 Open in App
Not now

# Check whether right angled triangle is valid or not for large sides

• Difficulty Level : Easy
• Last Updated : 09 Aug, 2022

Given three integers a, b and c as triplets. Check if it is possible to make right angled triangle or not. Print Yes if possible, else No. 10-18 <= a, b, c <= 1018
Examples:

```Input: 3 4 5
Output: Yes
Explanation:
Since 3*3 + 4*4 = 5*5
Hence print "Yes"

Input: 8 5 13
Since 8 + 5 < 13 which violates the property of
triangle. Hence print "No"```

Recommended Practice

For a right angled triangle to be valid it must satisfies the following criteria:-

1. a, b and c should be greater than 0.

2. Sum of any two sides of triangle must be greater than the third side.

3. Pythagorean Theorem i.e., a2 + b2 = c2

First two conditions can be easily checked but for third condition we have to take care of overflow. Since a, b and c can be large so we can’t compare them directly unless we use python or BigInteger library in Java. For languages like C and C++, we have to reduce the expression in fraction form. Before comparing the fraction we need convert them in simplified form by dividing the numerator and denominator by gcd of both of them. Now compare both numerator and denominator of both the fractions of LHS and RHS such that if both would become same then it signifies the valid right angled triangle otherwise not.

## C++

 `// C++ program to check validity of triplets``#include ``using` `namespace` `std;` `// Function to check pythagorean triplets``bool` `Triplets(``long` `long` `a, ``long` `long` `b, ``long` `long` `c)``{``    ``if` `(a <= 0 || b <= 0 || c <= 0)``        ``return` `false``;` `    ``vector<``long` `long``> vec{ a, b, c };``    ``sort(vec.begin(), vec.end());` `    ``// Re-initialize a, b, c in ascending order``    ``a = vec, b = vec, c = vec;` `    ``// Check validation of sides of triangle``    ``if` `(a + b <= c)``        ``return` `false``;` `    ``long` `long` `p1 = a, p2 = c - b;` `    ``// Reduce fraction to simplified form``    ``long` `long` `div` `= __gcd(p1, p2);``    ``p1 /= ``div``, p2 /= ``div``;` `    ``long` `long` `q1 = c + b, q2 = a;` `    ``// Reduce fraction to simplified form``    ``div` `= __gcd(q1, q2);``    ``q1 /= ``div``, q2 /= ``div``;` `    ``// If fraction are equal return``    ``// 'true' else 'false'``    ``return` `(p1 == q1 && p2 == q2);``}` `// Function that will return 'Yes' or 'No'``// according to the correction of triplets``string checkTriplet(``long` `long` `a, ``long` `long` `b, ``long` `long` `c)``{``    ``if` `(Triplets(a, b, c))``        ``return` `"Yes"``;``    ``else``        ``return` `"No"``;``}` `// Driver code``int` `main()``{``    ``long` `long` `a = 4, b = 3, c = 5;``    ``cout << checkTriplet(a, b, c) << endl;` `    ``a = 8, b = 13, c = 5;``    ``cout << checkTriplet(a, b, c) << endl;` `    ``a = 1200000000000, b = 1600000000000,``    ``c = 2000000000000;``    ``cout << checkTriplet(a, b, c) << endl;` `    ``return` `0;``}`

## Java

 `// Java program to check validity of triplets``import` `java.util.*;` `class` `GFG``{``    ` `// Function to check pythagorean triplets``static` `boolean` `Triplets(``long` `a,``                        ``long` `b, ``long` `c)``{``    ``if` `(a <= ``0` `|| b <= ``0` `|| c <= ``0``)``        ``return` `false``;` `    ``long` `[]vec = { a, b, c };``    ``Arrays.sort(vec);` `    ``// Re-initialize a, b, c in ascending order``    ``a = vec[``0``]; b = vec[``1``]; c = vec[``2``];` `    ``// Check validation of sides of triangle``    ``if` `(a + b <= c)``        ``return` `false``;` `    ``long` `p1 = a, p2 = c - b;` `    ``// Reduce fraction to simplified form``    ``long` `div = __gcd(p1, p2);``    ``p1 /= div; p2 /= div;` `    ``long` `q1 = c + b, q2 = a;` `    ``// Reduce fraction to simplified form``    ``div = __gcd(q1, q2);``    ``q1 /= div; q2 /= div;` `    ``// If fraction are equal return``    ``// 'true' else 'false'``    ``return` `(p1 == q1 && p2 == q2);``}` `// Function that will return 'Yes' or 'No'``// according to the correction of triplets``static` `String checkTriplet(``long` `a,``                           ``long` `b, ``long` `c)``{``    ``if` `(Triplets(a, b, c))``        ``return` `"Yes"``;``    ``else``        ``return` `"No"``;``}` `static` `long` `__gcd(``long` `a, ``long` `b)``{``    ``if` `(b == ``0``)``        ``return` `a;``    ``return` `__gcd(b, a % b);``    ` `}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``long` `a = ``4``, b = ``3``, c = ``5``;``    ``System.out.println(checkTriplet(a, b, c));` `    ``a = ``8``; b = ``13``; c = ``5``;``    ``System.out.println(checkTriplet(a, b, c));` `    ``a = 1200000000000L; b = 1600000000000L;``    ``c = 2000000000000L;``    ``System.out.println(checkTriplet(a, b, c));``}``}` `// This code is contributed``// by Princi Singh`

