Pythagorean Triplet in an array

Given an array of integers, write a function that returns true if there is a triplet (a, b, c) that satisfies a² + b² = c².

Example: 

Input: arr[] = {3, 1, 4, 6, 5} 
Output: True 
There is a Pythagorean triplet (3, 4, 5).

Input: arr[] = {10, 4, 6, 12, 5} 
Output: False 
There is no Pythagorean triplet. 

Method 1 (Naive)
A simple solution is to run three loops, three loops pick three array elements, and check if the current three elements form a Pythagorean Triplet. 

Below is the implementation of the above idea :

C++

// A C++ program that returns true if there is a Pythagorean
// Triplet in a given array.
#include <iostream>

using namespace std;

// Returns true if there is Pythagorean triplet in ar[0..n-1]
bool isTriplet(int ar[], int n)
{
    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
            for (int k = j + 1; k < n; k++) {
                // Calculate square of array elements
                int x = ar[i] * ar[i], y = ar[j] * ar[j], z = ar[k] * ar[k];

                if (x == y + z || y == x + z || z == x + y)
                    return true;
            }
        }
    }

    // If we reach here, no triplet found
    return false;
}

/* Driver program to test above function */
int main()
{
    int ar[] = { 3, 1, 4, 6, 5 };
    int ar_size = sizeof(ar) / sizeof(ar[0]);
    isTriplet(ar, ar_size) ? cout << "Yes" : cout << "No";
    return 0;
}

Java

// A Java program that returns true if there is a Pythagorean
// Triplet in a given array.
import java.io.*;

class PythagoreanTriplet {

    // Returns true if there is Pythagorean triplet in ar[0..n-1]
    static boolean isTriplet(int ar[], int n)
    {
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                for (int k = j + 1; k < n; k++) {
                    // Calculate square of array elements
                    int x = ar[i] * ar[i], y = ar[j] * ar[j], z = ar[k] * ar[k];

                    if (x == y + z || y == x + z || z == x + y)
                        return true;
                }
            }
        }

        // If we reach here, no triplet found
        return false;
    }

    // Driver program to test above function
    public static void main(String[] args)
    {
        int ar[] = { 3, 1, 4, 6, 5 };
        int ar_size = ar.length;
        if (isTriplet(ar, ar_size) == true)
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}
/* This code is contributed by Devesh Agrawal */

Python3

# Python program to check if there is Pythagorean
# triplet in given array

# Returns true if there is Pythagorean
# triplet in ar[0..n-1]

def isTriplet(ar, n):
    j = 0

    for i in range(n - 2):
        for j in range(i + 1, n):
            for k in range(j + 1, n - 1):
                # Calculate square of array elements
                x = ar[i]*ar[i]
                y = ar[j]*ar[j]
                z = ar[k]*ar[k]
                if (x == y + z or y == x + z or z == x + y):
                    return 1

    # If we reach here, no triplet found
    return 0


# Driver program to test above function
ar = [3, 1, 4, 6, 5]
ar_size = len(ar)

if(isTriplet(ar, ar_size)):
    print("Yes")
else:
    print("No")

# This code is contributed by Anvesh Govind Saxena

C#

// A C# program that returns true
// if there is a Pythagorean
// Triplet in a given array.
using System;

class GFG {

    // Returns true if there is Pythagorean
    // triplet in ar[0..n-1]
    static bool isTriplet(int[] ar, int n)
    {
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                for (int k = j + 1; k < n; k++) {

                    // Calculate square of array elements
                    int x = ar[i] * ar[i], y = ar[j] * ar[j], z = ar[k] * ar[k];

                    if (x == y + z || y == x + z || z == x + y)
                        return true;
                }
            }
        }

        // If we reach here,
        // no triplet found
        return false;
    }

    // Driver code
    public static void Main()
    {
        int[] ar = { 3, 1, 4, 6, 5 };
        int ar_size = ar.Length;
        if (isTriplet(ar, ar_size) == true)
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
    }
}

// This code is contributed by shiv_bhakt.

