# Array Index with same count of even or odd numbers on both sides

Given an array of N integers. We need to find an index such that Frequency of Even numbers on its left side is equal to the frequency of even numbers on its right sides Or frequency of odd numbers on its left side is equal to the frequency of Odd numbers on its right sides. If No such index exist in an array print -1 Else print required index. Note-(If more than one index exist then return index that comes first)

Examples:

```Input : arr[] = {4, 3, 2, 1, 2, 4}
Output : index = 2
Explanation: At index 2, there is one
odd number on its left and one odd on
its right.

Input :arr[] = { 1, 2, 4, 5, 8, 3, 12}
Output : index = 3
```

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

Method 1 : (Simple Approach)
Run two loops. For every element, count evens and odds on its left and right sides.

## C++

 `// CPP program to find an index which has ` `// same number of even elements on left and ` `// right, Or same number of odd elements on ` `// left and right. ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find index ` `int` `findIndex(``int` `arr[], ``int` `n) { ` ` `  `  ``for` `(``int` `i = 0; i < n; i++) { ` `    ``int` `odd_left = 0, even_left = 0; ` `    ``int` `odd_right = 0, even_right = 0; ` ` `  `    ``// To count Even and Odd numbers of left side ` `    ``for` `(``int` `j = 0; j < i; j++) { ` `      ``if` `(arr[j] % 2 == 0) ` `        ``even_left++; ` `      ``else` `        ``odd_left++; ` `    ``} ` ` `  `    ``// To count Even and Odd numbers of right side ` `    ``for` `(``int` `k = n - 1; k > i; k--) { ` `      ``if` `(arr[k] % 2 == 0) ` `        ``even_right++; ` `      ``else` `        ``odd_right++; ` `    ``} ` ` `  `    ``// To check Even Or Odd of Both sides are equal or not ` `    ``if` `(even_right == even_left || odd_right == odd_left) ` `      ``return` `i; ` `  ``} ` ` `  `  ``return` `-1; ` `} ` ` `  `// Driver's Function ` `int` `main() { ` `  ``int` `arr[] = {4, 3, 2, 1, 2}; ` `  ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` `  ``int` `index = findIndex(arr, n); ` ` `  `  ``((index == -1) ? cout << ``"-1"` `:  ` `          ``cout << ``"index = "` `<< index); ` `  ``return` `0; ` `} `

## Java

 `// Java program to find ` `// an index which has ` `// same number of even ` `// elements on left and ` `// right, Or same number ` `// of odd elements on ` `// left and right. ` ` `  `class` `GFG{ ` ` `  `// Function to find index ` `static` `int` `findIndex(``int` `arr[], ``int` `n) { ` ` `  `for` `(``int` `i = ``0``; i < n; i++) { ` ` `  `    ``int` `odd_left = ``0``, even_left = ``0``; ` `    ``int` `odd_right = ``0``, even_right = ``0``; ` ` `  `    ``// To count Even and Odd ` `        ``// numbers of left side ` `    ``for` `(``int` `j = ``0``; j < i; j++) { ` `    ``if` `(arr[j] % ``2` `== ``0``) ` `        ``even_left++; ` `    ``else` `        ``odd_left++; ` `    ``} ` ` `  `    ``// To count Even and Odd ` `        ``// numbers of right side ` `    ``for` `(``int` `k = n - ``1``; k > i; k--) { ` `    ``if` `(arr[k] % ``2` `== ``0``) ` `        ``even_right++; ` `    ``else` `        ``odd_right++; ` `    ``} ` ` `  `    ``// To check Even Or Odd of Both ` `        ``// sides are equal or not ` `    ``if` `(even_right == even_left || odd_right == odd_left) ` `    ``return` `i; ` `} ` ` `  `return` `-``1``; ` ` `  `} ` ` `  `// Driver's Function ` `public` `static` `void` `main(String[] args) { ` ` `  `int` `arr[] = {``4``, ``3``, ``2``, ``1``, ``2``}; ` `int` `n = arr.length; ` `int` `index = findIndex(arr, n); ` ` `  `if` `(index == -``1``)  ` `    ``System.out.println(``"-1"``);  ` `else``{ ` `    ``System.out.print(``"index = "``); ` `    ``System.out.print(index); ` `} ` `} ` `} ` ` `  `// This code is contributed by ` `// Smitha Dinesh Semwal `

