# Given N and Standard Deviation, find N elements

Given N and Standard deviation find the N elements.

Mean is average of element.
Mean of arr[0..n-1] = Σ(arr[i]) / n
where 0 <= i < n

Variance is sum of squared differences from the mean divided by number of elements.

Variance = Σ(arr[i] – mean)2 / n

Standard Deviation is square root of variance
Standard Deviation = Σ(variance)

Please refer Mean, Variance and Standard Deviation for details.

Examples:

```Input: 6 0
Output: 0 0 0 0 0 0
Explanation:
The standard deviation of 0, 0, 0, 0, 0, 0 is 0.
Also the standard deviation of 4, 4, 4, 4, 4, 4
is 0, we print any of the possible N elements.

Input: 3 3
Output: 0 -3.67423 3.67423
Explanation:
On calculating SD of these N elements,
we get standard deviation to be 3.

```

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

Approach:
If we look at the formula, we have two unknown terms one is xi and the other is mean. The main motive is to make the mean 0 so that we can get the formula for X elements. There will be two cases, one for even and one for odd.

When N is even:
To make mean of N elements 0, best way is to express N elements as -X +X -X +X …. Formula will be sqrt(summation of (x^2)/n), x2+x^2+x^2+………N terms, so formula turns out to be sqrt (N*(x^2)/N). N cancel out each other, so sqrt (x^2) turns out to be SD. So, we get the N elements as -SD +SD -SD +SD…… to get the mean 0. We need to print -SD +SD -SD +SD……

When N is odd:
The mean of N elements will be 0. So, one element will be 0 and other N-1 elements will be -X +X -X …. Formula will be sqrt(summation of (x^2)/n), x2+x^2+x^2+………N-1 terms, so formula turns out to be sqrt((N-1)*(x^2)/N), so
X= SD * sqrt(n/(n-1)). The n elements are 0 -X +X -X +X …

When SD is 0 then all elements will be same, so we can print 0 for it.

Below is the implementation of the above approach:

## C++

 `// CPP program to find n elements ` `#include ` `using` `namespace` `std; ` ` `  `// function to print series of n elements ` `void` `series(``int` `n, ``int` `d) ` `{ ` ` `  `    ``// if S.D. is 0 then print all ` `    ``// elements as 0. ` `    ``if` `(d == 0) { ` ` `  `        ``// print n 0's ` `        ``for` `(``int` `i = 0; i < n; i++) ` `            ``cout << ``"0 "``; ` ` `  `        ``cout << endl; ` `        ``return``; ` `    ``} ` ` `  `    ``// if S.D. is even ` `    ``if` `(n % 2 == 0) { ` ` `  `        ``// print -SD, +SD, -SD, +SD ` `        ``for` `(``int` `i = 1; i <= n; i++) { ` `            ``cout << ``pow``(-1, i) * d << ``" "``; ` `        ``} ` `        ``cout << endl; ` `    ``} ` `    ``else` `// if odd ` `    ``{ ` `        ``// convert n to a float integer ` `        ``float` `m = n; ` `        ``float` `r = (m / (m - 1)); ` `        ``float` `g = (``float``)(d * (``float``)sqrtf(r)); ` ` `  `        ``// print one element to be 0 ` `        ``cout << ``"0 "``; ` ` `  `        ``// print (n-1) elements as xi derived ` `        ``// from the formula ` `        ``for` `(``int` `i = 1; i < n; i++) { ` `            ``cout << ``pow``(-1, i) * g << ``" "``; ` `        ``} ` `        ``cout << endl; ` `    ``} ` `} ` ` `  `// driver program to test the above function ` `int` `main() ` `{ ` `    ``int` `n = 3, d = 3; ` `    ``series(n, d); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find n elements ` `import` `java.util.*; ` `import` `java.lang.*; ` ` `  `public` `class` `GfG { ` ` `  `    ``// function to print series of n elements ` `    ``public` `static` `void` `series(``int` `n, ``int` `d) ` `    ``{ ` ` `  `        ``// if S.D. is 0 then print all ` `        ``// elements as 0. ` `        ``if` `(d == ``0``) { ` ` `  `            ``// print n 0's ` `            ``for` `(``int` `i = ``0``; i < n; i++) ` `                ``System.out.print(``"0 "``); ` `            ``System.out.println(); ` `            ``return``; ` `        ``} ` ` `  `        ``// if S.D. is even ` `        ``if` `(n % ``2` `== ``0``) { ` ` `  `            ``// print -SD, +SD, -SD, +SD ` `            ``for` `(``int` `i = ``1``; i <= n; i++) { ` `                ``System.out.print(Math.pow(-``1``, i) * d + ``" "``); ` `            ``} ` `            ``System.out.println(); ` `        ``} ` `        ``else` `// if odd ` `        ``{ ` `            ``// convert n to a float integer ` `            ``float` `m = n; ` `            ``float` `r = (m / (m - ``1``)); ` `            ``float` `g = (``float``)(d * (``float``)(Math.sqrt(r))); ` ` `  `            ``// print one element to be 0 ` `            ``System.out.print(``"0 "``); ` ` `  `            ``// print (n-1) elements as xi ` `            ``// derived from the formula ` `            ``for` `(``int` `i = ``1``; i < n; i++) { ` `                ``System.out.print(Math.pow(-``1``, i) * g + ``" "``); ` `            ``} ` `            ``System.out.println(); ` `        ``} ` `    ``} ` ` `  `    ``// driver function ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `n = ``3``, d = ``3``; ` `        ``series(n, d); ` `    ``} ` `} ` ` `  `/* This code is contributed by Sagar Shukla */`