PHP

<?php
// A PHP program that returns
// true if there is a Pythagorean
// Triplet in a given array.

// Returns true if there is
// Pythagorean triplet in
// ar[0..n-1]
function isTriplet($ar, $n)
{
    for ($i = 0; $i < $n; $i++)
    {
    for ($j = $i + 1; $j < $n; $j++)
    {
        for ($k = $j + 1; $k < $n; $k++)
        {

            // Calculate square of
            // array elements
            $x = $ar[$i] * $ar[$i];
            $y = $ar[$j] * $ar[$j];
            $z = $ar[$k] * $ar[$k];

            if ($x == $y + $z or
                $y == $x + $z or
                $z == $x + $y)
                return true;
        }
    }
    }

    // If we reach here,
    // no triplet found
    return false;
}

    // Driver Code
    $ar = array(3, 1, 4, 6, 5);
    $ar_size = count($ar);
    if(isTriplet($ar, $ar_size))
        echo "Yes";
    else
        echo "No";

// This code is contributed by anuj_67.
?>

Javascript

<script>

// A Javascript program that returns
// true if there is a Pythagorean
// Triplet in a given array.

// Returns true if there is
// Pythagorean triplet in ar[0..n-1]
function isTriplet( ar, n)
{
    for (let i = 0; i < n; i++) {
        for (let j = i + 1; j < n; j++) {
            for (let k = j + 1; k < n; k++) {
          // Calculate square of array elements
                let x = ar[i] * ar[i], y = ar[j] *
                ar[j], z = ar[k] * ar[k];

                if (x == y + z || y == x + z ||
                    z == x + y)
                    return true;
            }
        }
    }

    // If we reach here, no triplet found
    return false;
}


    // driver code

    let ar = [ 3, 1, 4, 6, 5 ];
    let ar_size = ar.length;
    if (isTriplet(ar, ar_size) == true)
        document.write("Yes");
    else
        document.write("No");

</script>

Output: 

Yes

The Time Complexity of the above solution is O(n³). 

Auxiliary Space: O(1)

Method 2 (Use Sorting)
We can solve this in O(n²) time by sorting the array first. 
1) Do the square of every element in the input array. This step takes O(n) time.
2) Sort the squared array in increasing order. This step takes O(nLogn) time.
3) To find a triplet (a, b, c) such that a² = b² + c², do following. 

1. Fix ‘a’ as the last element of the sorted array.
2. Now search for pair (b, c) in subarray between the first element and ‘a’. A pair (b, c) with a given sum can be found in O(n) time using the meet in middle algorithm discussed in method 1 of this post.
3. If no pair is found for current ‘a’, then move ‘a’ one position back and repeat step 3.2.

Below image is a dry run of the above approach: 

Below is the implementation of the above approach: 

C++

// A C++ program that returns true if there is a Pythagorean
// Triplet in a given array.
#include <algorithm>
#include <iostream>

using namespace std;

// Returns true if there is a triplet with following property
// A[i]*A[i] = A[j]*A[j] + A[k]*[k]
// Note that this function modifies given array
bool isTriplet(int arr[], int n)
{
    // Square array elements
    for (int i = 0; i < n; i++)
        arr[i] = arr[i] * arr[i];

    // Sort array elements
    sort(arr, arr + n);

    // Now fix one element one by one and find the other two
    // elements
    for (int i = n - 1; i >= 2; i--) {
        // To find the other two elements, start two index
        // variables from two corners of the array and move
        // them toward each other
        int l = 0; // index of the first element in arr[0..i-1]
        int r = i - 1; // index of the last element in arr[0..i-1]
        while (l < r) {
            // A triplet found
            if (arr[l] + arr[r] == arr[i])
                return true;

            // Else either move 'l' or 'r'
            (arr[l] + arr[r] < arr[i]) ? l++ : r--;
        }
    }

