# Possible pairs forming a Pythagorean Triple with a given value

Given an integer C, the task is to find all possible pairs (A, B) in range [1, C) such that:

1. A2 + B2 = C2
2. A < B

Examples:

Input: C = 5
Output:(3, 4)
Explanation:
(3)2 + (4)2 = 9 + 16 = 25 = 52

Input: C = 25
Output:(15, 20), (7, 24)
Explanation: Both the pairs satisfy the necessary conditions.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

1. Check all possible values of A and B in the range [1, C).
2. Store all pair that satisfies the given conditions.

Below is the implementation of the above approach:

## C++

 `// C++ program to compute ` `// all the possible ` `// pairs that forms a ` `// pythagorean triple ` `// with a given value ` `#include ` `using` `namespace` `std; ` ` `  `// Function to generate all ` `// possible pairs ` `vector > Pairs(``int` `C) ` `{ ` `    ``// Vector to store all the ` `    ``// possible pairs ` `    ``vector > ans; ` ` `  `    ``// Checking all the possible ` `    ``// pair in the range of [1, c) ` `    ``for` `(``int` `i = 1; i < C; i++) { ` `        ``for` `(``int` `j = i + 1; j < C; ` `             ``j++) { ` ` `  `            ``// If the pair satisfies ` `            ``// the condition push it ` `            ``// in the vector ` `            ``if` `((i * i) + (j * j) == (C * C)) { ` `                ``ans.push_back(make_pair(i, j)); ` `            ``} ` `        ``} ` `    ``} ` `    ``return` `ans; ` `} ` ` `  `// Driver Program ` `int` `main() ` `{ ` `    ``int` `C = 13; ` `    ``vector > ans ` `        ``= Pairs(C); ` ` `  `    ``// If no valid pair exist ` `    ``if` `(ans.size() == 0) { ` `        ``cout << ``"No valid pair exist"` `             ``<< endl; ` `        ``return` `0; ` `    ``} ` ` `  `    ``// Print all valid pairs ` `    ``for` `(``auto` `i = ans.begin(); ` `         ``i != ans.end(); i++) { ` `        ``cout << ``"("` `<< i->first << ``", "` `             ``<< i->second << ``")"` `<< endl; ` `    ``} ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to compute all  ` `// the possible pairs that forms ` `// a pythagorean triple with a  ` `// given value ` `import` `java.util.*; ` ` `  `class` `GFG{ ` `static` `class` `pair ` `{  ` `    ``int` `first, second;  ` `     `  `    ``public` `pair(``int` `first, ``int` `second)  ` `    ``{  ` `        ``this``.first = first;  ` `        ``this``.second = second;  ` `    ``}  ` `}  ` ` `  `// Function to generate all ` `// possible pairs ` `static` `Vector Pairs(``int` `C) ` `{ ` `     `  `    ``// Vector to store all the ` `    ``// possible pairs ` `    ``Vector ans = ``new` `Vector(); ` ` `  `    ``// Checking all the possible ` `    ``// pair in the range of [1, c) ` `    ``for``(``int` `i = ``1``; i < C; i++)  ` `    ``{ ` `       ``for``(``int` `j = i + ``1``; j < C; j++) ` `       ``{ ` `            `  `          ``// If the pair satisfies ` `          ``// the condition push it ` `          ``// in the vector ` `          ``if` `((i * i) + (j * j) == (C * C))  ` `          ``{ ` `              ``ans.add(``new` `pair(i, j)); ` `          ``} ` `       ``} ` `    ``} ` `    ``return` `ans; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `C = ``13``; ` `    ``Vector ans = Pairs(C); ` ` `  `    ``// If no valid pair exist ` `    ``if` `(ans.size() == ``0``)  ` `    ``{ ` `        ``System.out.print(``"No valid pair "` `+ ` `                         ``"exist"` `+ ``"\n"``); ` `        ``return``; ` `    ``} ` ` `  `    ``// Print all valid pairs ` `    ``for``(pair i:ans) ` `    ``{ ` `       ``System.out.print(``"("` `+ i.first +  ` `                       ``", "` `+ i.second +  ` `                        ``")"` `+ ``"\n"``); ` `    ``} ` `} ` `} ` ` `  `// This code is contributed by gauravrajput1 `

Output:

```(5, 12)
```

Time Complexity: O(C2)

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Improved By : GauravRajput1