Questions tagged [counting]
The term Counting in Computer Science is usually used to refer counting objects in certain arrangements or with certain properties.
134
questions
3
votes
1answer
692 views
Radix, merge, counting sort and when to use
Okay can't figure this out. I want to make sure I understand it.
There are n random keys each being float numbers with p decimal places.
So, for example,
123.456,
343.645,
234.543,
863.238,
956....
0
votes
1answer
58 views
Algorithm. Input: pointers to k unsorted arrays of different lengths. Needed output: k sorted arrays
$k = \Theta(n)$
The arrays consist only natural numbers $1$ to $n$
The sum of the length of all arrays = $\Theta(n)$
It should return the $k$ original arrays, each sorted on its own.
The running ...
1
vote
0answers
41 views
Approximate count per element in list/stream via Counting Bloom+Morris
I've a large list A of elements. Given another list B of elements, I need B to be sorted by ...
0
votes
1answer
225 views
Sorting an array in linear time
I need to find a method to sort an array in $O(n)$ time complexity.
I saw this link,
however I'm not sure how to apply it to the elements I need.
Input: an array $A$ of length $n$, containing ...
2
votes
1answer
63 views
On lowness of $\oplus P$
$\oplus P$ is low for itself ($\oplus P^{\oplus P}=\oplus P$).
Are there other complexity classes $\mathcal D$ that satisfy $\mathcal D^{\oplus P}=\oplus P$?
Are there complexity classes $\mathcal C$ ...
2
votes
1answer
1k views
How to count all contiguous subsequences with positive sum?
I have array $t$ with size $n \leq 10^6$. It has only two kinds of elements inside: $1$ or $-1$.
I need to count how many contiguous subsequences have positive sum.
This pseudocode demonstrates ...
5
votes
0answers
133 views
Count Wildcard Parenthesizations of a String
Let $\Sigma = \{ (, ), ? \}$ be an alphabet. For a given string $s \in \Sigma^*$, we denote by $f(s)$ the number of ways to replace each symbol $?$ either with $($ or with $)$ such that $s$ is ...
0
votes
1answer
276 views
Using Pascal's Triangle to implement queues and stacks using heaps
I have the following question as homework in an algorithms, analysis and data structures class:
And here's an answer I wrote up:
A queue is a first-in-first-out data structure. A heap is a data ...
2
votes
1answer
93 views
Number of minimal unsatisfiable partial assignments in 2-SAT/3-SAT
A minimal unsatisfiable partial assignment for 3-CNF is a partial assignment that:
There exist a clause where all variables are unsatisfied.
Unfixing any variable make every clause contain at least ...
-2
votes
1answer
314 views
How to use Bitmasking to solve this problem?
http://codeforces.com/problemset/problem/535/B
The problem is:
You are given a lucky number n. Lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 ...
4
votes
1answer
375 views
Can counting problems have optimal substructure?
I understand that for a problem to be solvable using dynamic programming, it needs to have the following properties:
optimal substructure
overlapping subproblems
I stumbled upon an article which ...
3
votes
1answer
202 views
How many different trees can we form from given graph?
I'm trying to practice some combinatorics and I faced this problem, let's say we have given graph with N nodes and M edges. $$N\leq500, M \leq N\cdot(N - 1)/2$$
In this graph I want to count the sub-...
1
vote
3answers
516 views
Are counting problems the same as problems involving listing all possible combinations?
I recently tried coming up with an algorithm that uses dynamic programming for the counting variant of the change problem. Given a set of target and a set of denominations, print the number of ...
0
votes
1answer
75 views
What's wrong with this [closed]
Here's the question: Do more baby names start with "A" or "B"? Write code to count and print those two counts ("A" count, then "B" count).
I then write this code down:
table = new SimpleTable("baby-...
2
votes
3answers
161 views
Count arrays with size n, sum k and largest element m
I'm trying to solve pretty complex problem with combinatorics.
Namely, we have given three numbers N, K, M. Now we want to count how many different arrays of integers are there with length N, sum K ...
7
votes
2answers
1k views
Count of distinct substrings in string inside range
Having string $S$ of length $n$, finding the count of distinct substrings can be done in linear time using LCP array. Instead of asking for unique substrings count in whole string $S$, query $q$ ...
0
votes
1answer
207 views
How to encode a sequence of non-decreasing integers with an integer without redundancy, loops, and recursions
How to encode a sequence of n non-decreasing integer of [0, ..., m] fulfilling the following conditions:
no or minimal redundancy
only use 1 integer variable or k independent integer variables with a ...