    // If we reach here, then no triplet found
    return false;
}

/* Driver program to test above function */
int main()
{
    int arr[] = { 3, 1, 4, 6, 5 };
    int arr_size = sizeof(arr) / sizeof(arr[0]);
    isTriplet(arr, arr_size) ? cout << "Yes" : cout << "No";
    return 0;
}

Java

// A Java program that returns true if there is a Pythagorean
// Triplet in a given array.
import java.io.*;
import java.util.*;

class PythagoreanTriplet {
    // Returns true if there is a triplet with following property
    // A[i]*A[i] = A[j]*A[j] + A[k]*[k]
    // Note that this function modifies given array
    static boolean isTriplet(int arr[], int n)
    {
        // Square array elements
        for (int i = 0; i < n; i++)
            arr[i] = arr[i] * arr[i];

        // Sort array elements
        Arrays.sort(arr);

        // Now fix one element one by one and find the other two
        // elements
        for (int i = n - 1; i >= 2; i--) {
            // To find the other two elements, start two index
            // variables from two corners of the array and move
            // them toward each other
            int l = 0; // index of the first element in arr[0..i-1]
            int r = i - 1; // index of the last element in arr[0..i-1]
            while (l < r) {
                // A triplet found
                if (arr[l] + arr[r] == arr[i])
                    return true;

                // Else either move 'l' or 'r'
                if (arr[l] + arr[r] < arr[i])
                    l++;
                else
                    r--;
            }
        }

        // If we reach here, then no triplet found
        return false;
    }

    // Driver program to test above function
    public static void main(String[] args)
    {
        int arr[] = { 3, 1, 4, 6, 5 };
        int arr_size = arr.length;
        if (isTriplet(arr, arr_size) == true)
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}
/*This code is contributed by Devesh Agrawal*/

Python3

# Python program that returns true if there is
# a Pythagorean Triplet in a given array.

# Returns true if there is Pythagorean
# triplet in ar[0..n-1]
def isTriplet(ar, n):
    # Square all the elements
    for i in range(n):
        ar[i] = ar[i] * ar[i]

    # sort array elements
    ar.sort()

    # fix one element
    # and find other two
    # i goes from n - 1 to 2
    for i in range(n-1, 1, -1):
        # start two index variables from
        # two corners of the array and
        # move them toward each other
        j = 0
        k = i - 1
        while (j < k):
            # A triplet found
            if (ar[j] + ar[k] == ar[i]):
                return True
            else:
                if (ar[j] + ar[k] < ar[i]):
                    j = j + 1
                else:
                    k = k - 1
    # If we reach here, then no triplet found
    return False

# Driver program to test above function */
ar = [3, 1, 4, 6, 5]
ar_size = len(ar)
if(isTriplet(ar, ar_size)):
    print("Yes")
else:
    print("No")

# This code is contributed by Aditi Sharma

C#

// C# program that returns true
// if there is a Pythagorean
// Triplet in a given array.
using System;

class GFG {

    // Returns true if there is a triplet
    // with following property A[i]*A[i]
    // = A[j]*A[j]+ A[k]*[k] Note that
    // this function modifies given array
    static bool isTriplet(int[] arr, int n)
    {

        // Square array elements
        for (int i = 0; i < n; i++)
            arr[i] = arr[i] * arr[i];

        // Sort array elements
        Array.Sort(arr);

        // Now fix one element one by one
        // and find the other two elements
        for (int i = n - 1; i >= 2; i--) {
            // To find the other two elements,
            // start two index variables from
            // two corners of the array and
            // move them toward each other
            // index of the first element
            // in arr[0..i-1]
            int l = 0;

            // index of the last element
            // in arr[0..i - 1]
            int r = i - 1;
            while (l < r) {

                // A triplet found
                if (arr[l] + arr[r] == arr[i])
                    return true;

                // Else either move 'l' or 'r'
                if (arr[l] + arr[r] < arr[i])
                    l++;
                else
                    r--;
            }
        }

        // If we reach here, then
        // no triplet found
        return false;
    }

    // Driver Code
    public static void Main()
    {
        int[] arr = { 3, 1, 4, 6, 5 };
        int arr_size = arr.Length;
        if (isTriplet(arr, arr_size) == true)
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
    }
}

// This code is contributed by shiv_bhakt.

