• Skip to primary navigation
  • Skip to content
  • Skip to primary sidebar
  • Skip to secondary sidebar

GoHired

Interview Questions asked in Google, Microsoft, Amazon

Join WeekEnd Online Batch from 4-April-2020 on How to Crack Coding Interview in Just 10 Weeks : Fees just 20,000 INR

  • Home
  • Best Java Books
  • Algorithm
  • Internship
  • Certificates
  • About Us
  • Contact Us
  • Privacy Policy
  • Array
  • Stack
  • Queue
  • LinkedList
  • DP
  • Strings
  • Tree
  • Mathametical
  • Puzzles
  • Graph

Find Pythagorean Triplets in an array in O(N)

March 27, 2014 by Dhaval Dave

Find Pythagorean Triplets in an array

We have an array in which random integers are there. we need to find Pythagorean triplets.
which solves equation a^2 + b^2 = c^2.
Method 1 : Brute Force Method
Loop the array for three times and find a, b, and c which are solving equation.
Time complexity : O(N^3)

Method 2 : Using Hash Map to search.

  1) Create two loops and find all pairs.
  2) Find +C, -C = SquareRoot ( A^2 + B^2)
  3) Using Hash find whether C is present in Array or not.
  4) If C is present print Triplet A, B, C 
  5) Else continue till both loop completes.

Method 3 : Using Maths 

We know that
a = m^2 – n^2, b = 2mn, c = m^2 + n^2
From here you can get clue..
If not .. read further.

1)Sort the array in O(N log N) time.
2)For each element B, find the prime factorization. such that  
b = 2mn , m > n. m and n are prime
3)Calculate C = m^2 + n^2 , A= m^2 - n^2
4)With Hashmap find If C and A are in Array. Then Print Triplet C,A,B
5)Else Continue.

Explanation :

Consider Array : {3,6,8,5,10,4,12,14}

Step 1) 
Finding prime factorization such that b=2mn.
3 - not possible.
6 - 2*1*3 so m=3, n=1
8 - 2*2*2 so m=2,n=2 (not allowed , as they need to be co-prime)
5 - not possible
10 - 2*1*5 so m=5, n=1
4 - 2*1*2 so m=2, n=1 ...

Step 2) 

6 - 2*1*3 so m=3, n=1 m^2 + n^2 = 10 , m^2 - n^2 = 8 , 
both numbers are present in array can be found in O(1) 
with Hash.
    C = 10, A =8 and B = 6

=> similarly for 3,4,5 we can find 
m=2,n=1, B=4, C=5, A=3.

You can write and code for this
Best luck

Similar Articles

Filed Under: Amazon Interview Question, Flipkart Interview Questions, Interview Questions, problem Tagged With: Mathematical

Reader Interactions

Primary Sidebar

Join WeekEnd Online/Offline Batch from 4-April-2020 on How to Crack Coding Interview in Just 10 Weeks : Fees just 20,000 INR

Join WeekEnd Online/Offline Batch from 4-April-2020

WhatsApp us

Secondary Sidebar

Custom Search

  • How I cracked AMAZON
  • LeetCode
  • Adobe
  • Amazon
  • Facebook
  • Microsoft
  • Hacker Earth
  • CSE Interview

Top Rated Questions

Practo Hiring Experience

The greedy coins game Dynamic Programming

C++ OOPs Part1

Advanced SQL Injection

Regular Expression Matching

How strtok() Works

Find shortest distances between every pair of vertices ( Dynamic Programming Floyd Warshall Algorithm)

Diagonal Traversal of Binary Tree

Calculate price of parking from parking start end time prices

N teams are participating. each team plays twice with all other teams. Some of them will go to the semi final. Find Minimum and Maximum number of matches that a team has to win to qualify for finals ?

Adobe Interview Questions 8 month Exp

Number of Islands BFS/DFS

Generic Object Oriented Stack with Template

C++ OOPs Part2

Find Nearest Minimum number in left side in O(n)

Find if two rectangles overlap

HackeEarth Flipkart’s Drone

Handle duplicates in Binary Search Tree

Difference between a LinkedList and a Binary Search Tree BST

Reversal of LinkedList

Stock Buy Sell to Maximize Profit

Spanning Tree

BFS (Breath First Search)

LeetCode: Container With Most Water

BlueStone E-commerce Interview Experience

Connect n ropes with minimum cost

‘N’ Story Building, with 1,2,3 steps how many ways can a person reach top of building.

Reverse a Linked List in groups of given size

Fibonacci Hashing & Fastest Hashtable

Max Sum in circularly situated Values

Copyright © 2025 · Genesis Framework · WordPress · Log in