# Program for average of an array without running into overflow

Given an array arr[] of size N, the task is to find the average of the array elements without running into overflow.

Examples:

Input: arr[] = { INT_MAX, INT_MAX }
Output:
Average by Standard method: -1.0000000000
Average by Efficient method: 2147483647.0000000000
Explanation:
The average of the two numbers by standard method is (sum / 2).
Since the sum of the two numbers exceed INT_MAX, the obtained output by standard method is incorrect.

Input: arr[] = { INT_MAX, 1, 2 }
Output:
Average by Standard method: -715827882.0000000000
Average by Efficient method: 715827883.3333332539

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

• The average of N array elements can be obtained by dividing the sum of the array elements by N. But, calculating sum of the array arr[] may lead to integer overflow, if the array contains large integers.
• Therefore, average of the array can be calculated efficiently by the following steps:
• Traverse the array, using a variable i over the range of indices [0, N – 1]
• Update avg = (avg+ (arr[i] – avg)/(i+1))

Follow the steps below to solve the problem:

• Initialize two variables, say sum as 0 and avg as 0, to store the sum and average of the array elements respectively.
• Traverse the array arr[], update avg = avg + (arr[i] – avg) / (i + 1) and update sum = sum + arr[i].
• After completing the above steps, print the average by the standard method, i.e. sum / N and print the average by the efficient method, i.e. avg

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach` `#include ` `using` `namespace` `std;`   `// Function to calculate average of` `// an array using standard method` `double` `average(``int` `arr[], ``int` `N)` `{` `    ``// Stores the sum of array` `    ``int` `sum = 0;`   `    ``// Find the sum of the array` `    ``for` `(``int` `i = 0; i < N; i++)` `        ``sum += arr[i];`   `    ``// Return the average` `    ``return` `(``double``)sum / N;` `}`   `// Function to calculate average of` `// an array using efficient method` `double` `mean(``int` `arr[], ``int` `N)` `{` `    ``// Store the average of the array` `    ``double` `avg = 0;`   `    ``// Traverse the array arr[]` `    ``for` `(``int` `i = 0; i < N; i++) {`   `        ``// Update avg` `        ``avg += (arr[i] - avg) / (i + 1);` `    ``}`   `    ``// Return avg` `    ``return` `avg;` `}`   `// Driver Code` `int` `main()` `{` `    ``// Input` `    ``int` `arr[] = { INT_MAX, 1, 2 };` `    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);`   `    ``// Function call` `    ``cout << ``"Average by Standard method: "` `<< fixed` `         ``<< setprecision(10) << average(arr, N) << endl;`   `    ``cout << ``"Average by Efficient method: "` `<< fixed` `         ``<< setprecision(10) << mean(arr, N) << endl;`   `    ``return` `0;` `}`

## Java

 `// Java program for the above approach` `import` `java.util.*;` `class` `GFG{` ` `  `// Function to calculate average of` `// an array using standard method` `static` `Double average(``int` `arr[], ``int` `N)` `{` `  `  `    ``// Stores the sum of array` `    ``int` `sum = ``0``;`   `    ``// Find the sum of the array` `    ``for` `(``int` `i = ``0``; i < N; i++)` `        ``sum += arr[i];`   `    ``// Return the average` `    ``return` `Double.valueOf(sum / N);` `}`   `// Function to calculate average of` `// an array using efficient method` `static` `Double mean(``int` `arr[], ``int` `N)` `{` `  `  `    ``// Store the average of the array` `    ``Double avg = ``0.0``;`   `    ``// Traverse the array arr[]` `    ``for` `(``int` `i = ``0``; i < N; i++)` `    ``{`   `        ``// Update avg` `        ``avg += Double.valueOf((arr[i] - avg) / (i + ``1``));` `    ``}`   `    ``// Return avg` `    ``return` `avg;` `}`   `// Driver Code` `public` `static` `void` `main(String args[])` `{` `  `  `    ``// Input` `    ``int` `arr[] = {Integer.MAX_VALUE, ``1``, ``2` `};` `    ``int` `N = arr.length;` `  `  `    ``// Function call` `    ``System.out.println(``"Average by Standard method: "``+ String.format(``"%.10f"``, average(arr, N)));` `    ``System.out.println(``"Average by Efficient method: "``+ String.format(``"%.10f"``, mean(arr, N)));` `}` `}`   `// This code is contributed by ipg2016107.`

## Python3

 `# Python3 program for the above approach` `import` `sys`   `# Function to calculate average of` `# an array using standard method` `def` `average(arr, N):` `    `  `    ``# Stores the sum of array` `    ``sum` `=` `0`   `    ``# Find the sum of the array` `    ``for` `i ``in` `range``(N):` `        ``sum` `+``=` `arr[i]`   `    ``# Return the average` `    ``return` `sum` `/``/` `N ``*` `1.0` `-` `1`   `# Function to calculate average of` `# an array using efficient method` `def` `mean(arr, N):` `    `  `    ``# Store the average of the array` `    ``avg ``=` `0`   `    ``# Traverse the array arr[]` `    ``for` `i ``in` `range``(N):` `        `  `        ``# Update avg` `        ``avg ``+``=` `(arr[i] ``-` `avg) ``/` `(i ``+` `1``)`   `    ``# Return avg` `    ``return` `round``(avg, ``7``)`   `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:` `    `  `    ``# Input` `    ``arr ``=` `[``2147483647``, ``1``, ``2``]` `    ``N ``=` `len``(arr)`   `    ``# Function call` `    ``print``(``"Average by Standard method: "``,``"{:.10f}"``.``format``(` `        ``-``1.0` `*` `average(arr, N)))`   `    ``print``(``"Average by Efficient method: "``,``"{:.10f}"``.``format``(` `        ``mean(arr, N)))`   `# This code is contributed by mohit kumar 29`

## C#

 `// C# program for the above approach` `using` `System;`   `class` `GFG{`   `// Function to calculate average of` `// an array using standard method` `static` `double` `average(``int``[] arr, ``int` `N)` `{` `    `  `    ``// Stores the sum of array` `    ``int` `sum = 0;`   `    ``// Find the sum of the array` `    ``for``(``int` `i = 0; i < N; i++)` `        ``sum += arr[i];`   `    ``// Return the average` `    ``return` `(``double``)(sum / N);` `}`   `// Function to calculate average of` `// an array using efficient method` `static` `double` `mean(``int``[] arr, ``int` `N)` `{`   `    ``// Store the average of the array` `    ``double` `avg = 0.0;`   `    ``// Traverse the array arr[]` `    ``for``(``int` `i = 0; i < N; i++)` `    ``{` `        `  `        ``// Update avg` `        ``avg += ((``double``)((arr[i] - avg) / (i + 1)));` `    ``}`   `    ``// Return avg` `    ``return` `avg;` `}`   `// Driver Code` `static` `public` `void` `Main()` `{`   `    ``// Input` `    ``int``[] arr = { Int32.MaxValue, 1, 2 };` `    ``int` `N = arr.Length;`   `    ``// Function call` `    ``Console.WriteLine(``"Average by Standard method: "` `+` `         ``(average(arr, N)).ToString(``"F10"``));` `    ``Console.WriteLine(``"Average by Efficient method: "` `+ ` `         ``(mean(arr, N)).ToString(``"F10"``));` `}` `}`   `// This code is contributed by Dharanendra L V.`

## Javascript

 ``

Output:

```Average by Standard method: -715827882.0000000000
Average by Efficient method: 715827883.3333332539```

Time Complexity: O(N)
Auxiliary Space: O(1)

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