Majority element divide and conquer n]), a majority element is defined as an elementthat appears more than n/2 times. Before we give the algorithm, we have to prove the following lemma Lemma 1 After the proposed procedure, there are atmost n 2 elements left and if A has a majority element, then remaining elements will have the same majority element Proof: Let m be a majority element of A. The goal is to apply divide-and-conquer techniques to solve these problems efficiently in O(n log n) time or better Give a divide-and-conquer algorithm that runs in O(log n) time. Be able to design and analyze new algorithms using the Divide & Conquer Exercise 4. Given an array, the task is to design an e cient algorithm to tell if it has a majority element, and, if so, to nd that element. For example in [a, b, a the majority element is a, but a, b, c] and [a The document presents three solutions for different algorithmic problems using divide and conquer strategies. Qn 1. n] of elements You can only do equality tests on the elements (e. Justify correctness and time complexity. 23. 6 marks] Divide-and-Conquer. Question: Q1 Given an array of size n, design a divide-and-conquer algorithm that finds the majority element (an element that appears more than n2 times) if it exists. The assignment also includes steps for input and output, as well as a Coursera's Algorithmic Toolbox Course (#1 in Data Structures and Algorithms) - py-zoid/Algorithmic-Toolbox Question: I need help creating a O (nlogn) divide and conquer algorithm to find the majority element in a unsorted array. Majority Element in Python, Java, C++ and more. An array A[1; : : : n] is said to have a majority element if more than half of its entries are the same. The code examples illustrate the implementation of these Introduction to Divide and Conquer Divide and Conquer is an algorithm design strategy of dividing a problem into sub problems, solving the sub problems and merging the solutions of the sub problems to get a solution for the larger problem. Feb 26, 2018 · Im writing an algorithm for finding a majority element in an array. In particular this means that you cannot sort the array. Aim for an algorithm that does A (or Divide and Conquer -- Leetcode problem169: Majority Element, Programmer Sought, the best programmer technical posts sharing site. If we perform this trial more and more, the chances of success will be higher. Does knowing the majority elements of Ai and A2 help you figure out the majority element of A? If so, you can use a divide-and-conquer approach. Here's another divide-and-conquer approach: • Pair up the elements of A arbitrarily, to get n/2 pairs . You want to find (if it exists) a majority element, i. Source: Algorithms by Dasgupta, Papadimitriou, Vazirani. (b) Can you give a linear-time algorithm? (Hint: Here’s another divide-and-conquer approach: • Pair up the elements of A arbitrarily, to get View Lecture-5-CS602-2024-Greedy-starts (2). I have to write a function that returns the majority element (if there is one, else return -1) and it must be O (nlogn). . It breaks down a problem into smaller, more manageable subproblems, solves them recursively Sep 30, 2024 · We have to find majority element in an array if it exists. they are large GIFs). Nov 24, 2020 · Majority element | Divide and Conquer | Leetcode 169 Deep Coding 25 subscribers Subscribed Feb 16, 2020 · I want to find the majority element from a list using divide & conquer algorithm. This article will go in-depth on the Python divide-and-conquer algorithm LeetCode 169. Better than official and forum solutions. if so. Given an array, the task is to design an efficient algorithm to tell whether the array has majority element, and, if so, to find that element. ) 2. Conquer : Solve Smaller Problems Combine : Use the Solutions of Smaller Problems to find the overall result. pptx from CS 602 at IIT Kanpur. (b) Can you provide a linear-time algorithm? Hint: Here's another divide-and-conquer approach: Pair up the elements of A arbitrarily to get n/2 pairs. Given an array, the task is to design an efficient algorithm to tell whether the array has a majority element, and, if so, to find that element. Brief description of the algorithm. 