# 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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54 views

### Binary Search return value

Google has the article Extra, Extra - Read All About It: Nearly All Binary Searches and Mergesorts are Broken. Which primarily discusses the overflow on the mid calculation. However, what I found ...
41 views

### Greedy approach behind SPOJ Aggressive Cows problem

My doubt is related to the given SPOJ problem: Farmer John has built a new long barn, with N (2 <= N <= 100,000) stalls. The stalls are located along a straight line at positions x1,...,xN (0 &...
36 views

### Algorithm to find approximate position of element from a noisy sorted list

Let's have a static function f(n) which for a given n returns only these answers "lower" or "higher" comparing against an imaginary number x In a sorted list ...
60 views

### while(l < r) vs. while(l <= r) advantages/disadvantages in binary search

There many many ways to code binary search, but one of the main distinctions I've seen in people's code is one group of people use while(l < r) and another uses <...
34 views

### Search algorithm for an expensive boolean function

I have the following problem. We have a boolean function $f$ that is expensive to compute for a given input. We need to find the smallest positive integer $n$ such that $f(n)$ is true. We don't know ...
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### 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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### 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 ...
54 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. ...
107 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 ...
259 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 ...
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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### 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 ...
66 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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### 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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### 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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### 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 ...
90 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 $O(n)$. ...
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 ...
215 views

### Proving O(log n) bound for the number of iterations when we select the average as the pivot

Motivation So the other day I had fun providing a new solution to this famous question. In the analysis part I showed that my little algorithm has space complexity: ...
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### 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 ...
44 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 ...
30 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....
148 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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### 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 ...
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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### 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. ...
363 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 ...
374 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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### 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 ...
148 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 ...
339 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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### 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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### 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 ...
235 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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### 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 ...
108 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. ...
169 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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### 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 ...
703 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 : ...
438 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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### 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. ...
55 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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### 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 ...
423 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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### 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 ...