PHP

<?php
// A PHP program that returns
// true if there is a Pythagorean
// Triplet in a given array.

// Returns true if there is a
// triplet with following property
// A[i]*A[i] = A[j]*A[j] + A[k]*[k]
// Note that this function modifies
// given array
function isTriplet( $arr, $n)
{

    // Square array elements
    for ($i = 0; $i < $n; $i++)
        $arr[$i] = $arr[$i] * $arr[$i];

    // Sort array elements
    sort($arr);

    // Now fix one element one by
    // one and find the other two
    // elements
    for($i = $n - 1; $i >= 2; $i--)
    {

        // To find the other two
        // elements, start two index
        // variables from two corners
        // of the array and move
        // them toward each other

        // index of the first element
        // in arr[0..i-1]
        $l = 0;

        // index of the last element
        // in arr[0..i-1]
        $r = $i - 1;
        while ($l < $r)
        {

            // A triplet found
            if ($arr[$l] + $arr[$r] == $arr[$i])
                return true;

            // Else either move 'l' or 'r'
            ($arr[$l] + $arr[$r] < $arr[$i])? $l++: $r--;
        }
    }

    // If we reach here,
    // then no triplet found
    return false;
}

    // Driver Code
    $arr = array(3, 1, 4, 6, 5);
    $arr_size = count($arr);
    if(isTriplet($arr, $arr_size))
        echo "Yes";
    else
        echo "No";

// This code is contributed by anuj_67.
?>

Javascript

<script>
// A javascript program that returns true if there is a Pythagorean
// Triplet in a given array.

    // Returns true if there is a triplet with following property
    // A[i]*A[i] = A[j]*A[j] + A[k]*[k]
    // Note that this function modifies given array
    function isTriplet(arr , n)
    {

        // Square array elements
        for (i = 0; i < n; i++)
            arr[i] = arr[i] * arr[i];

        // Sort array elements
        arr.sort((a,b)=>a-b);

        // Now fix one element one by one and find the other two
        // elements
        for (i = n - 1; i >= 2; i--)
        {

            // To find the other two elements, start two index
            // variables from two corners of the array and move
            // them toward each other
            var l = 0; // index of the first element in arr[0..i-1]
            var r = i - 1; // index of the last element in arr[0..i-1]
            while (l < r)
            {

                // A triplet found
                if (arr[l] + arr[r] == arr[i])
                    return true;

                // Else either move 'l' or 'r'
                if (arr[l] + arr[r] < arr[i])
                    l++;
                else
                    r--;
            }
        }

        // If we reach here, then no triplet found
        return false;
    }

    // Driver program to test above function
        var arr = [ 3, 1, 4, 6, 5 ];
        var arr_size = arr.length;
        if (isTriplet(arr, arr_size) == true)
            document.write("Yes");
        else
            document.write("No");

// This code is contributed by umadevi9616
</script>

Output:

 Yes 

The time complexity of this method is O(n²).

Auxiliary Space: O(1)

Method 3: (Using Hashing) 
The problem can also be solved using hashing. We can use a hash map to mark all the values of the given array. Using two loops, we can iterate for all the possible combinations of a and b, and then check if there exists the third value c. If there exists any such value, then there is a Pythagorean triplet. 