1 Solutions Answer 1 We will use divide-and-conquer to solve this problem. . H. The majority element is the element thait ap pears more than In/2] times. Complete Solution to Majority Element Class problem: (Das Gupta) An array A[1 . The range of length of array is n (1≤n≤5,000,000) and the element في الفيديوا ده هنحل الـ Assignment اللي كنا طلبناه منكم قبل كده وهو Majority Element Problem Chapters00:00 Episode Contents 00:37 Problem explanation Question: Write a C function to find if a given integer x appears more than n/2 times in a sorted array of n integers. Aug 28, 2024 · Majority Element in an Array using Python Introduction Finding the majority element, which appears more than half the way down the array, is a fundamental challenge in array manipulation. You may assume that the array is non-empty and the majority element always exist in the array. It always returns the element itself I'm trying to learn about Divide and Conquer algorithms as part of the Algorithmic Toolbox on coursera and there is a question as follows: Input. ) Provide a runtime analysis and proof of correctness. Running time is O (nlog (n)) ##Input Format: The first line contains an integer n, the next one contains a sequence of n non-negative integers. Each method is accompanied by pseudocode and Java code implementations, along with an analysis of their time complexities. 给定一个大小为 n 的数组 nums，返回其中的多数元素。 The majority element is the element that appears more than ⌊n / 2⌋ times. n 1] contains a majority element, and if so, returns it. Give a divide-and-conquer algorithm that runs in O(log n) time. ) Design an eficient divide and conquer algorithm to find a majority element in determine that no majority element exists). e. A sequence of n ≤ 10^5 integers. is that a good\correct idea? btw, apparently i had to write the algorithm in a divide-n-conquer method, so mine isn't good (also its runtime 花花酱 LeetCode 2220. com/roelvandepaarWith thanks & pra Computer Science questions and answers Problem 4: Given an array A of size n (denoted as [1 . Majority Element--Divide and Conquer (divide and conquer), Programmer Sought, the best programmer technical posts sharing site. Given an arrayAofnintegers, design a divide and conquer algorithm that returns the majority element if there exists one inA, or “No majority” if there is no such element. Solution 1 implements a merge sort algorithm to sort an array of strings, while Solution 2 provides two approaches to find the majority element in an array, one using brute force and the other using divide and conquer. So, if we choose some random element from the input, then there is more than a 50% probability that the chosen element will be the majority element. Suppose you have an unsorted array A [1. , an ofnintegers is said to have a majority element if there exists an element inAthat appears greater than⌊n 2 ⌋times. Examples: Mar 17, 2024 · Divide and Conquer is a powerful algorithmic paradigm widely used in computer science and programming. Examples: Input: arr[] = {1, 2, 3 Oct 12, 2019 · Majority Element (Divide and Conquer) you can find this problem in LeetCode-169 Problem description Given an array of size n, find the majority element. A majority element in an array is an element that appears more than n/2 times. Vazirani, Question 2. Jul 10, 2024 · Divide and Conquer: Divide the array into two halves, find the majority element in each half, and then combine the results. Bitwise AND of Numbers Range More from Divide and conquer More posts in Divide and conquer » Aug 1, 2015 · as mentioned in the titled, my function doesn't end well. Basically, if an element appears at least length/2 in an array, its a majority element. I am trying to do the following : " Implement, with the DC method, a function which has this interface : Returns the majority element of the Jan 3, 2024 · Does knowing the majority elements of A1 and A2 help you determine the majority element of A? If so, you can use a divide-and-conquer approach. It has 6 problems covering topics like binary search, finding majority elements, improving quicksort, counting inversions, organizing a lottery, and finding closest pairs of points. Learn more about Stack Overflow the company, and our products. The hint should say that, after this procedure, the leftover elements have a majority element if A has one. to find that element. Dasgupta, C. Apr 28, 2016 · I'm having trouble getting the right output on my "Majority Element" divide and conquer algorithm implementation in Python 3. , an element that appears more than half the time. If both halves agree on the majority element, that is the global majority. If one value forms a majority of the elements, the median must have that value, so we've just found the value we're looking for. Given the array a [], it is intended to draw an efficient algorithm (at time N. Therefore once we apply the algorithm and come up with a majority element, it is mandatory to check if m is indeed a majority element of the array. The task is to output 1 if an array with n elements contains an ele LeetCode 169. If it was, that element is the majority and should be returned. However, neither of them contained what I'm looking for. Finding a Candidate: The algorithm for first phase that works in O (n) is known as Moore’s Voting Algorithm. The document describes a programming assignment on implementing divide-and-conquer solutions. Power of Two 花花酱 LeetCode 201. The task is to write a function say