# Find n-variables from n sum equations with one missing

You are given an array a[] of n values as a, a…a[n] which are part of n-equations in n-variables where equations are as:
Eqn1 => X2 + X3 +…..+Xn = a1
Eqn2 => X1 + X3 +…..+Xn = a2
Eqni => X1 + X2 +…+Xi-1 + Xi+1..+Xn = ai
Eqnn => X1 + X2 +…..+Xn-1 = an

As you have n-equations in n-variables find the value of all variables(X1, X2…Xn).

Examples :

```Input : a[] = {4, 4, 4, 4, 4}
Output : X1 = 1
X2 = 1
X3 = 1
X4 = 1
X5 = 1

Input : a[] = {2, 5, 6, 4, 8}
Output : X1 = 4.25
X2 = 1.25
X3 = 0.25
X4 = 2.25
X5 = -1.75
```

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

Approach:
Let, X1+X2+X3+….Xn= SUM
Using value SUM we have our equations as

```SUM - X1 = a1 -----(1)
SUM - X2 = a2  -----(2)
SUM - Xi = ai  -----(i)
SUM - Xn = an -------(n)
---------------------------------------------------------------
Now, if we add all these equation we will have an equation as :
n*SUM -(X1+X2+...Xn) = a1 + a2 + ...an
n*SUM - SUM = a1 + a2 + ...an
SUM = (a1+a2+...an)/(n-1)

Calculate SUM from above equation.
putting value of SUM in (i), (ii).... we have
X1 = SUM - a1
X2 = SUM - a2
```

Solution :

```X1 = SUM - a1
X2 = SUM - a2
Xi = SUM - ai
Xn = SUM - an
```

## C++

 `// CPP program to find n-variables ` `#include ` `using` `namespace` `std; ` ` `  `// function to print n-variable values ` `void` `findVar(``int` `a[], ``int` `n) ` `{     ` `    ``// calculate value of array SUM ` `    ``float` `SUM = 0; ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``SUM += a[i]; ` ` `  `    ``// Every variable contributes n-1 ` `    ``// times to sum. So dividing by  ` `    ``// n-1 to get sum of all. ` `    ``SUM /= (n - 1); ` ` `  `    ``// print the values of n-variables ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``cout << ``"X"` `<< (i + 1)  ` `             ``<< ``" = "` `<< SUM - a[i] << endl; ` `} ` ` `  `// driver program ` `int` `main() ` `{ ` `    ``int` `a[] = { 2, 5, 6, 4, 8 }; ` `    ``int` `n = ``sizeof``(a) / ``sizeof``(a); ` `    ``findVar(a, n); ` `    ``return` `0; ` `} `

## Java

 `// Java program to  ` `// find n-variables ` `import` `java.io.*; ` ` `  `class` `GFG ` `{ ` `    ``// function to print ` `    ``// n-variable values ` `    ``static` `void` `findVar(``int` `[]a,  ` `                        ``int` `n) ` `    ``{  ` `        ``// calculate value+ ` `        ``// of array SUM ` `        ``float` `SUM = ``0``; ` `        ``for` `(``int` `i = ``0``; i < n; i++) ` `            ``SUM += a[i]; ` `     `  `        ``// Every variable contributes  ` `        ``// n-1 times to sum. So dividing  ` `        ``// by n-1 to get sum of all. ` `        ``SUM /= (n - ``1``); ` `     `  `        ``// print the values ` `        ``// of n-variables ` `        ``for` `(``int` `i = ``0``; i < n; i++) ` `            ``System.out.print(``"X"` `+ (i + ``1``) +  ` `                             ``" = "` `+ (SUM -  ` `                             ``a[i]) + ``"\n"``); ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `[]a = ``new` `int``[]{``2``, ``5``, ``6``, ``4``, ``8``}; ` `        ``int` `n = a.length; ` `        ``findVar(a, n); ` `    ``} ` `} ` ` `  `// This code is contributed by  ` `// Manish Shaw(manishshaw1) `

## Python3

 `# Python3 program to  ` `# find n-variables ` ` `  `# function to print  ` `# n-variable values ` `def` `findVar(a, n): ` `     `  `    ``# calculate value of  ` `    ``# array SUM ` `    ``SUM` `=` `0``; ` `    ``for` `i ``in` `range``(n): ` `        ``SUM` `+``=` `a[i]; ` ` `  `    ``# Every variable contributes  ` `    ``# n-1 times to sum. So   ` `    ``# dividing by n-1 to get sum  ` `    ``# of all. ` `    ``SUM` `=` `SUM` `/` `(n ``-` `1``); ` ` `  `    ``# print the values  ` `    ``# of n-variables ` `    ``for` `i ``in` `range``(n): ` `        ``print``(``"X"` `, (i ``+` `1``),  ` `              ``" = "``, ``SUM` `-` `a[i]); ` ` `  `# Driver Code ` `a ``=` `[``2``, ``5``, ``6``, ``4``, ``8``]; ` `n ``=` `len``(a); ` `findVar(a, n); ` `     `  `# This code is contributed  ` `# by mits `

## C#

 `// C# program to find n-variables ` `using` `System; ` `using` `System.Linq; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG ` `{ ` `    ``// function to print ` `    ``// n-variable values ` `    ``static` `void` `findVar(``int` `[]a,  ` `                        ``int` `n) ` `    ``{  ` `        ``// calculate value+ ` `        ``// of array SUM ` `        ``float` `SUM = 0; ` `        ``for` `(``int` `i = 0; i < n; i++) ` `            ``SUM += a[i]; ` `     `  `        ``// Every variable contributes  ` `        ``// n-1 times to sum. So dividing  ` `        ``// by n-1 to get sum of all. ` `        ``SUM /= (n - 1); ` `     `  `        ``// print the values ` `        ``// of n-variables ` `        ``for` `(``int` `i = 0; i < n; i++) ` `            ``Console.Write(``"X"` `+ (i + 1) +  ` `                   ``" = "` `+ (SUM - a[i]) + ``"\n"``); ` `    ``} ` `     `  `    ``// Driver Code ` `    ``static` `void` `Main() ` `    ``{ ` `        ``int` `[]a = { 2, 5, 6, 4, 8 }; ` `        ``int` `n = a.Length; ` `        ``findVar(a, n); ` `    ``} ` `} ` ` `  `// This code is contributed by  ` `// Manish Shaw(manishshaw1) `

## PHP

 ` `

Output :

```X1 = 4.25
X2 = 1.25
X3 = 0.25
X4 = 2.25
X5 = -1.75
```

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

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Improved By : vt_m, manishshaw1, Mithun Kumar

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