Below is the implementation of the above approach:  

C++

#include <bits/stdc++.h>
using namespace std;

// Function to check if the
// Pythagorean triplet exists or not
bool checkTriplet(int arr[], int n)
{
    int maximum = 0;

    // Find the maximum element
    for (int i = 0; i < n; i++) {
        maximum = max(maximum, arr[i]);
    }

    // Hashing array
    int hash[maximum + 1] = { 0 };

    // Increase the count of array elements
    // in hash table
    for (int i = 0; i < n; i++)
        hash[arr[i]]++;

    // Iterate for all possible a
    for (int i = 1; i < maximum + 1; i++) {

        // If a is not there
        if (hash[i] == 0)
            continue;

        // Iterate for all possible b
        for (int j = 1; j < maximum + 1; j++) {

            // If a and b are same and there is only one a
            // or if there is no b in original array
            if ((i == j && hash[i] == 1) || hash[j] == 0)
                continue;

            // Find c
            int val = sqrt(i * i + j * j);

            // If c^2 is not a perfect square
            if ((val * val) != (i * i + j * j))
                continue;

            // If c exceeds the maximum value
            if (val > maximum)
                continue;

            // If there exists c in the original array,
            // we have the triplet
            if (hash[val]) {
                return true;
            }
        }
    }
    return false;
}
// Driver Code
int main()
{
    int arr[] = { 3, 2, 4, 6, 5 };
    int n = sizeof(arr) / sizeof(arr[0]);
    if (checkTriplet(arr, n))
        cout << "Yes";
    else
        cout << "No";
}

Java

import java.util.*;

class GFG
{

// Function to check if the
// Pythagorean triplet exists or not
static boolean checkTriplet(int arr[], int n)
{
    int maximum = 0;

    // Find the maximum element
    for (int i = 0; i < n; i++)
    {
        maximum = Math.max(maximum, arr[i]);
    }

    // Hashing array
    int []hash = new int[maximum + 1];

    // Increase the count of array elements
    // in hash table
    for (int i = 0; i < n; i++)
        hash[arr[i]]++;

    // Iterate for all possible a
    for (int i = 1; i < maximum + 1; i++)
    {

        // If a is not there
        if (hash[i] == 0)
            continue;

        // Iterate for all possible b
        for (int j = 1; j < maximum + 1; j++)
        {

            // If a and b are same and there is only one a
            // or if there is no b in original array
            if ((i == j && hash[i] == 1) || hash[j] == 0)
                continue;

            // Find c
            int val = (int) Math.sqrt(i * i + j * j);

            // If c^2 is not a perfect square
            if ((val * val) != (i * i + j * j))
                continue;

            // If c exceeds the maximum value
            if (val > maximum)
                continue;

            // If there exists c in the original array,
            // we have the triplet
            if (hash[val] == 1)
            {
                return true;
            }
        }
    }
    return false;
}

// Driver Code
public static void main(String[] args)
{
    int arr[] = { 3, 2, 4, 6, 5 };
    int n = arr.length;
    if (checkTriplet(arr, n))
        System.out.print("Yes");
    else
        System.out.print("No");
}
}

// This code is contributed by Rajput-Ji

Python3

# Function to check if the
# Pythagorean triplet exists or not
import math

def checkTriplet(arr, n):
    maximum = 0

    # Find the maximum element
    maximum = max(arr)

        # Hashing array
    hash = [0]*(maximum+1)

    # Increase the count of array elements
    # in hash table
    for i in range(n):
        hash[arr[i]] += 1

        # Iterate for all possible a
    for i in range(1, maximum+1):
        # If a is not there
        if (hash[i] == 0):
            continue

        # Iterate for all possible b
        for j in range(1, maximum+1):
            # If a and b are same and there is only one a
            # or if there is no b in original array
            if ((i == j and hash[i] == 1) or hash[j] == 0):
                continue

            # Find c
            val = int(math.sqrt(i * i + j * j))

            # If c^2 is not a perfect square
            if ((val * val) != (i * i + j * j)):
                continue

            # If c exceeds the maximum value
            if (val > maximum):
                continue

            # If there exists c in the original array,
            # we have the triplet
            if (hash[val]):
                return True
    return False


# Driver Code
arr = [3, 2, 4, 6, 5]
n = len(arr)
if (checkTriplet(arr, n)):
    print("Yes")
else:
    print("No")


# This code is contributed by ankush_953

C#

using System;

class GFG
{

// Function to check if the
// Pythagorean triplet exists or not
static bool checkTriplet(int []arr, int n)
{
    int maximum = 0;