isMajority () that takes an array (arr [] ), array’s size (n) and a number to be searched (x) as parameters and returns true if x is a majority element (present more than n/2 times). Design and Analysis of Algorithms CS602 Lecture 5 Divide and Conquer Paradigm - III - Finding Majority Element Greedy Give a detailed verbal description and pseudocode for a divide and conquer algorithm to find a majority element in A (or determine that no majority element exists). I'm trying to learn about Divide and Conquer algorithms as part of the Algorithmic Toolbox on coursera and there is a question as follows: Input. Can you give a linear-time algorithm? Does knowing the majority elements of A 1 and A 2 help you figure out the majority element of A? If so, you can use a divide-and-conquer approach. Majority Element--Divide and Conquer (divide and conquer) The design idea of the divide-and-conquer method is: to divide a big problem that is difficult to solve directly into some smaller-scale same problems, so that each can be broken and divide and conq (13 p oin ts) Giv ea O ( n log ) time divide-and-conquer algorithm for this task. Find the majority element in an array. Each solution is accompanied by a brute force approach and a more efficient divide and conquer method, detailing their time complexities. Papadimitriou, and U. I'm trying to solve the problem for finding majority element of given array. However you can answer questions of the form: \is A[i] = A[j]?" in constant time. The majority element is the element that appears more than ( n / 2 ) times. Apr 14, 2012 · first, thanks for you help! second, my idea was that in every array which has a majority element, there must be two identical numbers one after the other (considering that the array is kind of a circle, such that the last element is close to the first). Divide and Conquer Algorithm - Programiz irrelevant (the function could simply return None). Mar 10, 2015 · Start by finding the median, such as with Hoare's Select algorithm. Aug 16, 2021 · Given an array arr [] consisting of N integers, the task is to find all the array elements which occurs more than floor (n/3) times. (a) Show how to solve this problem in O (n log n) time via a divide and conquer method. The majority element is the element that appears more than ⌊ n/2 ⌋ times. , find an element that appears in more than n/3 positions of A). Jan 9, 2022 · A list is said to have a “majority element” if more than half of its entries are identical. Computer Science: Divide and Conquer majority element algorithmHelpful? Please support me on Patreon: https://www. An array A::: majority element An array A[: : :] is said to have a majority element if more than half of its entries are the same. Divide : Break the given problem into smaller non-overlapping problems. Your algorithm should run in O (n log n) time. How to find the majority element in an array in O(n)? Example input: {2,1,2,3,4,2,1,2,2} Expected output: 2 In data structures and algorithms, Divide and Conquer is a recursive problem-solving approach that divides the problem into smaller subproblems, recursively solves each subproblem, and combines the subproblem's solutions to get the solution of the original problem. Does knowing the majority elements of A1 and A2 help you gure out the majority element of A? If so, you can use a divide-and-conquer approach. Otherwise, the array has no majority elem Sep 23, 2020 · I am using a divide and conquer strategy to solve the majority problem. Given an array of size n, Write a code to find majority element in an array. You may assume that n is a power of 2. If A has a majority element, MajorityElement will return that element. It seems to be a very simple question at first glance but solving Oct 25, 2022 · Leetcode 169 - majority element: Given an array nums of size n, return the majority element. Question: You are given an array of n integers. V. You may assume that the majority element always exists in the array. CSE 5050 Algorithms and Complexity Problem Set 5. ) Design an efficient divide and conquer algorithm to find a majority element in A (or determine that no majority element exists) Question: Q1 Given an array of size n, design a divide-and-conquer algorithm that finds the majority element (an element that appears more than n2 times) if it exists. Jan 31, 2017 · I checked SO and saw two issues dealing with the same problem statement. The key observation is the following: Suppose we split the array Ainto two arrays A and Ar , then, if A has a majority element v, vmust also be a majority element of either A orAr or both. I just can't seem to make the final output of majority_element () to be either 0 or 1. Problem 4: Majority Element (50/100 points) -Design of Divide and Conquer Algorithm An array of integers a1…an is said to have a majority element if more