Questions tagged [arrays]
A sequential random-access data structure whose size can typically not be changed after creation.
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Number of comparisons in array where each element appears n/k times
Given an array of $n$ elements with $k$ distinct elements, each appearing $n/k$ times, how can I show that the number of comparisons to the sort the array in the worst case is in $\Omega(n \log k)$?
2
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1answer
49 views
Thought process for the following problem?
We are given a 1-d array and we have to return the smallest array attainable after removing all the continuous same numbers. We can only eliminate those numbers which repeat continuously more than or ...
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0answers
35 views
Is it possible to write a fully-decidable type system for the J language?
I'm experimenting with the J array language, a dynamically-typed array language with mutable assignment, subtyping, and function overloading (just like traditional APL).
It is unclear to me whether ...
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2answers
38 views
Check if two separate ranges have some number in common
We are given two permutations: A of size N and B of size M. We need to process Q queries, each query is given by two ranges, one subarray range in permutation A and one in B. We should check if there ...
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1answer
24 views
What is an array that can be iterated circularly an infinite amount of times called?
I have a feeling that the answer is either a "circular linked list" or a finite state machine, but the answer is probably a circular linked list.
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2answers
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Copying items in arrays while checking their indexes
Array $P$ of length $n$ is a permutations of $\{0, ..., n-1\}$
Write a code, which would in $O(n)$ create an array $R$ of length $n$, so
for values $x_i, x_j \in P$, $R[x_i] < R[x_j]$ if $...
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1answer
53 views
If an array is full of the same integer, like 0s or 1s, are they all the peak of the array?
I am learning the MIT course Introduction to Algorithms.
The professor is saying
In particular, as an example, position 2 is a peak if, and only if, b
greater than or equal to a, and b greater ...
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1answer
20 views
Kth smallest element in an arra [duplicate]
What would be an efficient method to find the kth smallest element in an array with worst case time complexity being $ O(n) $?
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2answers
44 views
2D peak reasoning to move to a half
You have a 2D integer matrix given. An element is a peak element if it is greater than or equal to its four neighbors, left, right, top and bottom. For example neighbors for A[i][j] are A[i-1][j], A[i+...
2
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1answer
51 views
How to reduce number of move operations in an array?
Say I have an array of numbers, e.g. [0, 1, 2, 3, 4, 5] and I want to end up with an array, e.g. [2, 1, 4, 0, 5, 3]. At my ...
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1answer
63 views
Is there any way to find the nodes in the each subtree of each node having distance equal to height of the subtree?
We are given a tree of N nodes from 1 to N where node 1 is the root of the tree.
For each node i from 1 to N, you have to find the numbers of nodes which are in the subtree of i and are at distance ...
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1answer
22 views
Why finding the difference between the adjacent elements of the array to find the maximum difference?
I want to understand a tricky method to find the maximum difference between two elements such that larger element appears after the smaller number. I found easy solution keeping track of the minimum ...
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1answer
47 views
The time complexity of finding the kth smallest number using buckets
I've implemented kth smallest number using buckets representing the current nibble value of each element in the array where ...
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1answer
51 views
Job scheduling approximation
In the course notes for Stanford MS&E-319: https://web.stanford.edu/class/msande319/lec1.pdf
Lemma 5 is given as:
The approximation factor of the modified greedy [scheduling] algorithm is 4/3....
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1answer
221 views
Partition array into k subsets
We are given an array and a number K. Partition array into K subsets such that
let MaxSum be the maximum sum of among subsets.
We have to minimize summation =$$\sum_{i=1}^{k}MaxSum-sum(i) $$
Is ...
7
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2answers
469 views
Find a point shared by maximum segments
Given: $N$ segments (arrays) of ordered integers, integers could be from $-K$ to $K$.
Example:
...