## Python3

 `'''Python program to find ` `   ``an index which has ` `   ``same number of even ` `   ``elements on left and ` `   ``right, Or same number ` `   ``of odd elements on ` `   ``left and right.'''` `  `  ` `  `  `  `# Function to find index ` `def` `findIndex(arr,n): ` ` `  `    ``for` `i ``in` `range``(n): ` `  `  `        ``odd_left ``=` `0` `        ``even_left ``=` `0` `        ``odd_right ``=` `0` `        ``even_right ``=` `0` `  `  `        ``# To count Even and Odd ` `        ``# numbers of left side ` `        ``for` `j ``in` `range``(i): ` `            ``if` `(arr[j] ``%` `2` `=``=` `0``): ` `                ``even_left``=``even_left``+``1` `            ``else``: ` `                ``odd_left``=``odd_left``+``1` `     `  `  `  `        ``# To count Even and Odd ` `        ``# numbers of right side ` `        ``for` `k ``in` `range``(n ``-` `1``, i, ``-``1``): ` `            ``if` `(arr[k] ``%` `2` `=``=` `0``): ` `                ``even_right``=``even_right``+``1` `            ``else``: ` `                ``odd_right``=``odd_right``+``1` `     `  `  `  `        ``# To check Even Or Odd of Both ` `        ``# sides are equal or not ` `        ``if` `(even_right ``=``=` `even_left ``and` `odd_right ``=``=` `odd_left): ` `            ``return` `i ` `  `  `    ``return` `-``1` `  `  ` `  `  `  `# Driver's Function ` ` `  `arr ``=` `[``4``, ``3``, ``2``, ``1``, ``2``] ` `n ``=` `len``(arr) ` `index ``=` `findIndex(arr, n) ` `  `  `if` `(index ``=``=` `-``1``): ` `    ``print``(``"-1"``)  ` `else``: ` `    ``print``(``"index = "``, index) ` ` `  ` `  ` `  `# This code is contributed ` `# by Anant Agarwal. `

## C#

 `// C# program to find an index which has ` `// same number of even elements on left  ` `// and right, Or same number of odd  ` `// elements on left and right. ` `using` `System; ` ` `  `class` `GFG{ ` ` `  `    ``// Function to find index ` `    ``static` `int` `findIndex(``int` `[]arr, ``int` `n) { ` `     `  `        ``for` `(``int` `i = 0; i < n; i++) { ` `         `  `            ``int` `odd_left = 0, even_left = 0; ` `            ``int` `odd_right = 0, even_right = 0; ` `         `  `            ``// To count Even and Odd ` `            ``// numbers of left side ` `            ``for` `(``int` `j = 0; j < i; j++) { ` `                ``if` `(arr[j] % 2 == 0) ` `                    ``even_left++; ` `                ``else` `                    ``odd_left++; ` `            ``} ` `         `  `            ``// To count Even and Odd ` `            ``// numbers of right side ` `            ``for` `(``int` `k = n - 1; k > i; k--) { ` `                ``if` `(arr[k] % 2 == 0) ` `                    ``even_right++; ` `                ``else` `                    ``odd_right++; ` `            ``} ` `         `  `            ``// To check Even Or Odd of Both ` `            ``// sides are equal or not ` `            ``if` `(even_right == even_left || ` `                        ``odd_right == odd_left) ` `                ``return` `i; ` `        ``} ` `         `  `        ``return` `-1; ` `    ``} ` `     `  `    ``// Driver's Function ` `    ``public` `static` `void` `Main() { ` `     `  `        ``int` `[]arr = {4, 3, 2, 1, 2}; ` `        ``int` `n = arr.Length; ` `         `  `        ``int` `index = findIndex(arr, n); ` `         `  `        ``if` `(index == -1)  ` `            ``Console.Write(``"-1"``);  ` `        ``else``{ ` `            ``Console.Write(``"index = "``); ` `            ``Console.Write(index); ` `        ``} ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