than half of its entries are the same. An element in said to be in the majority if repeats more than n/2 times where n is the number of elements given in the input. A majority element appears more than `n/2` times, where `n` is the array size. So, there are four steps of the divide and conquer method: divide, conquer, combine and base case. Can you give a linear-time algorithm? (Hint: Here's another divide-and-conquer approach: 2. Please don't do that, as it makes all comments, answers and the efforts of their authors meaningless. To do this, she challenges her students to find the majority element in a large array. Aim for an algorithm that does O(nlgn) equality comparisons between the elements. Solutions to the Assignments for the Algorithmic Toolbox course offered by UCSanDiego on Coursera. The algorithm MajorityElement defined below finds the majority element of A if it exists. Feb 7, 2025 · The divide and conquer approach can be applied to efficiently find the majority element in a given array by dividing the array into smaller subarrays, finding the majority element in each subarray Feb 21, 2014 · Return: For each array, output an element of this array occurring strictly more than $n/2$ times if such element exists, and "-1" otherwise. If it contains, the function will return * a pointer to an instance of this element and store in *frequency the number of times that * this element appears. It returns an array with two elements, the name of the majority element and a number that is less than or equals to its Sep 4, 2019 · @chen Your last edit completely changes the question - and is still unclear: what you mean by 'majority element' is the 'most common element', while 'majority element''s meaning is 'the one which appears more than n/2 times, if it exists'. A majority candidate is defined as more than 50%. Majority Element LeetCode | Interview Preparation | Sorting | Divide and Conquer | Techies Code Techies Code 586 subscribers 22 The algorithm should return the majority element if it exists (majority meaning that there are $> n/2$ occurrences in the array) I came up with this linear divide and conquer algorithm, but I'm not sure if it's correct. A. So in a given array of integers you have different methods to find it. Number of occurrences of that element must be greater than half of the size of the array. I made two attempts to solve the problem, but seems that both have something wrong in them. Space Complexity The space complexity is O (1). Otherwise print no Majority Element Found. Solution: The follo wing algorithm outputs the ma jorit y elemen t if there is one, and outputs F ALSE otherwise: Giv en an arra y N of size n , divide it in to t w o arra ys, A and B , of size n 2 . I saw this code on Leetcode with this solution: class Solution: def majorityElement(self, nums, lo=0, hi=None Problem Highlights 🔗 Leetcode Link: Majority Element 💡 Difficulty: Easy ⏰ Time to complete: 10 mins 🛠️ Topics: Array, Hash, Divide And Conquer, Sorting 🗒️ Similar Questions: Check If a Number Is Majority Element in a Sorted Array, Most Frequent Even Element, Majority Element II 1: U-nderstand Understand what the interviewer is asking for by using test cases and questions Dec 1, 2010 · The majority element is the element that occurs more than half of the size of the array. There can be atmost one majo Nov 7, 2021 · The majority element in an array of size n is an element that appears more than n/2 times. Intuitions, example walk through, and complexity analysis. Jul 22, 2025 · When you encounter a new element, check if the count of the previous element was more than half the total number of elements in the array. 1, if there is an element that is repeated more than n/2 times, and 0 otherwise. Question: Divide and conquer An array. 2. log (N) and using divide-and-conquer) to check if it contains a majority element and to determine it. Latest commit History History 18 lines (16 loc) · 385 Bytes master Algorithmic-Toolbox / week4_divide_and_conquer / 2_majority_element / Nov 20, 2007 · (Hint: Here’s another divide-and-conquer approach: <BR>• Pair up the elements of A arbitrarily, to get n/2 pairs <BR>• Look at each pair: if the two elements are different, discard both of 4) (25 points) Write pseudocode to design a divide and conquer algorithim for majority item of an array of size n. Algorithm 2 - Using Divide and Conquer (Binary Search Tree) Intuition: Add elements in Binary Search Tree one by one and if any element is already there Can you solve this real interview question? Majority Element - Given an array nums of size n, return the majority element. n] of n elements. This should be relatively correct; however, it would still appear that Can you solve this real interview question? Majority Element - Given an array nums of size n, return the majority element. For eg, an array