Questions tagged [binary-search]

Questions about the binary search algorithm, which can be used to find elements of an ordered list in O(log n) time.

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80 views

how can turing machines be universal models of computation if they can't perform binary search?

I have searched around and it seems like it is impossible for a Turing machine to implement binary search for an arbitrary sized array. How can a turing machine be called universally computable if it ...
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1answer
72 views

How to do binary search on a path in a binary heap

I am trying to solve this question: Let's say you have a binary heap and an index $i$, design an algorithm that finds if a number $x$ appears in the path between the root of the heap and $heap[i]$ in ...
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1answer
46 views

How can we prove that in binary search, low – high ≤ 1

How can we prove that in binary search $$\mathit{low} - \mathit{high} ≤ 1$$ Below is a sample algorithm for Binary Search. ...
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1answer
103 views

Determine whether a sorted array contain at least 4 distinct elements in O(log n) time

On one of my previous courseworks, I was faced with the following problem, which I think is unrealistic when using a direct / straightforward approach that usually algorithms have by leveraging ...
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1answer
101 views

Upper and lower tangent line to convex hull from a point

Is it possible to find an upper and lower tangent line to a convex hull in $log(n)$ time where $n$ is number of points on a convex hull? I have just done it in linear time where I checked for upper ...
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1answer
48 views

How can I make my algorithm more efficient?

I came across an algorithmic problem. I do not know how to do it optimally. The problem is as follows: There is an increasing array $A$ of size $n_1$ There is an array $M$ of queries of size $n_2$ ...
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1answer
19 views

Clarification for binary search in solving optimal TSP when a polynomial algorithm with a budge exists

Below is Question 8.1 in Algorithms by Dasgupta et al. There's a solution to this problem that uses binary search from here. Pasting the answer for posterity. My questions are: When they say input ...
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1answer
25 views

How to split the array into two subarrays with the smallest sum difference?

Given An array of elements, all elements are positive (unsorted, but sorting is not a problem if required) The objective: To create two subarrays, so that ...
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1answer
29 views

How to determine the max offset of a value, given the range, step size and amount of steps

Given The starting and the end values of X The maximum step (maximum delta) Exact amount of steps I need to determinte the maximum and the minimum possible values that X could become during this ...
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1answer
59 views

Find out if a path exists avoiding circular obstacles

Given a rectangle defined by its corners $(0, 0)$ and $(w,h)$, $n$ circles $\{ (x_1, y_1), (x_2, y_2), \dots, (x_n, y_n)$ with the same radius $r$, I need to determine the smallest possible radius r ...
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1answer
34 views

If possible, use binary search to find an element in sorted array

Given sorted array $A[1..n]$, we want to find an element such that, $A[i]=i^2$,Can we use binary search to find such a element? My Attempt: initially, I read this link, but I can't understand the ...
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1answer
60 views

Finding pair of sum in sorted array in time complexity less than $O(n)$

In a sorted array, I am trying to find just one pair that sum up to a certain value. I was wondering if anyone could help me improve my code in performance or memory. I know the code which is $O(n)$. ...
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1answer
28 views

Time complexity of binary search

Proposition: The binary search algorithm runs in $O(\log n)$ time for a sorted sequence with $n$ elements. When justifying this claim, first we say that with each recursive call the number of ...
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1answer
57 views

Find Index In Sorted Array Such That A[i] = C1 * i + C2

I'm already know that there is an algorithm that can solve A[i]=i in O(log(n)) in a sorted array. But I want to know if there is any kind of algorithm that also can solve A[i] = C1 * i + C2 (witch C1 ...
2
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1answer
43 views

Error in pivot selection algorithm for merge phase [Sorting]

In the paper Comparison Based Sorting for Systems with Multiple GPUs, the authors describe the selection of a pivot element with respect to the partition on the first GPU (and its mirrored counterpart ...
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0answers
26 views

Splay tree amortized analysis cost using Access Lemma

Currently studying for an algorithms exam and I came across this question and solution, but I can't understand the solution where it references nodes of depth less than $4\log n$ and not restructuring....
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1answer
145 views