## PHP

 ` ``\$i``; ``\$k``--) ` `            ``{ ` `                ``if` `(``\$arr``[``\$k``] % 2 == 0) ` `                    ``\$even_right``++; ` `                ``else` `                    ``\$odd_right``++; ` `            ``} ` ` `  `        ``// To check Even Or Odd of ` `        ``// Both sides are equal or not ` `        ``if` `(``\$even_right` `== ``\$even_left` `||  ` `                ``\$odd_right` `== ``\$odd_left``) ` `        ``return` `\$i``; ` `    ``} ` ` `  `    ``return` `-1; ` `} ` ` `  `// Drivers Code ` `{ ` `    ``\$arr` `= ``array``(4, 3, 2, 1, 2); ` `    ``\$n` `= sizeof(``\$arr``) / sizeof(``\$arr``); ` `    ``\$index` `= findIndex(``\$arr``, ``\$n``); ` `     `  `    ``if``(``\$index` `== -1)  ` `    ``echo` `"-1"``; ` `    ``else` `    ``echo` `(``"index = \$index"` `); ` `    ``return` `0; ` `} ` ` `  `// This code is contributed by nitin mittal. ` `?> `

Output:

```index = 2
```

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

Method 2:(Efficient solution)
1- Create two vectors of pair types i.e v_left and v_right
2- v_left[i] stores the frequency of odd and even numbers of its left sides
3- v_right[i] stores the frequency of odd and even numbers of its right sides
4- Now check (v_left[i].first == v_right[i].first || v_left[i].second == v_right[i].second)
if True return i
5- At last if no such index exist return -1

## C++

 `// CPP program to find an index which has ` `// same number of even elements on left and ` `// right, Or same number of odd elements on ` `// left and right. ` `#include ` `#include ` `using` `namespace` `std; ` ` `  `// Function to Find index ` `int` `Find_Index(``int` `n, ``int` `arr[]) { ` ` `  `  ``int` `odd = 0, even = 0; ` ` `  `  ``// Create two vectors of pair type ` `  ``vector> v_left, v_right; ` ` `  `  ``v_left.push_back(make_pair(odd, even)); ` `  ``for` `(``int` `i = 0; i < n - 1; i++) { ` `    ``if` `(arr[i] % 2 == 0) ` `      ``even++; ` `    ``else` `      ``odd++; ` ` `  `    ``v_left.push_back(make_pair(odd, even)); ` `  ``} ` ` `  `  ``odd = 0, even = 0; ` `  ``v_right.push_back(make_pair(odd, even)); ` `  ``for` `(``int` `i = n - 1; i > 0; i--) { ` `    ``if` `(arr[i] % 2 == 0) ` `      ``even++; ` `    ``else` `      ``odd++; ` ` `  `    ``v_right.push_back(make_pair(odd, even)); ` `  ``} ` ` `  `  ``reverse(v_right.begin(), v_right.end()); ` ` `  `  ``for` `(``int` `i = 0; i < v_left.size(); i++) { ` ` `  `    ``// To check even or odd of Both sides are  ` `    ``// equal or not ` `    ``if` `(v_left[i].first == v_right[i].first || ` `        ``v_left[i].second == v_right[i].second) ` `      ``return` `i; ` `  ``} ` `  ``return` `-1; ` `} ` ` `  `// Driver's Function ` `int` `main() { ` `  ``int` `arr[] = {4, 3, 2, 1, 2}; ` `  ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` `  ``int` `index = Find_Index(n, arr); ` `  ``((index == -1) ? cout << ``"-1"` `: cout << ``"index = "` `<< index); ` `  ``return` `0; ` `} `

