the unique users in a date range. Solutions I thought: Put the data in bigquery, and then use ...
1 vote
672 views

### Algorithm to find number of occurrences in mutually exclusive sets

Given multiple sets of three items, how can I find the most-commonly occurring item among the sets using only one item from each set. The sets don't have duplicates, but if I'm thinking about this ...
47 views

### DJNZ command in Universal Register Machine

How do I represent DJNZ command of counting machine via commands of Universal Register Machine, those commands are CLR JNE INC and TR, via this commands i have to represent DJNZ command, any help ...
261 views

### Sorted list of counters in constant time

Summary. A data structure maintains in constant time a sorted list of counter values, for a dynamic set of counters. I am interested in references using this structure, and in possible improvements. ...
53 views

### Universal quantification and the number of solutions

How would one count the amount of solutions to quantified formulas that have universal quantifiers? For example, for a boolean formula $\Phi(X)$ with a number of solutions $\#\Phi(X)$ let's construct ...
1 vote
74 views

60 views

### Is there a reduction from 2sat to bpm?

Given a 2SAT instance can we convert into bipartite perfect matching in parsimonious reduction?
116 views

### Sorting elements into k subarrays

Given are $n$ integer numbers in the range $0$ to $5n$. A SubSort algorithm organizes the numbers into $k=n/100$ sets, $s_{1}$, …, $s_{k}$ , each containing $100$ numbers, such that the following ...
1 vote
45 views

### Determine if for given some $L$, $S_L={L(M) : <M>\in L}$ then for any $L$, if $S_L=RE$ then $L\in R$ is True or False and explain

Determine if for given some $L$, $S_L=\{\ L(M) | <M>\in L \}$ then for any $L$, if $S_L=RE$ then $L\in R$. Correct or Incorrect and explain why. I think the claim is incorrect, and I'm trying ...
104 views

### Find the total no. of strings ( len n ) possible given a set of sets of letters such that no two letter from a single set should be in that string

This was an algorithm problem but I am having problems in formulating it. I have a certain approach but I do not know how to fully execute: Given 26 letters in total All possible strings of length n ...
1 vote
35 views

### CountDistinct on a range

I have a dataset with and ID and a date looking like: ...
3k views

### How can we count the number of pairs of coprime integers in an array of integers? (CSES)

For reference, I am trying to solve this CSES Problem. The problem basically states that given up to $10^5$ positive integers in the range $[1, 10^6]$, find the number of pairs of those positive ...
263 views

### Count of different ways to express N as the sum of given numbers

I'm working on a case and I need some help :) I need to find number of ways and solutions itself to express N as the sum of given numbers. So, Sum (N) = 600 and the numbers from which I need to get ...
44 views

### Model Counting for Sum of Conjunctive Formulas

Problem: Let $X=\{x_1, ..., x_N \}$ be a set of binary variables. Each variable can be assigned to either $0$ or $1$ so there are $2^N$ possible assignments. Input: We are given a positive integer $C$ ...
330 views

### Why does my code work: bijecting binary trees to Dyck paths

The number of Dyck paths (paths on a 2-d discrete grid where we can go up and down in discrete steps that don't cross the y=0 line) where we take $n$ steps up and $n$ steps down follows the Catalan ...
119 views

### Counting substrings that belong to a regular language

Given a regular language $L$ and a string $x$ give an efficient algorithm to count the occurrences of substrings $x[i,j] \in L$. More in particular, I am looking for a linear time algorithm in the ...
493 views

### Number of substrings possible with even characters

Consider a string 'ABBAA' Possible substrings with even number of characters are $4$ 'ABBA' : Count of 'A' is even and 'B' is even 'AA' : Count of 'A' is even and 'B' is even - ($0$) Similarly 'BB' ...
62 views

### Is there a #$P$-complete counting problem such that every (valid) instance of its decision version is a Yes-instance?

I want to know whether there is a decision problem, written EasyProblem, satisfying the follow property: For every valid instance $x$, $x$ is a Yes-instance for EasyProblem (if we construct ...
75 views

### #perfectMatchings is self-reducible

How can one show that the counting problem: Given a graph, output the number of perfect matchings Is self reducible? I found a hint in Moore's Chapter on Counting, Sampling and Statistical Physics: ...
1 vote
75 views

### What is the solve of F(n,n) = F(n-1,n) + F(n, n-1) + 1 Where F(0,a) = 1 and F(a, 0) = 1 for every a

I'm given the following python function: ...
37 views

### Counting paths by their type

An edge-labelled directed graph is the data of $G = (V, E, l)$ where $(V, E)$ is a directed graph, and $l \colon E \to \mathbb{P}$ is some function. (For the graph I am considering, labels take values ...
1 vote