0
votes
1answer
148 views
Proving $\#CYCLE \in \#P$
I'm trying to find a way to count distinct simple cycles in a graph in order to prove that $\#CYCLE \in \#P$, if I could represent a distinct cycle, then I'll have a witness.
I saw this question:
...
-1
votes
1answer
60 views
Display Counting Algorithm
I am writing some firmware for a display that will take measurements and present them in real time on an LCD screen. I would like for the measurements to display as smoothly as possible... What I mean ...
9
votes
2answers
873 views
Counting islands in Boolean matrices
Given an $n \times m$ Boolean matrix $\mathrm X$, let $0$ entries represent the sea and $1$ entries represent land. Define an island as vertically or horizontally (but not diagonally) adjacent $1$ ...
0
votes
0answers
34 views
Number of possible balanced binary trees [duplicate]
A tree is balanced if the subtrees of each node differ in height by at most one.
How many balanced binary trees can we create from $n$ nodes?
0
votes
0answers
146 views
Finding all possible bottom-most overlapping rectangles on a table
Let's say that I'm given a $n\times n$ ($n\leq 1000$) grid (more of like a table) and I color the grid with $n^2$ rectangles, each of a different color (let's say they have colors 1 to $n^2$ for ...
2
votes
0answers
332 views
Estimating size of state space search problem
Im currently enrolled in an AI course and we are starting with state space search problems. My professor always seems to ask, given a certain problem, what is the estimate size of the state space? It'...
5
votes
0answers
600 views
Sorting in place & stable in linear time
Given an array with only 0 & 1. Can we have an algorithm which has all the following desirable characteristics-
The algorithm runs in $O(n)$ time.
The algorithm is stable.
The algorithm sorts ...
5
votes
2answers
842 views
Counting substrings with a given number of different characters in O(N)
Given a string $S$ of length $n$, and a number $k$, count the number of substrings (regardless of their length) that contain exactly $k$ different characters.
The obvious solution takes $O(n^2)$ time ...
2
votes
1answer
300 views
Find number of nodes that seperate graph to two or more subgrahps when removed individually - Find articulation points on a non-directed graph
Suppose that we have an undirected graph, and that for any two nodes there is a path from one to another. In such a graph, there might be some nodes that, if removed from the graph individually, leave ...
0
votes
1answer
60 views
Finding alternative way of combinatorial counting
The question is related to databases:
There is a relation $R(A_1,A_2,...,A_n)$. Every $(n-2)$ attributes of $R$ forms candidate key. Number of superkeys of $R$ are?
I thought if any one of the $(n-...
1
vote
0answers
96 views
What are widely-used, practical applications to come from the study #P problems?
When, beyond theoretical exercises, do we care how many solutions we can find for something?
I had an analogous question for TMs before - why is it useful to study machines that can only deliver ...
2
votes
1answer
112 views
Computing counts of combinations (?)
I'm not sure what terminology to use. Here is some input:
John has items: A B D
Peter has items: A C D
And I want to produce such a table, that would count the #...
1
vote
0answers
80 views
Count all possible 2-3-monotone sequences
Let $N \leq 1000$, a 2-3-monotone sequence $s$ of length $N$ is defined as:
$s_i < s_{i+2}$, for $1 \leq i \leq N-2$
$s_i < s_{i+3}$, for $1 \leq i \leq N-3$
$s_i \in \{1,\dots, N\}$
Given $N$...
1
vote
3answers
56 views
Count elements in the real world in constant time by weighing them
I suppose that counting n elements should be linear time, right? It takes double time to count double number of elements. But in the real world, it is faster and O(1) to weigh elements and find out ...
-1
votes
1answer
924 views
DFS for all possible walks from a source to a destination with exactly k edges
Problem Statement: Given a directed graph and two vertices ‘u’ and ‘v’ in it, count all possible walks from ‘u’ to ‘v’ with exactly k edges on the walk.
My question is that, say we have a DAG (...
-2
votes
2answers
629 views
Count all numbers up to X that are divisible by at least two of their digits
I want to count how may numbers are there in range [1,X] which are divisible by at least two of their digits, different and >1. I found a sequence on OEIS, but this will take lot of time to generate ...
2
votes
1answer
71 views
Counting specific subgraphs
For a given undirected graph G, I want to count all the subgraphs H that satisfies the following conditions:
H.V = G.V (The subgraph will containt all the original graph nodes)
H is connected
(Note: ...