    // Find the maximum element
    for (int i = 0; i < n; i++)
    {
        maximum = Math.Max(maximum, arr[i]);
    }

    // Hashing array
    int []hash = new int[maximum + 1];

    // Increase the count of array elements
    // in hash table
    for (int i = 0; i < n; i++)
        hash[arr[i]]++;

    // Iterate for all possible a
    for (int i = 1; i < maximum + 1; i++)
    {

        // If a is not there
        if (hash[i] == 0)
            continue;

        // Iterate for all possible b
        for (int j = 1; j < maximum + 1; j++)
        {

            // If a and b are same and there is only one a
            // or if there is no b in original array
            if ((i == j && hash[i] == 1) || hash[j] == 0)
                continue;

            // Find c
            int val = (int) Math.Sqrt(i * i + j * j);

            // If c^2 is not a perfect square
            if ((val * val) != (i * i + j * j))
                continue;

            // If c exceeds the maximum value
            if (val > maximum)
                continue;

            // If there exists c in the original array,
            // we have the triplet
            if (hash[val] == 1)
            {
                return true;
            }
        }
    }
    return false;
}

// Driver Code
public static void Main(String[] args)
{
    int []arr = { 3, 2, 4, 6, 5 };
    int n = arr.Length;
    if (checkTriplet(arr, n))
        Console.Write("Yes");
    else
        Console.Write("No");
}
}

// This code is contributed by Rajput-Ji

Javascript

<script>

    // Function to check if the
    // Pythagorean triplet exists or not
    function checkTriplet(arr , n) {
        var maximum = 0;

        // Find the maximum element
        for (i = 0; i < n; i++) {
            maximum = Math.max(maximum, arr[i]);
        }

        // Hashing array
        var hash = Array(maximum + 1).fill(0);

        // Increase the count of array elements
        // in hash table
        for (i = 0; i < n; i++)
            hash[arr[i]]++;

        // Iterate for all possible a
        for (i = 1; i < maximum + 1; i++) {

            // If a is not there
            if (hash[i] == 0)
                continue;

            // Iterate for all possible b
            for (j = 1; j < maximum + 1; j++) {

                // If a and b are same and there is only one a
                // or if there is no b in original array
                if ((i == j && hash[i] == 1) || hash[j] == 0)
                    continue;

                // Find c
                var val = parseInt( Math.sqrt(i * i + j * j));

                // If c^2 is not a perfect square
                if ((val * val) != (i * i + j * j))
                    continue;

                // If c exceeds the maximum value
                if (val > maximum)
                    continue;

                // If there exists c in the original array,
                // we have the triplet
                if (hash[val] == 1) {
                    return true;
                }
            }
        }
        return false;
    }

    // Driver Code
        var arr = [ 3, 2, 4, 6, 5 ];
        var n = arr.length;
        if (checkTriplet(arr, n))
            document.write("Yes");
        else
            document.write("No");

// This code is contributed by gauravrajput1

</script>

Output

Yes

Thanks to Striver for suggesting the above approach. 
Time Complexity: O( max * max ), where max is the maximum most element in the array. 

Auxiliary Space: O(max)

Method -4:Using STL

Approach:

The problem can be solved using ordered maps and unordered maps. There is no need to store the elements in an ordered manner so implementation by an unordered map is faster. We can use the unordered map to mark all the values of the given array. Using two loops, we can iterate for all the possible combinations of a and b, and then check if there exists the third value c. If there exists any such value, then there is a Pythagorean triplet.