Binary-ish search through partially ordered set

I have an interesting function. It takes subsets of {1,...,N} to positive integers, i.e. $f:P([N]) \rightarrow Z^+$. I know that if S is a subset of S', $f(S) < f(S')$. Also, if S and S' have the ...
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2answers
62 views

Theoretical lower bound of finding number of occurrences of a target integer in a sorted array

Given a sorted array of integers and a target integer, find the number of occurrences of the target integer. It is well-known that a binary search has time complexity $O(\lg n) $ where $n$ is the ...
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6answers
1k views

Find the number using binary search against one possible lie

We all know this classic problem, "there is some hidden number and you have to interactively guess it.", which could be solved using binary search when we know that maximum number that we can guess. ...
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0answers
32 views

Does this problem have a formal name?

I have come across the following problem but am unable to understand the solution for it. Hence I would like to know if it has a formal name then, I can search for it and read about it in more detail. ...
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1answer
264 views

can we do binary search to solve quadratic equation?

Suppose i have a quadratic equation like this, 2x^2 - 4x - 5 = 0, the solution here is x1=2.87 and x2=-0.87. I tried this python snippet to find the non-negative ...
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1answer
304 views

Is there a faster than O(n^2) solution for Box stacking problem?

The Box Stacking problem is as follows: You are given a set of $n$ types of rectangular 3-D boxes, where the $i^{th}$ box has height $h_i$, width $w_i$ and depth $d_i$ (all real numbers). You ...
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1answer
544 views

binary search terminating condition (left != right) vs (left <= right)

I have seen several implementations of binary search where they can use either (left != right) or (left <= right). For example, in normal binary search where you check if target value is in the ...
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1answer
132 views

Find number of triples that sum up to zero in query-intervals

My problem is that we have an array of $N$ integers $(N <=5000)$ on the interval $[-10^6,10^6]$. We also have $Q$ queries $(Q <= 10^5)$ giving us some range in the array. For each query, we ...
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0answers
274 views

Job Scheduling with deadline with $nlogn$ algorithm

We know that there is a Greedy algorithm for scheduling of $n$ jobs which each job has its own deadline and profit. In greedy algorithm, we sort the set by their profit descendant, And if a job can ...
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1answer
303 views

Worst case runtime for binary search

The run time of binary search is O(log(n)). log(8) = 3 It takes 3 comparisons to decide if an array of 8 elements contains a given element. It takes 4 comparisons in the example below. python2.7 <...
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0answers
106 views

Is there an O(n) solution for this problem?

I have found this problem on CodeForces.The problem is in the following link: https://codeforces.com/problemset/problem/729/C Problem Starts here: Vasya is currently at a car rental service, and he ...
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1answer
205 views

Find $n'th$ perfect number , where perfect number is a positive integer whose sum of digits is $10$

For example $46$ is a perfect number , since $4+6=10$ . If $n=1$ , answer is $19$. If $n=2$ , answer is $28$. If $n=3$ , answer is $37$ and so on .We need to make a program which takes $n$ and ...
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0answers
26 views

Intersection of 2 arrays

Here is a question i came across : Given two arrays, write a function to compute their intersection.Here we will allow the duplicates. Note: Each element in the result should appear as many ...
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3answers
94 views

Dividing 2 integers with some constraints

This a problem i came across while practicing binary search. Here is the problem: Given two integers dividend and divisor, divide two integers without using multiplication, division and mod operator. ...
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2answers
136 views

Is there a O(log n)-time algorithm to find the maximum element of a circular shift of a sorted array?

