# Find the element whose multiplication with -1 makes array sum 0

Given an array of N integers. The task is to find the smallest index of an element such that when multiplied by -1 the sum of whole array becomes 0. If there is no such index return -1.

Examples:

```Input : arr[] = {1, 3, -5, 3, 4}
Output : 2

Input : arr[] = {5, 3, 6, -7, -4}
Output : -1
```

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

Naive Approach :
The simple solution will be to take each element, multiply it by -1 and check if the new sum is 0. This algorithm works in O(N2).

Efficient Approach :
If we take S as our initial sum of the array and we multiply current element Ai by -1 then the new sum will become S – 2*Ai and this should be equal to 0. So when for the first time S = 2*Ai then the current index is our required and if no element satisfies the condition then our answer will be -1. The time complexity of this algorithm is O(N).

Below is the implementation of the above idea :

 `// C++ program to find minimum index ` `// such that sum becomes 0 when the ` `// element is multiplied by -1 ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to find minimum index ` `// such that sum becomes 0 when the ` `// element is multiplied by -1 ` `int` `minIndex(``int` `arr[], ``int` `n) ` `{ ` `    ``// Find array sum ` `    ``int` `sum = 0; ` `    ``for` `(``int` `i = 0; i < n; i++)  ` `        ``sum += arr[i]; ` ` `  `    ``// Find element with value equal to sum/2 ` `    ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `        ``// when sum is equal to 2*element ` `        ``// then this is our required element ` `        ``if` `(2 * arr[i] == sum)  ` `            ``return` `(i + 1); ` `    ``} ` ` `  `    ``return` `-1; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 3, -5, 3, 4 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` `    ``cout << minIndex(arr, n) << endl; ` `    ``return` `0; ` `} `

 `// Java program to find minimum index ` `// such that sum becomes 0 when the ` `// element is multiplied by -1 ` ` `  `import` `java.io.*; ` ` `  `class` `GFG { ` `    `  `// Function to find minimum index ` `// such that sum becomes 0 when the ` `// element is multiplied by -1 ` ` ``static` `int` `minIndex(``int` `arr[], ``int` `n) ` `{ ` `    ``// Find array sum ` `    ``int` `sum = ``0``; ` `    ``for` `(``int` `i = ``0``; i < n; i++)  ` `        ``sum += arr[i]; ` ` `  `    ``// Find element with value equal to sum/2 ` `    ``for` `(``int` `i = ``0``; i < n; i++) { ` ` `  `        ``// when sum is equal to 2*element ` `        ``// then this is our required element ` `        ``if` `(``2` `* arr[i] == sum)  ` `            ``return` `(i + ``1``); ` `    ``} ` ` `  `    ``return` `-``1``; ` `} ` ` `  `// Driver code ` ` `  ` `  `    ``public` `static` `void` `main (String[] args) { ` `            ``int` `[]arr = { ``1``, ``3``, -``5``, ``3``, ``4` `}; ` `    ``int` `n =arr.length; ` `    ``System.out.print( minIndex(arr, n)); ` `    ``} ` `} ` ` `  `// This code is contributed by anuj_67.. `

 `# Python 3 program to find minimum index ` `# such that sum becomes 0 when the ` `# element is multiplied by -1 ` ` `  `# Function to find minimum index ` `# such that sum becomes 0 when the ` `# element is multiplied by -1 ` `def` `minIndex(arr, n): ` ` `  `    ``# Find array sum ` `    ``sum` `=` `0` `    ``for` `i ``in` `range` `(``0``, n):  ` `        ``sum` `+``=` `arr[i] ` ` `  `    ``# Find element with value  ` `    ``# equal to sum/2 ` `    ``for` `i ``in` `range``(``0``, n): ` ` `  `        ``# when sum is equal to 2*element ` `        ``# then this is our required element ` `        ``if` `(``2` `*` `arr[i] ``=``=` `sum``):  ` `            ``return` `(i ``+` `1``) ` ` `  `    ``return` `-``1` ` `  `# Driver code ` `arr ``=` `[ ``1``, ``3``, ``-``5``, ``3``, ``4` `]; ` `n ``=` `len``(arr); ` `print``(minIndex(arr, n)) ` ` `  `# This code is contributed  ` `# by Akanksha Rai `

 `// C# program to find minimum index ` `// such that sum becomes 0 when the ` `// element is multiplied by -1 ` `  `  `using` `System; ` `  `  `class` `GFG { ` `     `  `// Function to find minimum index ` `// such that sum becomes 0 when the ` `// element is multiplied by -1 ` ` ``static` `int` `minIndex(``int``[] arr, ``int` `n) ` `{ ` `    ``// Find array sum ` `    ``int` `sum = 0; ` `    ``for` `(``int` `i = 0; i < n; i++)  ` `        ``sum += arr[i]; ` `  `  `    ``// Find element with value equal to sum/2 ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `  `  `        ``// when sum is equal to 2*element ` `        ``// then this is our required element ` `        ``if` `(2 * arr[i] == sum)  ` `            ``return` `(i + 1); ` `    ``} ` `  `  `    ``return` `-1; ` `} ` `  `  `// Driver code ` `  `  `  `  `    ``public` `static` `void` `Main () { ` `            ``int``[] arr = { 1, 3, -5, 3, 4 }; ` `    ``int` `n =arr.Length; ` `    ``Console.Write( minIndex(arr, n)); ` `    ``} ` `} `

 ` `

Output:
```2
```

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