Below is the implementation of the above approach:

C++

#include <bits/stdc++.h>
using namespace std;

//  Returns true if there is Pythagorean triplet in
//  ar[0..n-1]
bool checkTriplet(int arr[], int n)
{
    // initializing unordered map with key and value as
    // integers
    unordered_map<int, int> umap;

    // Increase the count of array elements in unordered map
    for (int i = 0; i < n; i++)
        umap[arr[i]] = umap[arr[i]] + 1;

    for (int i = 0; i < n - 1; i++)
    {
        for (int j = i + 1; j < n; j++)
        {
            // calculating the squares of two elements as
            // integer and float
            int p = sqrt(arr[i] * arr[i] + arr[j] * arr[j]);
            float q
                = sqrt(arr[i] * arr[i] + arr[j] * arr[j]);

            // Condition is true if the value is same in
            // integer and float and also the value is
            // present in unordered map
            if (p == q && umap[p] != 0)
                return true;
        }
    }

    // If we reach here, no triplet found
    return false;
}

// Driver Code
int main()
{
    int arr[] = { 3, 2, 4, 6, 5 };
    int n = sizeof(arr) / sizeof(arr[0]);
    if (checkTriplet(arr, n))
        cout << "Yes";
    else
        cout << "No";
}
// This code is contributed by Vikkycirus

Java

import java.util.*;
class GFG{

  //  Returns true if there is Pythagorean triplet in
  //  ar[0..n-1]
  static boolean checkTriplet(int arr[], int n)
  {

    // initializing unordered map with key and value as
    // integers
    HashMap<Integer,Integer> umap = new HashMap<>();

    // Increase the count of array elements in unordered map
    for (int i = 0; i < n; i++)
      if(umap.containsKey(arr[i]))
        umap.put(arr[i] , umap.get(arr[i]) + 1);
    else
      umap.put(arr[i], 1);

    for (int i = 0; i < n - 1; i++)
    {
      for (int j = i + 1; j < n; j++)
      {

        // calculating the squares of two elements as
        // integer and float
        int p =(int) Math.sqrt(arr[i] * arr[i] + arr[j] * arr[j]);
        float q
          =(float) Math.sqrt(arr[i] * arr[i] + arr[j] * arr[j]);

        // Condition is true if the value is same in
        // integer and float and also the value is
        // present in unordered map
        if (p == q && umap.get(p) != 0)
          return true;
      }
    }

    // If we reach here, no triplet found
    return false;
  }

  // Driver Code
  public static void main(String[] args)
  {
    int arr[] = { 3, 2, 4, 6, 5 };
    int n = arr.length;
    if (checkTriplet(arr, n))
      System.out.print("Yes");
    else
      System.out.print("No");
  }
}

// This code is contributed by umadevi9616

C#

using System;
using System.Collections.Generic;

public class GFG {

  // Returns true if there is Pythagorean triplet in
  // ar[0..n-1]
  static bool checkTriplet(int []arr, int n) {

    // initializing unordered map with key and value as
    // integers
    Dictionary<int, int> umap = new Dictionary<int,int>();

    // Increase the count of array elements in unordered map
    for (int i = 0; i < n; i++)
      if (umap.ContainsKey(arr[i]))
        umap.Add(arr[i], umap[arr[i]] + 1);
    else
      umap.Add(arr[i], 1);

    for (int i = 0; i < n - 1; i++) {
      for (int j = i + 1; j < n; j++) {

        // calculating the squares of two elements as
        // integer and float
        int p = (int) Math.Sqrt(arr[i] * arr[i] + arr[j] * arr[j]);
        float q = (float) Math.Sqrt(arr[i] * arr[i] + arr[j] * arr[j]);

        // Condition is true if the value is same in
        // integer and float and also the value is
        // present in unordered map
        if (p == q && umap[p] != 0)
          return true;
      }
    }

    // If we reach here, no triplet found
    return false;
  }

  // Driver Code
  public static void Main(String[] args) {
    int []arr = { 3, 2, 4, 6, 5 };
    int n = arr.Length;
    if (checkTriplet(arr, n))
      Console.Write("Yes");
    else
      Console.Write("No");
  }
}

// This code is contributed by umadevi9616

Javascript

<script>

    // Returns true if there is Pythagorean triplet in
    // ar[0..n-1]
    function checkTriplet(arr , n) {

