Questions tagged [counting]
The term Counting in Computer Science is usually used to refer counting objects in certain arrangements or with certain properties.
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questions
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Count total number of k length paths in a tree
This is a question from a competitive programming competition.
Given a tree with n nodes and a number k, find the total number of paths of length k in that tree.
I know for a fact that a solution can ...
0
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0answers
14 views
Count to infinity problem (routing) between unsynchronized stations(tricky)
i was wondering, will count to infinity can occur in the following cases? if so, will it necessarily occur or can the routing tables stabilize themselves?
Distances:
From A to B - 3
from B to C - 4
...
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2answers
80 views
How is the set of functions from ${\{a,b\}}$ to $N$ countable?
Assume a set of functions from ${\{a,b\}}$ to $N$
Where $N$ is the set of Natural numbers.
Let us assume that the size of $N$ is $n$.
i.e $|N|=n$
The first element $a$ have $n$ choices for mapping....
4
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1answer
65 views
Counting big enough elements
Let $v$ be a vector of positive integers of length $n$. I want to find the highest $k$ such as there are at least $k$ elements of $v$ that are greater or equal to $k$.
What would be the best ...
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0answers
32 views
Estimating number of points in 1D space
There are some arbitrary-chosen points in 1D space. What needs to be found is the approximate number of them without counting all of them. It is possible to choose some coordinates (numbers) and for ...
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1answer
22 views
Build a histogram from a very large data sample
I want to calculate a histogram from an array of size N. N is very large.
I know 2 ways to do so:
The naive approach is to ...
3
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2answers
110 views
Fastest algorithm to find all the possible paths of length $n$ from a give node in a directed graph?
I am trying to find the fastest algorithm to find all the possible paths of length $N$ from a given node in a directed graph.
My solution is to do a modification of breadth first search from the ...
3
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1answer
25 views
Given a set of intervals $(I_n)_n$ contained in $[0, L]$, compute the longest interval in $[0, L]$ which has empty intersection with all $(I_n)_n$
Let be $(I_n)_n$ a set of $p$ intervals each contained in $[0, L]$ for $L \geq 1$.
I define $(J_n = [a_n, b_n])_n$ the set of intervals which have empty intersection with $I_n$ for all $n \in [[1, p]]...
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48 views
Counting number of apples in an apple tree with given number of layers
This problem comes from a competitive programming question, and it seems to require dynamic programming.
There are several layers of apples arranged in a formation with each apple having a value ...
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0answers
15 views
Calculating Time Complexity of Algorithm Using Incrementor Variable [duplicate]
I am trying to calculate the time complexity of an algorithm using n in the code below.
I have a working solution to a coding challenge to sort a stack using only ...
2
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1answer
79 views
Number of ways painting graph in two colors, such that two nodes of same color are linked by edge
We are given undirected graph of $N$ nodes and $M$ edges, we want to count the number of possible ways to paint this graph in $2$ colors such that for each two nodes having the same color, there must ...
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2answers
95 views
Are $\mathsf{\#P}$ problems harder than $\mathsf{NP}$ problems
I have a method to solve the $\mathsf{\#P}$ version of 3SAT in a way that seemingly reduces it to an $\mathsf{NP}$ problem. - I don't have a formal understanding of these terms so I will just show an ...
2
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1answer
40 views
Estimation of the number of solutions by Counting
This is a question from a quantum computation textbook.
Consider a classical algorithm for counting the number of solutions to a problem. The algorithm samples uniformly and independently $k$ times ...
1
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1answer
111 views
How to find the Big-O for finding combinations of balanced parentheses?
Given n pairs of parentheses, a function which returns the total number of all combinations well-formed parentheses could be:
...
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2answers
66 views
Prove that this language is NP-Hard
Given
$$\mathrm{\#3SAT} = \{ (w, y) \mid w\text{ is a $\mathrm{3SAT}$ instance with at least $y$ satisfying assignments}\}\,,$$
prove that $\mathrm{\#3SAT}$ is NP-Hard.
I am currently stuck with ...
3
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1answer
44 views
Why does not valiant's reduction show NP=RP?
Valiant converts $SAT$ formula to a $0/1$ matrix such that $Permanent$ of the matrix is $4^m\#SAT$.
We know $Permanent$ can be approximated to $1+\epsilon$ factor with probability $1-\frac1\delta$ in ...
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1answer
643 views
How many ways to express N as sum of 2, 3 and 5?
