Python3 Program to Print all triplets in sorted array that form AP Last Updated : 05 Sep, 2024 Comments Improve Suggest changes Like Article Like Report Given a sorted array of distinct positive integers, print all triplets that form AP (or Arithmetic Progression)Examples : Input : arr[] = { 2, 6, 9, 12, 17, 22, 31, 32, 35, 42 };Output :6 9 122 12 2212 17 222 17 3212 22 329 22 352 22 4222 32 42Input : arr[] = { 3, 5, 6, 7, 8, 10, 12};Output :3 5 75 6 76 7 86 8 108 10 12 A simple solution is to run three nested loops to generate all triplets and for every triplet, check if it forms AP or not. Time complexity of this solution is O(n3)A better solution is to use hashing. We traverse array from left to right. We consider every element as middle and all elements after it as next element. To search the previous element, we use a hash table. Python3 # Python program to print all # triplets in given array # that form Arithmetic # Progression # Function to print # all triplets in # given sorted array # that forms AP def printAllAPTriplets(arr, n) : s = []; for i in range(0, n - 1) : for j in range(i + 1, n) : # Use hash to find if # there is a previous # element with difference # equal to arr[j] - arr[i] diff = arr[j] - arr[i]; if ((arr[i] - diff) in arr) : print ("{} {} {}" . format((arr[i] - diff), arr[i], arr[j]), end = " "); s.append(arr[i]); # Driver code arr = [2, 6, 9, 12, 17, 22, 31, 32, 35, 42]; n = len(arr); printAllAPTriplets(arr, n); # This code is contributed by # Manish Shaw(manishshaw1) Output : 6 9 122 12 2212 17 222 17 3212 22 329 22 352 22 4222 32 42Time Complexity : O(n2) Auxiliary Space : O(n)An efficient solution is based on the fact that the array is sorted. We use the same concept as discussed in GP triplet question. The idea is to start from the second element and fix every element as a middle element and search for the other two elements in a triplet (one smaller and one greater). Below is the implementation of the above idea. Python 3 # python 3 program to print all triplets in given # array that form Arithmetic Progression # Function to print all triplets in # given sorted array that forms AP def printAllAPTriplets(arr, n): for i in range(1, n - 1): # Search other two elements of # AP with arr[i] as middle. j = i - 1 k = i + 1 while(j >= 0 and k < n ): # if a triplet is found if (arr[j] + arr[k] == 2 * arr[i]): print(arr[j], "", arr[i], "", arr[k]) # Since elements are distinct, # arr[k] and arr[j] cannot form # any more triplets with arr[i] k += 1 j -= 1 # If middle element is more move to # higher side, else move lower side. elif (arr[j] + arr[k] < 2 * arr[i]): k += 1 else: j -= 1 # Driver code arr = [ 2, 6, 9, 12, 17, 22, 31, 32, 35, 42 ] n = len(arr) printAllAPTriplets(arr, n) # This article is contributed # by Smitha Dinesh Semwal Output : 6 9 122 12 2212 17 222 17 3212 22 329 22 352 22 4222 32 42Time Complexity : O(n2) Auxiliary Space : O(1) Please refer complete article on Print all triplets in sorted array that form AP for more details! Comment More infoAdvertise with us Next Article Python3 Program to Print all triplets in sorted array that form AP kartik Follow Improve Article Tags : Searching Hash Python Python Programs DSA Arrays cpp-unordered_set arithmetic progression +4 More Practice Tags : ArraysHashpythonSearching Similar Reads Python3 Program to Find a triplet that sum to a given value Given an array and a value, find if there is a triplet in array whose sum is equal to the given value. If there is such a triplet present in array, then print the triplet and return true. Else return false.Examples: Input: array = {12, 3, 4, 1, 6, 9}, sum = 24; Output: 12, 3, 9 Explanation: There is 6 min read Python3 Program for Check if an array is sorted and rotated Given an array of N distinct integers. The task is to write a program to check if this array is sorted and rotated counter-clockwise. 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