        // initializing unordered map with key and value as
        // integers
        var umap = new Map();

        // Increase the count of array elements in unordered map
        for (i = 0; i < n; i++)
            if (umap.has(arr[i]))
                umap.set(arr[i], umap.get(arr[i]) + 1);
            else
                umap.set(arr[i], 1);

        for (i = 0; i < n - 1; i++) {
            for (j = i + 1; j < n; j++) {

                // calculating the squares of two elements as
                // integer and float
                var p = parseInt( Math.sqrt(arr[i] * arr[i] + arr[j] * arr[j]));
                var q =  Math.sqrt(arr[i] * arr[i] + arr[j] * arr[j]);

                // Condition is true if the value is same in
                // integer and var and also the value is
                // present in unordered map
                if (p == q && umap.get(p) != 0)
                    return true;
            }
        }

        // If we reach here, no triplet found
        return false;
    }

    // Driver Code

        var arr = [ 3, 2, 4, 6, 5 ];
        var n = arr.length;
        if (checkTriplet(arr, n))
            document.write("Yes");
        else
            document.write("No");

// This code contributed by gauravrajput1
</script>

Python3

# Function to check if the
# Pythagorean triplet exists or not
import math

def checkTriplet(arr, n):

    # creating dictionary/unordered map
    h = {arr[i]: 1 for i in range(n)}
    for i in range(n-1):
        for j in range(i+1, n):

            # Calculating the squares of 2 elements
            q = math.sqrt(arr[i]*arr[i] + arr[j]*arr[j])

            # Checking if squareroot is integer and present in map
            if q == int(q) and int(q) in h:
                return True
    return False

# Driver Code
arr = [3, 2, 4, 6, 5]
n = len(arr)
if (checkTriplet(arr, n)):
    print("Yes")
else:
    print("No")

# This code is contributed by Anvesh Govind Saxena

Output

Yes

Time Complexity:O(n²)
Auxiliary Space:O(n)

This article is contributed by Harshit Gupta. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Method 5 – A better hashing based approach

This approach uses Set. Firstly, we’ll square the elements of the array and then sort the array in increasing order. Run two loops where the outer loop starts from the last index of the array to the second index (0 based indexing is assumed) and the inner loop starts from outerLoopIndex – 1 to the start. Create a set to store the elements in between outerLoopIndex and innerLoopIndex. Check if there is a number in the set which is equal to arr[outerLoopIndex] – arr[innerLoopIndex]. If yes, then return “True”.

C++

#include <bits/stdc++.h>
using namespace std;
bool checkTriplet(int arr[],int n)
{
  for(int i = 0; i < n; i++)
    arr[i] = arr[i]*arr[i];

  sort(arr, arr + n);

  for(int i = n - 1; i > 1; i--)
  {
    unordered_set<int> s;
    for(int j = i - 1; j >- 1; j--)
    {
      if(s.count(arr[i] - arr[j]))
        return true;

      s.insert(arr[j]);
    }
  }

  return false;
}
int main()
{
  int arr[] = {3, 2, 4, 6, 5};
  int n = sizeof(arr)/sizeof(arr[0]);

  if (checkTriplet(arr, n))
    cout << "Yes";
  else
    cout << "No";

  return 0;
}

// This code is contributed by aditya942003patil

Python3

# Python program to check if there exists a pythagorean triplet
def checkTriplet(arr, n):
    for i in range(n):
        arr[i] = arr[i] * arr[i]

    arr.sort()

    for i in range(n - 1, 1, -1):
        s = set()
        for j in range(i - 1, -1, -1):
            if (arr[i] - arr[j]) in s:
                return True
            s.add(arr[j])
    return False

# Driver Program
arr = [3, 2, 4, 6, 5]
n = len(arr)
if (checkTriplet(arr, n)):
    print("Yes")
else:
    print("No")

# This is contributed by Manvi Pandey

Output

Yes

Time Complexity: O(n²)
Auxiliary Space: O(n)