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.
138
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Time complexity of an uneven binary search
I have a concept binary search which doesn't split at the midpoint of a list, but at a ratio of 1:2.
If we abstract the search function time complexity into $T(n)$ then the function can recurse into ...
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Finding minimum in a descending rotated sorted array with duplicates
For this question (154. Find Minimum in Rotated Sorted Array II
), I have a solution:
...
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1
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Number of steps of binary search given a stopping criterion
Reading a paper, I have found an algorithm that uses binary search to find a number between $0$ and $n\in\mathbb{N}$. The stopping criterion for this binary search is that $t_2-t_1<\frac{1}{k^2}$ ...
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Finding an approximate double-zero using binary search
Let $f$ be a continuous real function on $[-1,1]$. The function is accessible via queries: for any $x$, the value of $f(x)$ can be computed in constant time.
If $f(-1)<0$ and $f(1)>0$, then by ...
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Inequality about External path length
First of all LPL is Leaf path length & IPL is internal path length. While i was studying algorithm analysis for average complexity of binary search , i saw that inequality. Before that, i proved ...
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113
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Guessing number game "hot" or "cold"
I thought up this problem and am trying to come up with an optimal solution.
I am thinking of a number uniformly randomly between 1-100, inclusive.
If you guess the number, you "win".
Else ...
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2
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98
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Find the largest possible number not larger than some integer N and is the product of K consecutive primes
Source: Hanoi student competition of unknown year (Kì thi học sinh giỏi thành phố)
Additional conditions:
N is a positive integer in range [1, 2^64 - 1]
K is a positive integer in range [3, 10]
...
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0
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Unusual version of a binary search algorithm
For one dimensional, continuous binary search most effective algorithm would remember boundaries.
For example if boundaries are 0.7 and 0.9, point to check would be 0.8. And if result is 'too small', ...
2
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2
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How can I apply binary search to find two adjacent increasing elements in an unsorted array?
I need to write a function that gets an array of numbers $a$ as an input and returns an index $i$ such that $a[i]<a[i+1]$ if it exists, if such $i$ doesn't exist return $-1$. (return any index $i$ ...
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optimal search algorithm for finding parameters and thresholds
I have the following problem:
There are $n$ variables $x_i$, $i=1...n$, each can take integer values from 1 to $m$. For every set of values I can run a test which has a binary outcome ('Pass' or 'Fail'...
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O(Log n) Search - Array
So, there's a LeetCode problem that has you find a O(log n) solution to finding a target number in a rotated sorted array.
As an example:
...
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Binary search with mid index equals to $\frac{(right + left )}{2}$
I have tried to implement traditional binary search on an array. Now, if I set the mid index to be $mid = \frac{(right + left )}{2}$, my code does not run within time quota specified already, however, ...
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2
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How to use the step count method correctly for binary search?
I've tried to use the step counting method to get the worst-case time complexity for binary search. But I seem to mess it up, as my final result would be O(n) and ...
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"Guess the number" Problem on Turing machines
I am currently learning about the concept of Turing Machines and trying to relate it with my knowledge on the application of the Binary Search algorithm.
The problem I am working on is to write an ...
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Fastest Algorithm for "Merge" step in Mergesort
Given two sorted arrays $a_1,a_2,\dots,a_n$ and $b_1,b_2,\dots,b_m$, merge them together into one sorted array $c_1,c_2,\dots,c_{n+m}$ containing the elements of $a$ and $b$.
The typical mergesort ...
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Split the given array into K subsets such that maximum sum of all subsets is minimum
Given an array of $N$ elements, $A$, and a number $K$. ($1 \leq K \leq N$) .
Partition the given array into $K$ subsets (they must cover all the elements but can be noncontiguous too). The maximum ...
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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 ...
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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 &...
1
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1
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117
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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 ...
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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 <...
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53
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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 ...
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1
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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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1
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165
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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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1
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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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1
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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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1
answer
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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 ...
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370
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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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2
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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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1
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130
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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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1
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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 ...
user132812
2
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1
answer
359
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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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1
answer
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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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1
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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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1
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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 ...
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1
answer
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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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0
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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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1
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165
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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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2
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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 ...
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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. ...
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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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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 ...
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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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0
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553
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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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1
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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 ...
user102382
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1
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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 ...
user109308