# geeks for geeks longest arithmetic progression

Input: arr[] = {5, 10, 15, 20, 25, 30}Output: 6Explanation:The whole set is in AP having common difference = 5.Therefore, the length is 4. We can also reduce space complexity to O(n). Please use ide.geeksforgeeks.org, generate link and share the link here. Input: arr[] = { 20, 1, 15, 3, 10, 5, 8 }Output: 4Explanation:The longest subsequence having the same difference is { 20, 15, 10, 5 }.The above subsequence has same difference for every consecutive pairs i.e., (15 – 20) = (10 – 15) = (5 – 10) = -5.Therefore, the length is 4. The longest subsequence having the same difference is { 20, 15, 10, 5 }. We use cookies to ensure you have the best browsing experience on our website. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview … Given an array A of integers, return the length of the longest arithmetic subsequence in A.. Recall that a subsequence of A is a list A[i_1], A[i_2], ..., A[i_k] with 0 <= i_1 < i_2 < ... < i_k <= A.length - 1, and that a sequence B is arithmetic if B[i+1] - B[i] are all the same value (for 0 <= i < B.length - 1).. If set[i] + set[k] is equal to 2*set[j], then we are done. Find the product of first and last numbers. For each test case, print "YES" without quotes if an arithmetic progression can be formed using all the given elements, else print "NO" without quotes. Last Updated: 09-09-2020. Given an array called set [] of sorted integers having no duplicates, find the length of the Longest Arithmetic Progression (LLAP) in it. We start from the second element and fix every element as middle element. Longest arithmetic progression with the given common difference; Ratio of mth and nth term in an Arithmetic Progression (AP) It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview … How to extend the above solution for the original problem? An entry L[i][j] in this table stores LLAP with set[i] and set[j] as first two elements of AP and j > i. Here is a list of some Suggested topics. First, there's the adversarial tone. 12. a, b, c and d are four numbers in arithmetic progression. Choose any one of them and start Writing. This is basic python program for all beginners in python programming language. Efficient Approach: The above approach can be optimized using Dynamic Programming. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. Example 1: Input: A = 1, B = 3, C = 2 Output: 1 Explaination: 3 is the second term of the sequence starting with 1 and having a common difference 2. The idea is to create a 2D table L[n][n]. Now let i >= 2. For all j, greater than some i ( arr[i - 1]; (ii) for all k, j < Explanation: A sequence a 1,a 2, … a n. Is Called arithmetic sequence or arithmetic progression if a n+1 – a n =d where d is constant. close, link How to reduce the space complexity for the above solution? Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. code. Therefore, the length is 4. In the arithmetic sequence the absolute difference between one term and next term is constant. The event invites geeks to write technical blog, articles and all the stuff related to coding. The subtext is a favorite geek quotation: First they ignore you, then… Following is C++ implementation of the above algorithm for the simpler problem. A Computer Science portal for geeks. Rest of the table is filled from bottom right to top left. Constraints: 1<=T<=100 1<=N<=10 5 1<=Arr[i]<=10 5 Example: Input: 2 4 0 12 4 8 4 12 40 11 20 Output: YES NO The required output of original problem is Length of the Longest Arithmetic Progression (LLAP) which is an integer value. Experience, Iterate over the array using nested loops. The common ratio of GP must be an integer. Following is the implementation of the Dynamic Programming algorithm. Longest arithmetic progression with the given common difference. Given three integers 'A' denoting the first term of an arithmetic sequence , 'C' denoting the common difference of an arithmetic sequence and an integer 'B'. Given an array of positive integers. Below are the steps: Below is the implementation of the above approach: edit Can't choose a Topic to write? To fill rest of the table, j (second element in AP) is first fixed. Don’t stop learning now. How to efficiently find i and k for a given j? Writing code in comment? Find the length of the longest sub-sequence such that elements in the subsequence are consecutive integers, the consecutive numbers can be in any order. By using our site, you For simplicity, we have assumed that the given set is sorted. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. If the given set has two or more elements, then the value of LLAP is at least 2 (Why?). I am not good in math, but I need to determine if two generic arithmetic progressions have an intersection point and, in that case, find the first intersection. Please use ide.geeksforgeeks.org, generate link and share the link here. Longest Arithmetic Progression. This process takes O(n3) time. Please write to us at contribute@geeksforgeeks.org to report any issue with the above content. The above function returns a boolean value. The last column of the table is always 2 (Why – see the meaning of L[i][j]). A Computer Science portal for geeks. By using our site, you code, Time Complexity: O(N2)Auxiliary Space: O(N2). Given a set of numbers, find the L ength of the L ongest G eometrix P rogression ( LLGP) in it. See your article appearing on the GeeksforGeeks main page and help other Geeks. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. Auxiliary Space: O(n2). The common difference between the numbers is 5. Ans. