Print all triplets in sorted array that form AP
Last Updated :
04 Aug, 2022
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 12
2 12 22
12 17 22
2 17 32
12 22 32
9 22 35
2 22 42
22 32 42
Input : arr[] = { 3, 5, 6, 7, 8, 10, 12};
Output :
3 5 7
5 6 7
6 7 8
6 8 10
8 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.
Implementation:
C++
// C++ program to print all triplets in given
// array that form Arithmetic Progression
// C++ program to print all triplets in given
// array that form Arithmetic Progression
#include <bits/stdc++.h>
using namespace std;
// Function to print all triplets in
// given sorted array that forms AP
void printAllAPTriplets(int arr[], int n)
{
unordered_set<int> s;
for (int i = 0; i < n - 1; i++)
{
for (int j = i + 1; j < n; j++)
{
// Use hash to find if there is
// a previous element with difference
// equal to arr[j] - arr[i]
int diff = arr[j] - arr[i];
if (s.find(arr[i] - diff) != s.end())
cout << arr[i] - diff << " " << arr[i]
<< " " << arr[j] << endl;
}
s.insert(arr[i]);
}
}
// Driver code
int main()
{
int arr[] = { 2, 6, 9, 12, 17,
22, 31, 32, 35, 42 };
int n = sizeof(arr) / sizeof(arr[0]);
printAllAPTriplets(arr, n);
return 0;
}
// Java program to print all
// triplets in given array
// that form Arithmetic
// Progression
import java.io.*;
import java.util.*;
class GFG
{
// Function to print
// all triplets in
// given sorted array
// that forms AP
static void printAllAPTriplets(int []arr,
int n)
{
ArrayList<Integer> s =
new ArrayList<Integer>();
for (int i = 0;
i < n - 1; i++)
{
for (int j = i + 1; j < n; j++)
{
// Use hash to find if
// there is a previous
// element with difference
// equal to arr[j] - arr[i]
int diff = arr[j] - arr[i];
boolean exists =
s.contains(arr[i] - diff);
if (exists)
System.out.println(arr[i] - diff +
" " + arr[i] +
" " + arr[j]);
}
s.add(arr[i]);
}
}
// Driver code
public static void main(String args[])
{
int []arr = {2, 6, 9, 12, 17,
22, 31, 32, 35, 42};
int n = arr.length;
printAllAPTriplets(arr, n);
}
}
// This code is contributed by
// Manish Shaw(manishshaw1)
# 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 = "\n");
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)
// C# program to print all
// triplets in given array
// that form Arithmetic
// Progression
using System;
using System.Collections.Generic;
class GFG
{
// Function to print
// all triplets in
// given sorted array
// that forms AP
static void printAllAPTriplets(int []arr,
int n)
{
List<int> s = new List<int>();
for (int i = 0;
i < n - 1; i++)
{
for (int j = i + 1; j < n; j++)
{
// Use hash to find if
// there is a previous
// element with difference
// equal to arr[j] - arr[i]
int diff = arr[j] - arr[i];
bool exists = s.Exists(element =>
element == (arr[i] -
diff));
if (exists)
Console.WriteLine(arr[i] - diff +
" " + arr[i] +
" " + arr[j]);
}
s.Add(arr[i]);
}
}
// Driver code
static void Main()
{
int []arr = new int[]{ 2, 6, 9, 12, 17,
22, 31, 32, 35, 42 };
int n = arr.Length;
printAllAPTriplets(arr, n);
}
}
// This code is contributed by
// Manish Shaw(manishshaw1)
<?php
// PHP program to pr$all
// triplets in given array
// that form Arithmetic
// Progression
// Function to print
// all triplets in
// given sorted array
// that forms AP
function printAllAPTriplets($arr, $n)
{
$s = array();
for ($i = 0; $i < $n - 1; $i++)
{
for ($j = $i + 1;
$j < $n; $j++)
{
// Use hash to find if
// there is a previous
// element with difference
// equal to arr[j] - arr[i]
$diff = $arr[$j] - $arr[$i];
if (in_array($arr[$i] -
$diff, $arr))
echo(($arr[$i] - $diff) .
