# Minimum size of Array possible with given sum and product values

• Last Updated : 08 Oct, 2021

Given two positive integers S and P, the task is to find the minimum possible size of the array such that the sum of elements is S and the product of the elements is P. If there doesn’t exist any such array, then print “-1”.

Examples:

Input: S = 5, P = 6
Output: 2
Explanation: The valid array can be {2, 3}, which is of minimum size.

Input: S = 5, P = 100
Output: -1

Approach: The given problem can be solved based on the following observations:

• Using N numbers, an array can be formed of size N having sum S.
• Any product values can be achieved when the value of P is between [0, (S/N)N].

Follow the steps below to solve the given problem:

• Initially check if the value of S and P are the same, then return 1 as the S value itself is used to make a minimum size array.
• Iterate over the range [2, S] using the variable i, and if the value of (S/i) >= pow(P, 1/i) then print the value of i as the resultant minimum size of the array formed.
• After completing the above steps, if there doesn’t any possible value i satisfying the above criteria, then print “-1”.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// Function to find the minimum size``// of array  with sum S and product P``int` `minimumSizeArray(``int` `S, ``int` `P)``{``    ``// Base Case``    ``if` `(S == P) {` `        ``return` `1;``    ``}` `    ``// Iterate through all values of S``    ``// and check the mentioned condition``    ``for` `(``int` `i = 2; i <= S; i++) {` `        ``double` `d = i;``        ``if` `((S / d) >= ``pow``(P, 1.0 / d)) {``            ``return` `i;``        ``}``    ``}` `    ``// Otherwise, print "-1"``    ``return` `-1;``}` `// Driver Code``int` `main()``{``    ``int` `S = 5, P = 6;``    ``cout << minimumSizeArray(S, P);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``class` `GFG{` `// Function to find the minimum size``// of array  with sum S and product P``static` `int` `minimumSizeArray(``int` `S, ``int` `P)``{``    ``// Base Case``    ``if` `(S == P) {` `        ``return` `1``;``    ``}` `    ``// Iterate through all values of S``    ``// and check the mentioned condition``    ``for` `(``int` `i = ``2``; i <= S; i++) {` `        ``double` `d = i;``        ``if` `((S / d) >= Math.pow(P, ``1.0` `/ d)) {``            ``return` `i;``        ``}``    ``}` `    ``// Otherwise, print "-1"``    ``return` `-``1``;``}` `// Driver Code``public` `static` `void` `main(String args[])``{``    ``int` `S = ``5``, P = ``6``;``       ``System.out.println(minimumSizeArray(S, P));``}``}` `// This code is contributed by AnkThon`

## Python3

 `# python program for the above approach` `# Function to find the minimum size``# of array with sum S and product P``def` `minimumSizeArray(S, P):` `    ``# Base Case``    ``if` `(S ``=``=` `P):``        ``return` `1` `    ``# Iterate through all values of S``    ``# and check the mentioned condition``    ``for` `i ``in` `range``(``2``, S``+``1``):` `        ``d ``=` `i``        ``if` `((S ``/` `d) >``=` `pow``(P, ``1.0` `/` `d)):``            ``return` `i` `    ``# Otherwise, print "-1"``    ``return` `-``1` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:``    ``S ``=` `5``    ``P ``=` `6``    ``print``(minimumSizeArray(S, P))` `    ``# This code is contributed by rakeshsahni`

## C#

 `// C# program for the above approach``using` `System;``using` `System.Collections.Generic;` `class` `GFG{` `// Function to find the minimum size``// of array  with sum S and product P``static` `int` `minimumSizeArray(``int` `S, ``int` `P)``{``    ``// Base Case``    ``if` `(S == P) {` `        ``return` `1;``    ``}` `    ``// Iterate through all values of S``    ``// and check the mentioned condition``    ``for` `(``int` `i = 2; i <= S; i++) {` `        ``double` `d = i;``        ``if` `((S / d) >= Math.Pow(P, 1.0 / d)) {``            ``return` `i;``        ``}``    ``}` `    ``// Otherwise, print "-1"``    ``return` `-1;``}` `// Driver Code``public` `static` `void` `Main()``{``    ``int` `S = 5, P = 6;``    ``Console.Write(minimumSizeArray(S, P));``}``}` `// This code is contributed by SURENDRA_GANGWAR.`

## Javascript

 ``

Output:

`2`

Time Complexity: O(log P)
Auxiliary Space: O(1)

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