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. Attention reader! If i and k are found such that i, j, k form an AP, then the value of L[i][j] is set as L[j][k] + 1. I've searched the web and found some solutions, but I couldn't understand them. acknowledge that you have read and understood our, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Longest arithmetic progression with the given common difference, Count of n digit numbers whose sum of digits equals to given sum, Print all n-digit numbers whose sum of digits equals to given sum, Finding sum of digits of a number until sum becomes single digit, Program for Sum of the digits of a given number, Compute sum of digits in all numbers from 1 to n, Count possible ways to construct buildings, Maximum profit by buying and selling a share at most twice, Maximum profit by buying and selling a share at most k times, Maximum difference between two elements such that larger element appears after the smaller number, Given an array arr[], find the maximum j – i such that arr[j] > arr[i], Sliding Window Maximum (Maximum of all subarrays of size k), Sliding Window Maximum (Maximum of all subarrays of size k) using stack in O(n) time, Next greater element in same order as input, Maximum product of indexes of next greater on left and right, Stack | Set 4 (Evaluation of Postfix Expression), Write a program to reverse an array or string, Find the smallest and second smallest elements in an array, http://www.cs.uiuc.edu/~jeffe/pubs/pdf/arith.pdf, Longest string in non-decreasing order of ASCII code and in arithmetic progression, Longest subarray forming an Arithmetic Progression (AP), Longest subsequence forming an Arithmetic Progression (AP), Check whether Arithmetic Progression can be formed from the given array, Count of AP (Arithmetic Progression) Subsequences in an array, Minimum De-arrangements present in array of AP (Arithmetic Progression), Program for N-th term of Arithmetic Progression series, Program to print Arithmetic Progression series, PHP program to print an arithmetic progression series using inbuilt functions, Ratio of mth and nth term in an Arithmetic Progression (AP), Convert given array to Arithmetic Progression by adding an element, Change one element in the given array to make it an Arithmetic Progression, Check whether nodes of Binary Tree form Arithmetic, Geometric or Harmonic Progression, Minimum elements inserted in a sorted array to form an Arithmetic progression, Count common elements in two arrays which are in Arithmetic Progression, Find the missing number in unordered Arithmetic Progression, Count of subarrays forming an Arithmetic Progression (AP), Arithmetic Progression containing X and Y with least possible first term, Given an array A[] and a number x, check for pair in A[] with sum as x, Stack Data Structure (Introduction and Program), Write Interview It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview … Therefore, the length is 4. To find the three elements, we first fix an element as middle element and search for other two (one smaller and one greater). We can find i and k in linear time using following simple algorithm. Last Updated: 01-07-2019. acknowledge that you have read and understood our, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Write a program to reverse an array or string, Find the smallest and second smallest elements in an array, Stack Data Structure (Introduction and Program), K'th Smallest/Largest Element in Unsorted Array | Set 1, Given an array A[] and a number x, check for pair in A[] with sum as x, Count Inversions in an array | Set 1 (Using Merge Sort), Search an element in a sorted and rotated array, Find subarray with given sum | Set 1 (Nonnegative Numbers), Sliding Window Maximum (Maximum of all subarrays of size k), Queue | Set 1 (Introduction and Array Implementation), Array of Strings in C++ (5 Different Ways to Create), k largest(or smallest) elements in an array | added Min Heap method, generate all the possible subsequences of the given array, Longest subarray forming an Arithmetic Progression (AP), Count of subarrays forming an Arithmetic Progression (AP), Longest subarray forming a Geometic Progression (GP), Count subarrays of atleast size 3 forming a Geometric Progression (GP), Longest string in non-decreasing order of ASCII code and in arithmetic progression, Longest arithmetic progression with the given common difference, Longest Increasing Subsequence using Longest Common Subsequence Algorithm, Check whether Arithmetic Progression can be formed from the given array, Count of AP (Arithmetic Progression) Subsequences in an array, Minimum De-arrangements present in array of AP (Arithmetic Progression), Program for N-th term of Arithmetic Progression series, Program to print Arithmetic Progression series, PHP program to print an arithmetic progression series using inbuilt functions, Ratio of mth and nth term in an Arithmetic Progression (AP), Convert given array to Arithmetic Progression by adding an element, Change one element in the given array to make it an Arithmetic Progression, Check whether nodes of Binary Tree form Arithmetic, Geometric or Harmonic Progression, Minimum elements inserted in a sorted array to form an Arithmetic progression, N digit numbers having difference between the first and last digits as K, Program to calculate area of a parallelogram, Python | Using 2D arrays/lists the right way, Maximum and minimum of an array using minimum number of comparisons, Write Interview Longest arithmetic progression with the given common difference; ... See your article appearing on the GeeksforGeeks main page and help other Geeks.