Consider this problem: You are given an array $A$ (of distinct integers) of one out of the following four types: Ascending (e.g., 1,2,4,6); Descending (e.g., 6,4,2,1); Ascending rotated (a non-...
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0answers
380 views

Understanding the behaviour of different variations of Binary Search

Binary Search is a fairly simple and standard algorithm that can be used (among other things) to find a target element in a sorted array. There are subtle variations in code to do this, however all of ...
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1answer
578 views

number of comparisons in searching algorithms

i was going thorugh different searching algorithms,Linear,binary and ternary search.Now i want to know the number of comparisons in these. For linear search : ...
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0answers
387 views

Finding the rightmost element in an array of duplicate elements using binary search

i was reading Binary Search in the wikipedia and i came across this part of 'rightmost index of an element in an array of duplicate elements'. i understood the process of determining the leftmost ...
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1answer
38 views

Smallest segment after whose removal all elements are distinct

I am interested in the following problem: We are given an array of integers and we need to find the size of smallest subsegment such that after removing it all elements in the array are distinct. ...
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1answer
53 views

Extend binary search

There is a way for finding K entries of N given entries using a binary search? I mean, I have N entries, indexed from 0 to $N-1$ and I have to find $K$ of them that satisfy some constraint. The ...
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0answers
51 views

Linearithmic solution to finding closest pairs in an array of N elements

I am reading Algorithms 4ed by Sedgewick and Wayne. I came across this algorithm design question that asks the following: Write a program that given an array of N integers, finds a closest pair: two ...
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2answers
325 views

Binary search uneven split number of queries?

For even split binary search (repeated halving) number of queries is log with base 2. According to Skiena's Algorithm Design Manual, if the split in binary search is by ratio 1/3:2/3 instead of 1/2:1/...
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1answer
71 views

Finding $k$-th element in prefix of size $i$

Let's say we are given array $A$ of size $n$. We need to answer some numbers of queries. For each query we are given index $i$ and integer value $k$, $k \le i$. If we take the first $i$ elements of ...
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0answers
60 views

Exponential search worst-case performance

I'm learning about Exponential search and I keep reading that the worst-case performance is $\log_2 i$ where $i$ is the searched index. I tried with an array containing $1073741824$ elements ($1024\...
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1answer
573 views

In which situation do we choose randomized binary search instead of the normal binary search?

Both randomized and normal binary search takes O(log n) time complexity but why does the randomized version exist? In other words what is the advantage of randomized binary search even if it has same ...
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1answer
158 views

How can I understand a hint for finding the lowest height of the last bulb in a Garland?

Disclaimer This is not from an ongoing contest, this is from my course on edx of ITMO. Also this is a paid courses so the direct link to the problem is not useful unless you also register this course....
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128 views

Minimum Ratio Spanning Tree

Problem statement: Given an undirected graph $G = (V, E)$ with edge $e_i$ having two associated positive values $c_1, c_2$. Find a spanning tree $ST$ such that (ratio of the spanning tree): $$\frac{...
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1answer
419 views

Finding an interval in a binary search tree that contains a point

I have a binary search tree where nodes are non-overlapping intervals. I'm given a point, and I need to determine which interval the point belongs to (if any). This is easy to do because I can compare ...
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0answers
268 views

Binary search on a path of minimum heap

WhereTo(H,X) is searching for the place to set X (an integer) in a minimum heap-H. The function is executing a binary search on a path of a heap. Assumption: We have the specific path because it ...
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1answer
735 views

An algorithm that find the max X/Y in a polygon in O(log n)

I got a task to create two functions one finds max $X$ and the other $Y$ in a polygon in $O(\log n)$. The polygon is represented by an array of its vertices where each vertex is represented by its ...
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3answers
582 views

Given a sorted array with n elements and element x that is inside the array at position k, find k in O(min(logk, log(n-k)))

Given a sorted array $A[1,\ldots,n]$ and element $x$ that located at position $k$. We know $x$, we don't know $k$. Write an algorithm that finds $k$, in $O(\min(\log k, \log(n-k))$ time complexity. ...
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1answer
417 views

Binary search in log time on a Turing Machine

I was thinking about TM (Turing Machine) as a computation model, and I came up with the following question : Is it possible to make a TM that answers binary search (tell wether $x$ belong to a sorted ...
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0answers
114 views

Worst case lower bound of binary search

For the question below, it is asking to prove the lower bound on the worst case is log(n). I have no problem proving this and the solution makes 100% sense to me. However, there is a comment at the ...
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1answer
3k views

How binary search works in real world scenario?

In binary search, we need an array of integers for it to search for an element. Also, many other sorting algorithm sorts array of integers. But in real world, we may search for a name of an employee ...