arr [] = [9, 4, 3, 9, 9, 4, 9, 9, 8] is given, Here 9 appears five times which is more than n/2, half of the size of the array size. Note that the lemma holds only if the array A has a majority element m. Output. (1) Design a Divide-and-Conquer style algorithm that runs in (n log n) time without sorting the arrayto determine if a majority element in A exists. In this classical problem the goal consists of determining whether a list a of length n has a majority el This video explains a very interesting counting based array interview question which is to find the majority element in the array. How many majority Jul 23, 2025 · Output: 3 appears more than 3 times in arr[] Time Complexity: O (Logn) Algorithmic Paradigm: Divide and Conquer METHOD 3: If it is already given that the array is sorted and there exists a majority element, checking if a particular element is as easy as checking if the middle element of the array is the number we are checking against. Feb 2, 2018 · 5 An array a [], with N elements, admitting repeated, is said to "contain a v element mostly" if more than half of its content equals v. Watch the video to learn 4 ways how Find the majority element in a sequence by using divide and conquer algorithm. Professor Ada is teaching her students about efficient algorithms. Review Majority Element for alternate solutions. Find the majority element in an array using divide and conquer. Basically, we need to write a function say isMajority () that takes an array (arr [] ), array’s size (n) and a number to be searched (x) as parameters and returns true if x is a majority element (present more than n/2 times). The majority element is the element that appears more than ⌊n / 2⌋ times. Since a majority element occurs more than n/2 times in an Sep 15, 2025 · Given an integer array containing duplicates, return the majority element if present. First one relies on the logi LeetCode: 169 Majority Elements Divide and Conquer/Hash Table/Sort, Programmer Sought, the best programmer technical posts sharing site. Jul 23, 2025 · Divide and Conquer algorithm is a problem-solving strategy that involves. Your task is to implement an efficient Divide and Conquer JAVA function to find the majority element in O (n log n) time. Apr 22, 2018 · I wrote this piece of code as solution to a problem set that required finding the majority element in a list using divide and conquer in \$ O (n \log n)\$. Since a majority element occurs more than n/2 times in an (You might think of the elements as chips, and there is a tester that can be used to determine whether or not two chips are identical. Since no extra space is used in the Program to Find majority element in an array. It always returns the element itself (Old) Leetcode 169 - Divide And Conquer | Majority Element Nideesh Terapalli 7. You'll still need to do an extra pass to confirm that the candidate is really a majority element in the original array. - prantosky/coursera-algorithmic-toolbox Jun 30, 2013 · Majority Element: A majority element in an array A [] of size n is an element that appears more than n/2 times (and hence there is at most one such element). Design an e cient divide and conquer algorithm to nd a majority element in A(or determine that no majority element exists). Apr 23, 2024 · In this post, we’ll explore an efficient approach to finding the majority element in an array using a combination of divide and conquer strategy and the Boyer-Moore Voting Algorithm. Does knowing the majority elements of A1and A2help you gure out the majority element of A ? If so, you can use a divide-and-conquer approach. The document presents multiple solutions for common algorithmic problems using divide and conquer techniques, including merge sort, finding the majority element, and counting inversions in an array. 25K subscribers Subscribed Jul 17, 2021 · Here's a question about using a divide and conquer approach to find a majority element in an array. Follow-up: Could you solve the problem in linear time and in O (1) space? We are given an array of integers Tags array | divide-and-conquer | bit-manipulation Companies adobe | zenefits Given an array nums of size n, return the majority element. In this video we have discussed on how to find the majority elements from an array of size n, using divide and conquer approach and also discussed how to inf In-depth solution and explanation for LeetCode 169. is that a good\correct idea? btw, apparently i had to write the algorithm in a divide-n-conquer method, so mine isn't good (also its runtime Does knowing the majority elements of Ai and A2 help you figure out the majority element of A? If so, you can use a divide-and-conquer approach. This unit covers the divide & conquer design paradigm analysis techniques, Master Theorems quickselect median of medians algorithm Karatsuba multiplication majority