# Construct an array from its pair-product

Given a pair-product array pair[], the task is to find the original array. A pair-product array for an array arr[] is the array that contains product of all the pairs in ordered form i.e. {(arr * arr), (arr * arr), …, (arr * arr), (arr * arr), …, (arr[n – 2] * arr[n – 1])}.

Examples:

Input: pair[] = {2, 3, 6}
Output: 1 2 3

Input: pair[] = {48, 18, 24, 24, 32, 12}
Output: 6 8 3 4

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

Approach: First find the size of the required array from the given pair-product array. Assuming the size of the original array to be N and size of the pair-product array be X. Therefore, by solving (N * (N – 1)) / 2 = X, the value of N can be calculated as N = (1 + (int)sqrt(1 + 8 * X)) / 2.
Now lets see the solution with an example, lets say the pair-product array of [A, B, C, D] be arr[AB, AC, AD, BC, BD, CD] then by taking sqrt((arr * arr) / arr[n – 1]) -> sqrt((AB * AC) / BC) will give the value A.
Once the value of the first element has been recovered then all the remaining elements of the pair-product array can be divided by it to get the remaining elements of the original array.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `#include ` `using` `namespace` `std; ` ` `  `// Utility function to print the array ` `void` `printArr(``int` `arr[], ``int` `n) ` `{ ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``cout << arr[i] << ``" "``; ` `} ` ` `  `// Function to generate the original ` `// array from the pair-product array ` `void` `constructArr(``int` `pair[], ``int` `n) ` `{ ` `    ``int` `size = (1 + (``int``)``sqrt``(1 + 8 * n)) / 2; ` `    ``int` `arr[size]; ` ` `  `    ``// First element of the resulting array ` `    ``arr = ``sqrt``((pair * pair) / pair[size - 1]); ` ` `  `    ``// Find all the other elements ` `    ``for` `(``int` `i = 1; i < size; i++) ` `        ``arr[i] = pair[i - 1] / arr; ` ` `  `    ``// Print the elements of the generated array ` `    ``printArr(arr, size); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `pair[] = { 48, 18, 24, 24, 32, 12 }; ` `    ``int` `n = ``sizeof``(pair) / ``sizeof``(``int``); ` ` `  `    ``constructArr(pair, n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `class` `GFG ` `{ ` ` `  `// Utility function to print the array ` `static` `void` `printArr(``int` `arr[], ``int` `n) ` `{ ` `    ``for` `(``int` `i = ``0``; i < n; i++) ` `        ``System.out.print(arr[i] + ``" "``); ` `} ` ` `  `// Function to generate the original ` `// array from the pair-product array ` `static` `void` `constructArr(``int` `pair[], ``int` `n) ` `{ ` `    ``int` `size = (``1` `+ (``int``)Math.sqrt(``1` `+ ``8` `* n)) / ``2``; ` `    ``int` `[]arr = ``new` `int``[size]; ` ` `  `    ``// First element of the resulting array ` `    ``arr[``0``] = (``int``) Math.sqrt((pair[``0``] * pair[``1``]) /  ` `                                        ``pair[size - ``1``]); ` ` `  `    ``// Find all the other elements ` `    ``for` `(``int` `i = ``1``; i < size; i++) ` `        ``arr[i] = pair[i - ``1``] / arr[``0``]; ` ` `  `    ``// Print the elements of the generated array ` `    ``printArr(arr, size); ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args)  ` `{ ` `    ``int` `pair[] = { ``48``, ``18``, ``24``, ``24``, ``32``, ``12` `}; ` `    ``int` `n = pair.length; ` ` `  `    ``constructArr(pair, n); ` `} ` `} ` ` `  `// This code is contributed by PrinciRaj1992 `

## Python3

 `# Python3 implementation of the approach  ` `from` `math ``import` `sqrt ` ` `  `# Utility function to print the array  ` `def` `printArr(arr, n) :  ` ` `  `    ``for` `i ``in` `range``(n) : ` `        ``print``(arr[i], end ``=` `" "``);  ` ` `  `# Function to generate the original  ` `# array from the pair-product array  ` `def` `constructArr(pair, n) :  ` ` `  `    ``size ``=` `int``((``1` `+` `sqrt(``1` `+` `8` `*` `n)) ``/``/` `2``);  ` `    ``arr ``=` `[``0``] ``*` `(size);  ` ` `  `    ``# First element of the resulting array  ` `    ``arr[``0``] ``=` `int``(sqrt((pair[``0``] ``*` `pair[``1``]) ``/`  `                       ``pair[size ``-` `1``]));  ` ` `  `    ``# Find all the other elements  ` `    ``for` `i ``in` `range``(``1``, size) : ` `        ``arr[i] ``=` `pair[i ``-` `1``] ``/``/` `arr[``0``];  ` ` `  `    ``# Print the elements of the generated array  ` `    ``printArr(arr, size);  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `:  ` ` `  `    ``pair ``=` `[ ``48``, ``18``, ``24``, ``24``, ``32``, ``12` `]; ` `    ``n ``=` `len``(pair);  ` ` `  `    ``constructArr(pair, n);  ` ` `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# implementation of the approach ` `using` `System; ` `     `  `class` `GFG ` `{ ` ` `  `// Utility function to print the array ` `static` `void` `printArr(``int` `[]arr, ``int` `n) ` `{ ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``Console.Write(arr[i] + ``" "``); ` `} ` ` `  `// Function to generate the original ` `// array from the pair-product array ` `static` `void` `constructArr(``int` `[]pair, ``int` `n) ` `{ ` `    ``int` `size = (1 + (``int``)Math.Sqrt(1 + 8 * n)) / 2; ` `    ``int` `[]arr = ``new` `int``[size]; ` ` `  `    ``// First element of the resulting array ` `    ``arr = (``int``) Math.Sqrt((pair * pair) /  ` `                                        ``pair[size - 1]); ` ` `  `    ``// Find all the other elements ` `    ``for` `(``int` `i = 1; i < size; i++) ` `        ``arr[i] = pair[i - 1] / arr; ` ` `  `    ``// Print the elements of the generated array ` `    ``printArr(arr, size); ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args)  ` `{ ` `    ``int` `[]pair = { 48, 18, 24, 24, 32, 12 }; ` `    ``int` `n = pair.Length; ` ` `  `    ``constructArr(pair, n); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

Output:

```6 8 3 4
```

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