0
votes
0answers
32 views
Complexity of Self avoiding walks in unary
In this paper http://eccc.hpi-web.de/report/2001/061/ by Maciej Liskiewicz, Mitsunori Ogihara, Seinosuke Toda the complexity of counting self-avoiding walks in subgraphs of two-dimensional grids and ...
3
votes
1answer
4k views
How to calculate an accurate estimated reading time of text?
I suppose the calculation should not be done by only two factors (average reading speed/words per minute, and word count). But at least by a third parameter, that in my opinion should measure the ...
29
votes
5answers
5k views
Boolean search explained
My mother is taking some online course in order to be a librarian of sorts, in this course they cover boolean searches, so they can search databases efficiently, however, she got a question sounding ...
3
votes
1answer
109 views
Number of states in an AND-OR DAG
Consider a DAG of $N$ nodes, where each node can take on one of two value, either false, $0$ or true, $1$. Additionally, let each non-leaf nodes (nodes with parents) be assigned a type: either an AND ...
14
votes
1answer
463 views
Why is the counting variant of a hard decision problem not automatically hard?
It is well-known that 2-SAT is in P. However, it seems quite interesting that counting the number of solutions to a given 2-SAT formula, i.e., #2-SAT is #P-hard. That is, we have an example of a ...
-2
votes
1answer
593 views
Count number of automata with 3 states and alphabet of size 2
How many different finite automata are there that have 3 states $q_0$, $q_1$ and $q_3$, have an alphabet of size 2, and where $q_0$ is starting state?
1
vote
1answer
93 views
Count all pairs of x,y such as x + y = c && x XOR y = d
Given two decimals $c$ and $d$; $1 \le c,d \le 10^{12}$. Count all pairs of $x$ and $y$ that satisfy the following statements:
$$
x+y = c\\
x \text{ XOR } y = d
$$
Killed already a day still can't ...
5
votes
2answers
281 views
Finding the number of square prefixes of a string in linear time
Let square denote a concatenation of two identical, nonempty
strings. Given a string $w$, devise an $O(|w|)$
algorithm that counts the number of prefixes of $w$ that are squares.
My initial idea ...
2
votes
0answers
66 views
Complexity class of a counting problem
Consider the following inequalities:
$\sum_j a_{ij}x_{ij}=1 \;\;\; i=1,...,n$
$\sum_i a_{ij}x_{ij} \le y_i \;\;\; j=1,...,n$
$x_{ij} \ge 0 \;\;\; i,j=1,...,n$
$y_i \in \{0,1,2\} \,\,\,\, i=1,...,...
3
votes
1answer
227 views
The most efficient algorithm for computing cardinality of sumset
Let A and B be two finite non-empty sets of positive integers. Their sumset is the set of all possible sums a + b where a is from A and b is from B. For example, if A = {1, 2} and B = {2, 3, 6} then A ...
1
vote
1answer
903 views
How do I find the number of inversions using a red black tree?
I'm trying to figure out a way to find the number of inversions in permutation time O(nlogn) using red black trees. Here's how I think it can be done. So if I have an algorithm that inserts a new node ...
1
vote
1answer
5k views
Seating arrangement problem
$n$ professors go to a conference and have to sit together at a table. See illustration below for $n=8$
Each professor has people they like to sit next to and people they do not want to sit next ...
2
votes
1answer
657 views
Count the number of Euler PATHs in directed graph?
I would like to find all Euler PATHs in a directed graph.
Counting (instead of finding) all the Euler PATHs is sufficient.
Circuits are not good for me, only Paths.
I am doing a problem, that I have ...
1
vote
2answers
148 views
Is there a known, fast algorithm for counting all subsets that sum to below a certain number?
I recognize that the subset sum problem is NP-Complete. I have a different, yet similar problem, which I'll call subset below-sum:
Given a set of integers, $S$, and a target number, $n$, what is the ...
3
votes
1answer
118 views
Counting words that satisfy SAT-like constraints with BDDs
I have the following #P-complete problem:
Given an alphabet $\Sigma$ and a matrix $M$ where each entry can be a symbol from $\Sigma$ or the wildcard symbol $*$, find the number of strings $s$ with ...
0
votes
0answers
350 views
Number of paths between two nodes in mesh topology
Is there any way to find generalized formula to calculate the number of paths of different length between two nodes of the network connected in mesh topology, given that the network contains n nodes?