algorithms closest pair of points Learning outcomes Know the steps of the Divide & Conquer paradigm. Find Unique Binary String 花花酱 LeetCode 231. Show the time and space complexity of your solution. Coursera's Algorithmic Toolbox Course (#1 in Data Structures and Algorithms) - py-zoid/Algorithmic-Toolbox Question: I need help creating a O (nlogn) divide and conquer algorithm to find the majority element in a unsorted array. The elements of the array are not necessarily from some ordered domain like the integers, and so there can be no comparisons of the form \is A[i] > A[j]?". Write a divide-and-conquer algorithm that determines whether a given array A [0. The elements of the array are not necessarily from some ordered domain like the integers, and so there can be no comparisons of the form “is A[i] > A[j]?”. Assume that elements cannot be ordered or sorted, but can be compared for equality. Exercise 4. If no element meets this requirement, no majority element exists. 25K subscribers 249 Nov 26, 2022 · I am trying to build the logic behind a divide and conquer algorithm that will find the majority element in a matrix $A$ with $n$ elements in $\mathcal {O} (nlogn)$ time. The majority element is defined as the element with number of repetitions more than half the length of the input list. A majority element is an element that appears more than n/2 times in an array of size n. Assume you have an array A [1. Can you solve this real interview question? Majority Element - Given an array nums of size n, return the majority element. Since there are two nested loops that traverse the array. She wants to illustrate the power of divide and conquer. Briefly explain why the algorithmn is O (nlogn) Question: (10 marks) Give a divide and conquer algorithm to find a “U3-majority" element in an array A, if such an element exists (i. (Hint: Split the array A into two arrays A1and A2of half the size. ) Grading: 10 ointsp where it will eb graded with the grading rubric and divided by 2. Frequency of m is greater than n where n is the number of 2 elements of A. Even though there are many ways to approach this issue, the divide and conquer algorithm stands out for its effectiveness and grace. Minimum Bit Flips to Convert Number 花花酱 LeetCode 1980. Algorithm- To solve the problem, the idea is to use Divide and… (Remade) Leetcode 169 - Divide And Conquer | Majority Element Nideesh Terapalli 7. A [t, n] is said to have a majority element if more than half of its entries are the same. Jul 23, 2025 · Output: 3 appears more than 3 times in arr[] Time Complexity: O (Logn) Algorithmic Paradigm: Divide and Conquer METHOD 3: If it is already given that the array is sorted and there exists a majority element, checking if a particular element is as easy as checking if the middle element of the array is the number we are checking against. 7 Assuming that the input sequence contains a majority element, carry out best-case analysis on element comparisons for the divide-and-conquer majority algorithm given previously. (You might think of the elements as chips, and there is a tester that can be used to determine whether or not two chips are identical. May 4, 2023 · Time Complexity The time complexity is O (n^2). g. Jul 23, 2025 · Given an array arr of N elements, A majority element in an array arr of size N is an element that appears more than N/2 times in the array. Question: (10 marks) Give a divide and conquer algorithm to find a “U3-majority" element in an array A, if such an element exists (i. The document outlines a lab assignment focused on finding the majority element in an array using four different algorithms: brute-force, sorting, divide and conquer, and Boyer-Moore voting algorithm. Given an array, the task is to design an algorithm to tell whether the array has a majority element, and. Then compare A1,A2. 1 Pair up the elements of A arbitrarily, to get n=2 pairs (Majority Element) An arrayA=a1, . Be able to solve simple Divide & Conquer recurrences. From there, find (for example) the 25th and 75th percentile items. 众数 是指在数组中出现次数 Feb 7, 2024 · Divide and Conquer Given an array A of n integers, where n is a power of 2, a majority element of A is an element in A that appears strictly more than n 2 times. patreon. (note: just "if", not "if and only if")With that you can make a recursive procedure to find a candidate element. It's taken from Algorithms by S. Feb 27, 2018 · How to use divide and conquer and the fact that if one subarray has a majority, the combined array has a majority to find majority element?. Divide-and-Conquer An array A [1n is said to have a majority element if more than half of its entries are the same. n] is said to have a majority element if more than half of its entries are the same. udff rdzqf vls twmxmsxr svn afso qacap lphxcw nubycb plde hbqwo itwntf meg gdfxl pmdyiwwz