## Python3

 `# Python3 program to check validity of triplets``def` `Triplets(a, b, c):``    ` `    ``if` `(a <``=` `0` `or` `b <``=` `0` `or` `c <``=` `0``):``        ``return` `False``        ` `    ``vec ``=` `[ a, b, c ]``    ``vec.sort()` `    ``# Re - initialize a, b, c in ascending order``    ``a ``=` `vec[``0``]; b ``=` `vec[``1``]; c ``=` `vec[``2``]` `    ``# Check validation of sides of triangle``    ``if` `(a ``+` `b <``=` `c):``        ``return` `False` `    ``p1 ``=` `a; p2 ``=` `c ``-` `b` `    ``# Reduce fraction to simplified form``    ``div ``=` `__gcd(p1, p2)``    ``p1 ``/``/``=` `div``    ``p2 ``/``/``=` `div` `    ``q1 ``=` `c ``+` `b``    ``q2 ``=` `a` `    ``# Reduce fraction to simplified form``    ``div ``=` `__gcd(q1, q2)``    ``q1 ``/``/``=` `div``    ``q2 ``/``/``=` `div` `    ``# If fraction are equal return``    ``# 'true' else 'false'``    ``return` `(p1 ``=``=` `q1 ``and` `p2 ``=``=` `q2)` `# Function that will return 'Yes' or 'No'``# according to the correction of triplets``def` `checkTriplet(a, b, c):``    ` `    ``if` `(Triplets(a, b, c)):``        ``return` `"Yes"``    ``else``:``        ``return` `"No"` `def` `__gcd(a, b):``    ``if` `(b ``=``=` `0``):``        ``return` `a``    ``return` `__gcd(b, a ``%` `b)` `# Driver code``a ``=` `4``b ``=` `3``c ``=` `5``print``(checkTriplet(a, b, c))` `a ``=` `8``b ``=` `13``c ``=` `5``print``(checkTriplet(a, b, c))` `a ``=` `1200000000000``b ``=` `1600000000000``c ``=` `2000000000000``print``(checkTriplet(a, b, c))` `# This code is contributed by ng24_7`

## C#

 `// C# program to check validity of triplets``using` `System;``    ` `class` `GFG``{``    ` `// Function to check pythagorean triplets``static` `Boolean Triplets(``long` `a,``                        ``long` `b, ``long` `c)``{``    ``if` `(a <= 0 || b <= 0 || c <= 0)``        ``return` `false``;` `    ``long` `[]vec = { a, b, c };``    ``Array.Sort(vec);` `    ``// Re-initialize a, b, c in ascending order``    ``a = vec; b = vec; c = vec;` `    ``// Check validation of sides of triangle``    ``if` `(a + b <= c)``        ``return` `false``;` `    ``long` `p1 = a, p2 = c - b;` `    ``// Reduce fraction to simplified form``    ``long` `div = __gcd(p1, p2);``    ``p1 /= div; p2 /= div;` `    ``long` `q1 = c + b, q2 = a;` `    ``// Reduce fraction to simplified form``    ``div = __gcd(q1, q2);``    ``q1 /= div; q2 /= div;` `    ``// If fraction are equal return``    ``// 'true' else 'false'``    ``return` `(p1 == q1 && p2 == q2);``}` `// Function that will return 'Yes' or 'No'``// according to the correction of triplets``static` `String checkTriplet(``long` `a,``                        ``long` `b, ``long` `c)``{``    ``if` `(Triplets(a, b, c))``        ``return` `"Yes"``;``    ``else``        ``return` `"No"``;``}` `static` `long` `__gcd(``long` `a, ``long` `b)``{``    ``if` `(b == 0)``        ``return` `a;``    ``return` `__gcd(b, a % b);``    ` `}` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ``long` `a = 4, b = 3, c = 5;``    ``Console.WriteLine(checkTriplet(a, b, c));` `    ``a = 8; b = 13; c = 5;``    ``Console.WriteLine(checkTriplet(a, b, c));` `    ``a = 1200000000000L; b = 1600000000000L;``    ``c = 2000000000000L;``    ``Console.WriteLine(checkTriplet(a, b, c));``}``}` `// This code has been contributed by 29AjayKumar`

## Javascript

 ``

Output:

```Yes
No
Yes```

Time complexity: O(log(M)) where M is the Maximum value among a, b and c.
Auxiliary space: O(1)
This article is contributed by Shubham Bansal. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

My Personal Notes arrow_drop_up