" " . $arr[$i] .
" " . $arr[$j] . "\n");
}
array_push($s, $arr[$i]);
}
}
// Driver code
$arr = array(2, 6, 9, 12, 17,
22, 31, 32, 35, 42);
$n = count($arr);
printAllAPTriplets($arr, $n);
// This code is contributed by
// Manish Shaw(manishshaw1)
?>
<script>
// JavaScript program to print all triplets in given
// array that form Arithmetic Progression
// Function to print all triplets in
// given sorted array that forms AP
function printAllAPTriplets( arr, n){
const s = new Set()
for (let i = 0; i < n - 1; i++)
{
for (let j = i + 1; j < n; j++)
{
// Use hash to find if there is
// a previous element with difference
// equal to arr[j] - arr[i]
let diff = arr[j] - arr[i];
if (s.has(arr[i] - diff))
document.write(arr[i] - diff +" " + arr[i]
+ " " + arr[j] + "<br>");
}
s.add(arr[i]);
}
}
// Driver code
let arr = [ 2, 6, 9, 12, 17,
22, 31, 32, 35, 42 ];
let n = arr.length;
printAllAPTriplets(arr, n);
</script>
Output6 9 12
2 12 22
12 17 22
2 17 32
12 22 32
9 22 35
2 22 42
22 32 42
Time 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.
C++
// C++ program to print all triplets in given
// array that form Arithmetic Progression
#include <bits/stdc++.h>
using namespace std;
// Function to print all triplets in
// given sorted array that forms AP
void printAllAPTriplets(int arr[], int n)
{
for (int i = 1; i < n - 1; i++)
{
// Search other two elements of
// AP with arr[i] as middle.
for (int j = i - 1, k = i + 1; j >= 0 && k < n;)
{
// if a triplet is found
if (arr[j] + arr[k] == 2 * arr[i])
{
cout << arr[j] << " " << arr[i]
<< " " << arr[k] << endl;
// Since elements are distinct,
// arr[k] and arr[j] cannot form
// any more triplets with arr[i]
k++;
j--;
}
// If middle element is more move to
// higher side, else move lower side.
else if (arr[j] + arr[k] < 2 * arr[i])
k++;
else
j--;
}
}
}
// Driver code
int main()
{
int arr[] = { 2, 6, 9, 12, 17,
22, 31, 32, 35, 42 };
int n = sizeof(arr) / sizeof(arr[0]);
printAllAPTriplets(arr, n);
return 0;
}
// Java implementation to print
// all the triplets in given array
// that form Arithmetic Progression
import java.io.*;
class GFG
{
// Function to print all triplets in
// given sorted array that forms AP
static void findAllTriplets(int arr[], int n)
{
for (int i = 1; i < n - 1; i++)
{
// Search other two elements
// of AP with arr[i] as middle.
for (int j = i - 1, k = i + 1; j >= 0 && k < n;)
{
// if a triplet is found
if (arr[j] + arr[k] == 2 * arr[i])
{
System.out.println(arr[j] +" " +
arr[i]+ " " + arr[k]);
// Since elements are distinct,
// arr[k] and arr[j] cannot form
// any more triplets with arr[i]
k++;
j--;
}
// If middle element is more move to
// higher side, else move lower side.
else if (arr[j] + arr[k] < 2 * arr[i])
k++;
else
j--;
}
}
}
// Driver code
public static void main (String[] args)
{
int arr[] = { 2, 6, 9, 12, 17,
22, 31, 32, 35, 42 };
int n = arr.length;
findAllTriplets(arr, n);
}
}
// This code is contributed by vt_m.