## Python3

 `# Python program to find n elements ` `import` `math ` ` `  `# function to print series of n elements ` `def` `series( n, d): ` ` `  `    ``# if S.D. is 0 then print all ` `    ``# elements as 0. ` `    ``if` `d ``=``=` `0``: ` `     `  `        ``# print n 0's ` `        ``for` `i ``in` `range``(n): ` `            ``print``(``"0"``, end ``=` `' '``) ` `        ``return` `1` `         `  `    ``# if S.D. is even ` `    ``if` `n ``%` `2` `=``=` `0``: ` `     `  `        ``# print -SD, +SD, -SD, +SD ` `        ``i ``=` `1` `        ``while` `i <``=` `n: ` `            ``print``(``"%.5f"``%``((math.``pow``(``-``1``, i) ``*` `d)), ` `                  ``end ``=``' '``) ` `            ``i ``+``=` `1` `    ``else``: ` `        ``# if odd ` `        ``# convert n to a float integer ` `        ``m ``=` `n ` `        ``r ``=` `(m ``/` `(m ``-` `1``)) ` `        ``g ``=` `(``float``)(d ``*` `float``(math.sqrt(r))) ` `         `  `        ``# print one element to be 0 ` `        ``print``(``"0 "``, end ``=` `' '``) ` `         `  `        ``# print (n-1) elements as xi derived ` `        ``# from the formula ` `        ``i ``=` `1` `        ``while` `i < n: ` `            ``print``(``"%.5f"``%``(math.``pow``(``-``1``, i) ``*` `g), ` `                  ``end ``=` `' '``) ` `            ``i ``=` `i ``+` `1` `    ``print``(``"\n"``) ` ` `  `# driver code to test the above function ` `n ``=` `3` `d ``=` `3` `series(n, d) ` ` `  `# This code is contributed by "Sharad_Bhardwaj". `

## C#

 `// C# program to find n elements ` `using` `System; ` ` `  `public` `class` `GfG { ` ` `  `    ``// function to print series of n ` `    ``// elements ` `    ``public` `static` `void` `series(``int` `n, ``int` `d) ` `    ``{ ` ` `  `        ``// if S.D. is 0 then print all ` `        ``// elements as 0. ` `        ``if` `(d == 0) { ` ` `  `            ``// print n 0's ` `            ``for` `(``int` `i = 0; i < n; i++) ` `                ``Console.Write(``"0"``); ` `                 `  `            ``Console.WriteLine(); ` `             `  `            ``return``; ` `        ``} ` ` `  `        ``// if S.D. is even ` `        ``if` `(n % 2 == 0) { ` ` `  `            ``// print -SD, +SD, -SD, +SD ` `            ``for` `(``int` `i = 1; i <= n; i++) { ` `                ``Console.Write(Math.Pow(-1, i) ` `                                   ``* d + ``" "``); ` `            ``} ` `             `  `            ``Console.WriteLine(); ` `        ``} ` `        ``else` `// if odd ` `        ``{ ` `             `  `            ``// convert n to a float integer ` `            ``float` `m = n; ` `            ``float` `r = (m / (m - 1)); ` `            ``float` `g = (``float``)(d *  ` `                       ``(``float``)(Math.Sqrt(r))); ` ` `  `            ``// print one element to be 0 ` `            ``Console.Write(``"0 "``); ` ` `  `            ``// print (n-1) elements as xi ` `            ``// derived from the formula ` `            ``for` `(``int` `i = 1; i < n; i++) { ` `                ``Console.Write(Math.Pow(-1, i) ` `                                   ``* g + ``" "``); ` `            ``} ` `             `  `            ``Console.WriteLine(); ` `        ``} ` `    ``} ` ` `  `    ``// driver function ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `n = 3, d = 3; ` `         `  `        ``series(n, d); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

## PHP

 ` `

Output:

```0 -3.67423 3.67423
```

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