4
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1answer
122 views
Maximum subarray of bounded length
I'm giving an array $A[0..n-1]$ and an integer $w$. The goal is to find indices $i,j$ that maximize
$$\Phi(i,j) = A[i] + A[i+1] + \dots + A[j-1],$$
subject to the requirements that $0 \le i \le j \...
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0answers
52 views
Minimum number of deleting palindromes to delete whole string
Let's say we have given array $A$ of size $n$. Our goal is to delete the whole array with minimum steps. In one step we can choose substring (consecutive elements from the string) and delete it only ...
3
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1answer
30 views
Finding maximum takes at least $\lceil n/2 \rceil$ comparisons
We are given an array $A$ with $n$ elements, $n \in \mathbb{N}$ and all elements are in the set $\{1,2,3, \cdots, n \}$.
I want to prove that finding the maximum in $A$ (that is, outputting the index ...
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0answers
68 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 ...
-2
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1answer
117 views
Count the number of subsets with product less than or equal to k [closed]
You are given an array $A$ of $n$ positive integers, you have to find the number of subsets the product of whose elements is less than or equal to a given integer $k$.
Is there an efficient algorithm ...
3
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1answer
52 views
Efficient algorithm to replace list of integers with nearest bigger element
The original question was in the context of an array, but I just used a list without changing the length for easier debugging purposes of toString().
Given an ...
3
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1answer
41 views
Using bit arrays to solve crossword puzzles
I have read Crossword Puzzles and Constraint Satisfaction by Connor, Duchi and Lo and I am trying to implement this variation of crossword solving algorithm. I can't understand the bit array data ...
2
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1answer
199 views
Time complexity to find Median of Medians
I recently wrote my Grad school Admission test few days back and the following question appeared in the test.
There are 'n' unsorted Arrays : A1, A2, ...., An. Assume that 'n' is odd. Each of A1, A2, ....
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2answers
191 views
Finding the maximum of a bitonic sequence
Given to us is an array $B[1],\ldots,B[n]$ as input, which satisfies the following property: there exists a special index $i^* ∈ \{1, \dots , n\}$ such that $$B[1] < B[2] < \dots < B[i^*− 1] &...
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1answer
139 views
Sort 2D arrays so that cost of reaching new position as described at each iteration is minimized
Problem is as following:
We are 8 trumpet players in an orchestra.
There are for example 4 parts so there are always two players on the same part.
Now, there are not always the same two players ...
0
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1answer
61 views
Applying minimax tree to this array [closed]
Please tell me how I should apply minimax algorithm to the array
$$ 15, 12, 14, 16, 11, 13$$
and make a tree?(I understand how minimax algorithm works but I can't apply it to an array)
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2answers
40 views
Find the minimum N such that the sum of beauty of all numbers from 1 to N is at least X
The beauty of a number is defined as follows :-
...
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0answers
28 views
Recurrence Relation for Column Major Form of multidimensional array
A two dimensional array is stored in column major form in memory if the elements are stored in the following sequence $$A[0][0] A[1][0] A[2][0]...A[n_1-1][0] ... A[0][1] A[1][1] ... A[n_1-1][1] .... A[...
3
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2answers
73 views
Is it possible to solve this problem in less than n^2 time without using additional space?
Here's the problem:
Given an array array containing integers, maximize array[i] + array [j] + |i - j| where i and j both range ...
2
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1answer
41 views
Find four sets where each element from those four appears in at least two of those four sets
I have a list of sorted arrays ("sets") of integers $A_1..A_n$ where each element is unique w.r.t. the other elements in the same array:
$A_i = \{x_{i,1}..x_{i,c_i}\}$
$x_{i,p} < x_{i,p+1}$
$A_i$ ...
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1answer
178 views
Array subset division with equal sums
Today I stumbled upon a problem which looked like the partition problem but certainly is different.
Given array of positive integers, guaranteed to not be divisible into two continious subsets of ...
3
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1answer
93 views
Find the smallest element greater than current element
my question is that given a list of integers (lets say A), for each element A[i], find the smallest element A[j] which could satisfy A[i] < A[j] and i < j. Return -1 if there is no such element.