# 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
// C# implementation to print
// all the triplets in given array
// that form Arithmetic Progression
using System;
class GFG
{
// Function to print all triplets in
// given sorted array that forms AP
static void findAllTriplets(int []arr, int n)
{
for (int i = 1; i < n - 1; i++)
{
// Search other two elements
// of AP with arr[i] as middle.
for (int j = i - 1, k = i + 1; j >= 0 && k < n;)
{
// if a triplet is found
if (arr[j] + arr[k] == 2 * arr[i])
{
Console.WriteLine(arr[j] +" " +
arr[i]+ " " + arr[k]);
// Since elements are distinct,
// arr[k] and arr[j] cannot form
// any more triplets with arr[i]
k++;
j--;
}
// If middle element is more move to
// higher side, else move lower side.
else if (arr[j] + arr[k] < 2 * arr[i])
k++;
else
j--;
}
}
}
// Driver code
public static void Main ()
{
int []arr = { 2, 6, 9, 12, 17,
22, 31, 32, 35, 42 };
int n = arr.Length;
findAllTriplets(arr, n);
}
}
// This code is contributed by vt_m.
<?php
// PHP implementation to print
// all the triplets in given array
// that form Arithmetic Progression
// Function to print all triplets in
// given sorted array that forms AP
function findAllTriplets($arr, $n)
{
for ($i = 1; $i < $n - 1; $i++)
{
// Search other two elements
// of AP with arr[i] as middle.
for ($j = $i - 1, $k = $i + 1;
$j >= 0 && $k < $n;)
{
// if a triplet is found
if ($arr[$j] + $arr[$k] == 2 *
$arr[$i])
{
echo $arr[$j] ." " .
$arr[$i]. " " .
$arr[$k] . "\n";
// Since elements are distinct,
// arr[k] and arr[j] cannot form
// any more triplets with arr[i]
$k++;
$j--;
}
// If middle element is more move to
// higher side, else move lower side.
else if ($arr[$j] + $arr[$k] < 2 *
$arr[$i])
$k++;
else
$j--;
}
}
}
// Driver code
$arr = array(2, 6, 9, 12, 17,
22, 31, 32, 35, 42);
$n = count($arr);
findAllTriplets($arr, $n);
// This code is contributed by Sam007
?>
<script>
// JavaScript program to print all triplets in given
// array that form Arithmetic Progression
// Function to print all triplets in
// given sorted array that forms AP
function printAllAPTriplets(arr, n)
{
for (let i = 1; i < n - 1; i++)
{
// Search other two elements of
// AP with arr[i] as middle.
for (let j = i - 1, k = i + 1; j >= 0 && k < n;)
{
// if a triplet is found
if (arr[j] + arr[k] == 2 * arr[i])
{
document.write(arr[j] + " " + arr[i]
+ " " + arr[k] + "<br>");
// Since elements are distinct,
// arr[k] and arr[j] cannot form
// any more triplets with arr[i]
k++;
j--;
}
// If middle element is more move to
// higher side, else move lower side.
else if (arr[j] + arr[k] < 2 * arr[i])
k++;
else
j--;
}
}
}
// Driver code
let arr = [ 2, 6, 9, 12, 17,
22, 31, 32, 35, 42 ];
let n = arr.length;
printAllAPTriplets(arr, n);
// This code is contributed by Surbhi Tyagi.
</script>
Output6 9 12
2 12 22
12 17 22
2 17 32
12 22 32
9 22 35
2 22 42
22 32 42
Time Complexity : O(n2)
Auxiliary Space : O(1)
Similar Reads
Basics & Prerequisites
Data Structures
Array Data Structure GuideIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
3 min read
String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut
2 min read
Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The
2 min read
Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List:
2 min read
Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first
2 min read
Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems
2 min read
Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most
4 min read
Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of
3 min read
Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this
15+ min read
Algorithms
Searching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input
2 min read
Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
3 min read
Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution
14 min read
Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get
3 min read
Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net
3 min read
Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of
3 min read
Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit
4 min read
Advanced
Segment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree
3 min read
Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i
2 min read
GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br
2 min read
Interview Preparation
Practice Problem