I've learnt about problems about express N as sum of 2, 3, 5. For examples, if N = 7:
N = 5 + 2
N = 2 + 5
N = 2 + 2 + 3
N = 2 + 3 + 2
N = 3 + 2 + 2
But most of I found on the Internet that the ...
3
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1answer
50 views
The expectation of the total number of pairs of keys in a hash table that collide using universal hashing
I am reading CLRS relating to perfect hashing. When computing the
$$
\mathbb{E}[\sum_{j=0}^{m-1}{n_j\choose{2}}]
$$
where $m$ is the number of slots in the hash table, and $n_j$ is the number of keys ...
0
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1answer
349 views
Limitations of DFA [duplicate]
In this link it is mentioned:
A DFA is not powerful enough to recognize many context-free languages because a DFA can't count.
But counting is not enough -- consider a language of ...
0
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1answer
83 views
Finding combinations of variables that can take value of -1/0/1 that produce sum of 0 with added constraint
I have 64 variables that can either take a value of -1, 0, or 1 and I am interested in finding all possible combinations of variables such that I have n variables in each the positive and negative ...
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11 views
List maximum number of three-sets
Suppose i'm given with pairs component-quantity. I need to list maximum number of possible three-sets.
{AA}, {BB}, {C}, {D} => {ABC},{ABD}.
To list two-sets ...
0
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1answer
41 views
Can someone give me the definition of #Monotone-2SAT?
In the decision problem, I set all variables to true and see if the formula is satisfiable.
My question is because I do not understand how there can be multiple solutions, though all variables are ...
1
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1answer
98 views
Find total count of all paths starting from a fixed vertex to all other vertexes of the graph
Given an directed graph (may contain cycles) we have to find total number of simple paths from a fixed source vertex to all other vertices of the graph, i.e.
$$
\text{#(paths from 1 to 2)}+\text{#(...
2
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0answers
117 views
Min no.of operations required to convert an array to which it should contain elements of equal frequency
I have come across this tricky problem. An array of N elements should be converted to another array within k operations such ...
1
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1answer
26 views
Is there an FPRAS for the number of min st cuts in general graphs?
Provan and Ball [1] showed that the problem of counting the number of minimum st cuts is #P-Complete. What is known about the problem of approximating the number of min st cuts? Is it possible to get ...
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0answers
34 views
Count paths in matrix that visit each number exactly once [duplicate]
Let's say we are given matrix of size $N \leq 21 \text{ by } M \leq 21$ each element of the matrix is either $-1$ or number in the interval $[0, 20]$.
We want to count the number of paths that start ...
2
votes
2answers
277 views
Count-min sketch
I don't understand the use case of count min sketch.
Based on Count–min sketch, it says "serves as a frequency table of events in a stream of data.".
If I know there are N types of events, why can't ...
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0answers
34 views
Find xor sum of all pairs raised to power of 3
We are given array $A$ of $N$ integers each in the range $1 \leq A_i \leq 2^{30}$, that is we can write each integer with at most 30 bits. The target is to compute $\sum_{1\leq i \leq N,1\leq j<i} (...
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36 views
Does $P=PP$ or $P=PSPACE$ have consequences for algebraic class problem $VP=VNP$?
Deciding majority of counting problem is $PP$ class.
Is there any relation between $PP$ and $VNP$ and is there consequence of $P=PP$ or $P=PSPACE$ to $VP=VNP$?
Is there a way to show $\#P$ is in $FP^...
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33 views
Counting on a matrix
I have an $n \times m$ matrix, and fill it with numbers of $1 \dots k$.
If a matrix can be turned into another matrix by exchanging its lines and exchanging its columns, the two matrices are ...
1
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1answer
38 views
Given tree with 0 or 1 assigned to each node, count paths with odd number of ones in it
Let's say we have given tree of $N$ nodes and $N-1$ edges, each of the $N$ nodes is assigned one integer, either $0$ or $1$. We want to count all paths between two nodes $u$ and $v$ such that on the ...
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0answers
53 views
Count submatrices with only zeros for each element of the matrix
Let's say we have given matrix of size $N \cdot M$, only with zeros and ones. For each element in the matrix, we want to count subrectangles that are covering this element and are made only of zeros. ...
4
votes
3answers
163 views
Sum of unique elements in all sub-arrays of an array
Given an array $A$, sum the number of unique elements for each sub-array of $A$. If $A = \{1, 2, 1, 3\}$ the desired sum is $18$.
Subarrays:
...
