# Maximum value of division of two numbers in an Array

Given an array A of size N (> 2). The task is to find the maximum value of A[i] / A[j]

Note: A[i] ≠ 0.

Examples:

Input : A[] = {1, 2, 3, 4}
Output : 4
4 / 1 = 4 is maximum possible value.

Input : A[] = {3, 7, 9, 3, 11}
Output : 3

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

Naive Approach: A naive approach is to run nested loops and find the maximum possible answer.

Time complexity : O(N2) .

Efficient Approach: An efficient approach is to find maximum and minimum element in the array and print maximum / minimum

Proof:

Lets take an array A[] = {a, b, c, d} where a < b < c < d .
Now :
(b / a) < ( c / a ) < (d / a) (since b < c < d, and denominator is constant )
and since a is minimum, therefore
d / a is maximum

Below is the implemenantion of the above approach:

## C++

 `// CPP program to maximum value of  ` `// division of two numbers in an array ` `#include ` `using` `namespace` `std; ` ` `  `// Function to maximum value of  ` `// division of two numbers in an array ` `int` `Divison(``int` `a[], ``int` `n) ` `{ ` `    ``int` `maxi = INT_MIN, mini = INT_MAX; ` `     `  `    ``// Traverse through the array ` `    ``for` `(``int` `i = 0; i < n; i++) ` `    ``{ ` `        ``maxi = max(a[i], maxi); ` `        ``mini = min(a[i], mini); ` `    ``} ` `     `  `    ``// Return the required answer ` `    ``return` `maxi / mini; ` `} ` ` `  `// Driver code ` `int` `main()  ` `{ ` `    ``int` `a[] = {3, 7, 9, 3, 11}; ` `     `  `    ``int` `n = ``sizeof``(a) / ``sizeof``(a); ` `     `  `    ``cout << Divison(a, n); ` `    ``return` `0; ` `} `

## Java

 `// Java program to maximum value of  ` `// division of two numbers in an array ` `import` `java.util.*; ` `import` `java.lang.*; ` `import` `java.io.*; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to maximum value of  ` `// division of two numbers in an array ` `static` `int` `Divison(``int` `a[], ``int` `n) ` `{ ` `    ``int` `maxi = Integer.MIN_VALUE,  ` `        ``mini = Integer.MAX_VALUE; ` `     `  `    ``// Traverse through the array ` `    ``for` `(``int` `i = ``0``; i < n; i++) ` `    ``{ ` `        ``maxi = Math.max(a[i], maxi); ` `        ``mini = Math.min(a[i], mini); ` `    ``} ` `     `  `    ``// Return the required answer ` `    ``return` `maxi / mini; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main (String[] args) ` `              ``throws` `java.lang.Exception ` `{ ` `    ``int` `a[] = {``3``, ``7``, ``9``, ``3``, ``11``}; ` `     `  `    ``int` `n = a.length; ` `     `  `    ``System.out.print(Divison(a, n)); ` `} ` `} ` ` `  `// This code is contributed by Nidhiva `

## Python3

 `#  Python3 program to maximum value of ` `# division of two numbers in an array ` ` `  `# Function to maximum value of ` `# division of two numbers in an array ` `def` `Divison(a, n): ` ` `  `    ``maxi ``=` `-``10``*``*``9` `    ``mini ``=` `10``*``*``9` ` `  `    ``# Traverse through the array ` `    ``for` `i ``in` `a: ` `        ``maxi ``=` `max``(i, maxi) ` `        ``mini ``=` `min``(i, mini) ` ` `  `    ``# Return the required answer ` `    ``return` `maxi ``/``/` `mini ` ` `  `# Driver code ` `a ``=` `[``3``, ``7``, ``9``, ``3``, ``11``] ` ` `  `n ``=` `len``(a) ` ` `  `print``(Divison(a, n)) ` ` `  `# This code is contributed by Mohit Kumar `

## C#

 `// C# program to maximum value of  ` `// division of two numbers in an array ` `using` `System; ` `     `  `class` `GFG ` `{ ` ` `  `// Function to maximum value of  ` `// division of two numbers in an array ` `static` `int` `Divison(``int` `[]a, ``int` `n) ` `{ ` `    ``int` `maxi = ``int``.MinValue,  ` `        ``mini = ``int``.MaxValue; ` `     `  `    ``// Traverse through the array ` `    ``for` `(``int` `i = 0; i < n; i++) ` `    ``{ ` `        ``maxi = Math.Max(a[i], maxi); ` `        ``mini = Math.Min(a[i], mini); ` `    ``} ` `     `  `    ``// Return the required answer ` `    ``return` `maxi / mini; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main (String[] args) ` `{ ` `    ``int` `[]a = {3, 7, 9, 3, 11}; ` `     `  `    ``int` `n = a.Length; ` `     `  `    ``Console.WriteLine(Divison(a, n)); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

Output :

```3
```

Time complexity : O(N)
Auxiliary space : O(1)

Note: Above solution works only for positive integers

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