...
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1answer
21 views
How to count stores in cache analysis of matrix multiplication
I'm trying to understand cache misses/iter and came across this that I couldn't understand or reason out.
For ijk iteration, my slides say that there are 2 loads and 0 stores.
...
2
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1answer
88 views
How to find efficiently the minimum modification to avoid close consecutive numbers?
I have an array of sorted numbers:
arr = [-0.1, 0.0, 0.5, 0.8, 1.2]
I want the difference (dist below) between consecutive ...
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0answers
83 views
How does prefix summing the count histogram in counting sort result in an array of output indices?
My implementation of counting sort is based on the description I found here. I've also included my code in this REPL, but here it is:
...
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1answer
38 views
How to compare an element with other elements within an array efficiently for a condition
I need to compare each index with one another and associated array value as well.
For example,
...
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1answer
30 views
How would you identify the size of a circular turing tape?
Came across this interesting problem in one of my interviews. Suppose you have a circular turing tape, i.e. simply a circular array. You do not know the size i.e. the number of cells available in that ...
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0answers
61 views
Sort arrays $A$ and $B$ of the same elements using only comparisons between an element of $A$ and one of $B$
Premise: Let $A := [ k(1), k(2), ..., k(n) ]$ and $B:=[ l(1), l(2), ..., l(n) ]$ be two Arrays where $k$ and $l$ are permutations. (What I'm trying to express: $A$ and $B$ contain the same elements in ...
2
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1answer
146 views
Maximum number of segments with no intersection [duplicate]
This is an interview question.
Suppose you have an array of n segments, when each segment is a pair of two integers: start point and end point. For example: ...
4
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3answers
118 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:
...
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1answer
93 views
Strengths and limitations of arrays [closed]
What are the strengths and limitations of arrays? What considerations go into choosing an array over another data structure, or vice-versa?
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1answer
44 views
Comparison between: Maximum Absolute Difference & Min Steps in Infinite Grid
There are two questions that I am trying to draw a comparison between:
...
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1answer
52 views
Algorithmic Design to Undo Rotation of Array
An array $A$ of $n$ distinct, ascending integers is rotated to the right by $k$ positions, resulting in the array $A_{k}$.
That is, the element at index $i$ in $A$ is moved to index $(i+k)\mod n$ in $...
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2answers
108 views
FInding the combination with the least number of elements from and array of integers, given an integer sum
I'm doing and assignment where the problem is to find the combination with the least number of elements form an array of integers, given an integer sum. I have solved this using a gready algorithm ...
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2answers
64 views
What does the “0 ≤ K < N-1” expression means?
Given the following statement:
"A nonempty array A consisting of N integers is given. Any integer K,
such that 0 ≤ K < N-1, splits array A into two non-empty parts"
What does the 0 ≤ K < ...
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2answers
27 views
Generate Evenly Distributed Pattern Based on Weights
I have an array of items $A = \{A_i\}, i \in I $ with integer weights $W_i, i \in I$. I need to build a function $f: I \rightarrow A $, that produces evenly distributed patterns of array elements ...
3
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1answer
240 views
what is actually a circular array and representation
There are two ways to implement a circular array either take a new array of size 2N where N is the size of the initial array and copy initial array twice into that ...
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1answer
34 views
Sorting Algorithm which prevents strings with at least one identical char from being next to each other
Imagine this Table:
All combinations represented in the table (1,2 ; 1,3 ; 1,4 ; etc.) are stored as strings in an array with a total of (n^2-n)/2 elements (combinations).
I'm looking for an ...
2
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1answer
196 views
Maximum Equal Sum K Subsequences
Given an array we need to find maximum equal sum $K$ subsequences, i.e. we want the sum to be maximized such that there are exactly $K$ non-overlapping subsequences each having the same sum.
Example:
...