4
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2answers
75 views
Count numbers less than $x$ co-prime to $p$
We have given two numbers $x$ and $p$. We want to count how many numbers are less than $x$ and are co-prime with $p$.
I know that we can solve the problem in $O(x\log x)$ with iterating over all ...
2
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1answer
468 views
How to find all topological sortings of a special DAG in O(N^2)
I came across the following question in a hackerrank competition, which is based on topological sorting of a DAG.
https://www.hackerrank.com/contests/hourrank-29/challenges/birthday-assignment/forum
...
2
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1answer
35 views
Count number of the ways to fill a N-lengthed binary string
From the problem, count the number of ways to fill a binary string of length $N$ with at least one $1$'s consecutive sequence of length $K$ and other $1$'s consecutive sequences have length no more ...
2
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0answers
81 views
Counting subarrays where each number either doesn't occur or occurs odd number of times
We have given array $V$ of $N$ integers, we want to count the number of subarrays of the array such that each elements in the subarray either doesn't occur at all, or it occurs odd number of times.
...
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2answers
65 views
Why it is not $O(m)$ but $O(\log m)$?
I am reading the lecture notes and have a question. I am trying to understand the beginning of Section 3 on page 2.
Problem: Given an input stream $\sigma$, compute (or approximate) its length $m$.
...
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115 views
Defining decision-problem complexity classes by counting branches of a polynomial-time NTM
This answer on another SE community discusses the concept of a "counting complexity class". As far as I can tell, the author is using that term in a slightly nonstandard way: most sources (PS format) ...
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1answer
169 views
Can I make last part of counting sort become to be starting from lowest index?
Counting sort is originally like below code.
...
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1answer
134 views
How to count number of 1s of the first k positions in a bitset (bitmap)?
Input: Given a bitset $b$, which is is an array of 0s and 1s, of length $L$, and a positive integer $k$.
Output: the total number of 1s in the first $k$ position of $b$.
Obviously it can be done in $...
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1answer
79 views
Counting (enumerating) minimal solutions of a dual horn formula
Is there an efficient algorithm ("does not necessarily have to be a polynomial time algorithm") to compute all "minimal" solutions for a Dual Horn formula (conjunction of clauses where each clause ...
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1answer
58 views
On FPTAS and many one parsimonious reductions
We have two $NP$ complete problems $\Pi_1$ and $\Pi_2$. Suppose $\Pi_1\rightarrow\Pi_2$ be a many one parsimonious reduction.
If $\Pi_1$ has an FPTAS then does $\Pi_2$ also have?
If $\Pi_2$ has an ...
1
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1answer
159 views
Counting solutions of a particular type in HORN SAT
I am interested in counting the number of solutions of a particular type (say #) in HORN SAT. I have 2 questions concerning the same.
Suppose we have a HORN SAT -: $(x_1) \land (x_2 \implies x_1)$, ...
0
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1answer
76 views
Modified Counting Inversions problem using divide and conquer
Given an array $A$, find the number of pairs $(i, j)$, such that $ i > j$ and $A[i] \ge A[j]$.
This is a modified version of the famous problem of Counting Inversions, only in this version it ...
3
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0answers
90 views
How hard is APPROXIMATE-#SAT? [closed]
It is well known that the problem of counting the satisfying assignments of SAT, namely the problem #SAT, is #P-complete.
It is also suspected (somewhat less widely) that even deciding SAT should ...
3
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1answer
391 views
Find smallest enclosing circle
On a 2d plane, there is a large circle centered at $(0, 0)$ with a radius of $R_{{o}}$. It encloses $\sim 100$ or so smaller circles distributed randomly across the parent circle otherwise with known ...
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0answers
31 views
Number of distinct single-assignment forms with $j$ binary function calls?
Given $n$ inputs and $k$ outputs and $j$ identical binary function calls to $g$, how many possible distinct single-assignment forms are there?
The only assumption made about $g$ is that if $a = c \...
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57 views
Is there a simple way to construct a Boolean formula that is true if and only if at most $k$ of the input variables are true? [duplicate]
I could of course construct a truth table for the function
$$f(x) = \left(\sum_i x_i\right) \leq k$$
Where $x$ is an assignment and I'm slightly abusing notation to count Booleans. And then I could ...
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1answer
20 views
Count points on same distance from set of points
Let's consider finite grid of points with size of $N$ by $M$ and set of $x$ points ($x$ is small number, up to 10, $N$ and $M$ are big numbers, up to 30000 )). Each of the $x$ points is described with ...