## Java

 `// Java program to find an index which has ` `// same number of even elements on left and ` `// right, Or same number of odd elements on ` `// left and right. ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` ` `  `    ``public` `static` `class` `pair ` `    ``{ ` ` `  `        ``int` `first, second; ` ` `  `        ``pair(``int` `f, ``int` `s)  ` `        ``{ ` `            ``first = f; ` `            ``second = s; ` `        ``} ` `    ``}; ` ` `  `    ``// Function to Find index ` `    ``static` `int` `Find_Index(``int` `n, ``int` `arr[])  ` `    ``{ ` ` `  `        ``int` `odd = ``0``, even = ``0``; ` ` `  `        ``// Create two vectors of pair type ` `        ``Vector v_left = ``new` `Vector<>();; ` `        ``Vector v_right = ``new` `Vector<>(); ` ` `  `        ``v_left.add(``new` `pair(odd, even)); ` `        ``for` `(``int` `i = ``0``; i < n - ``1``; i++)  ` `        ``{ ` `            ``if` `(arr[i] % ``2` `== ``0``)  ` `            ``{ ` `                ``even++; ` `            ``}  ` `            ``else` `            ``{ ` `                ``odd++; ` `            ``} ` ` `  `            ``v_left.add(``new` `pair(odd, even)); ` `        ``} ` ` `  `        ``odd = ``0``; ` `        ``even = ``0``; ` `        ``v_right.add(``new` `pair(odd, even)); ` `        ``for` `(``int` `i = n - ``1``; i > ``0``; i--) ` `        ``{ ` `            ``if` `(arr[i] % ``2` `== ``0``) ` `            ``{ ` `                ``even++; ` `            ``}  ` `            ``else` `            ``{ ` `                ``odd++; ` `            ``} ` ` `  `            ``v_right.add(``new` `pair(odd, even)); ` `        ``} ` `        ``Collections.reverse(v_right); ` ` `  `        ``for` `(``int` `i = ``0``; i < v_left.size(); i++) ` `        ``{ ` ` `  `            ``// To check even or odd of Both sides are  ` `            ``// equal or not ` `            ``if` `(v_left.get(i).first == v_right.get(i).first ` `                    ``|| v_left.get(i).second == v_right.get(i).second) ` `            ``{ ` `                ``return` `i; ` `            ``} ` `        ``} ` `        ``return` `-``1``; ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String[] args)  ` `    ``{ ` `        ``int` `arr[] = {``4``, ``3``, ``2``, ``1``, ``2``}; ` `        ``int` `n = arr.length; ` `        ``int` `index = Find_Index(n, arr); ` `        ``if` `(index == -``1``) ` `        ``{ ` `            ``System.out.println(``"-1"``); ` `        ``} ` `        ``else` `        ``{ ` `            ``System.out.println(``"index = "` `+ index); ` `        ``} ` `    ``} ` `} ` ` `  `/* This code contributed by PrinciRaj1992 */`

## C#

 `// C# program to find an index which has ` `// same number of even elements on left and ` `// right, Or same number of odd elements on ` `// left and right. ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG ` `{ ` `    ``public` `class` `pair ` `    ``{ ` `        ``public` `int` `first, second; ` ` `  `        ``public` `pair(``int` `f, ``int` `s)  ` `        ``{ ` `            ``first = f; ` `            ``second = s; ` `        ``} ` `    ``}; ` ` `  `    ``// Function to Find index ` `    ``static` `int` `Find_Index(``int` `n, ``int` `[]arr)  ` `    ``{ ` `        ``int` `odd = 0, even = 0; ` ` `  `        ``// Create two vectors of pair type ` `        ``List v_left = ``new` `List();; ` `        ``List v_right = ``new` `List(); ` ` `  `        ``v_left.Add(``new` `pair(odd, even)); ` `        ``for` `(``int` `i = 0; i < n - 1; i++)  ` `        ``{ ` `            ``if` `(arr[i] % 2 == 0)  ` `            ``{ ` `                ``even++; ` `            ``}  ` `            ``else` `            ``{ ` `                ``odd++; ` `            ``} ` ` `  `            ``v_left.Add(``new` `pair(odd, even)); ` `        ``} ` ` `  `        ``odd = 0; ` `        ``even = 0; ` `        ``v_right.Add(``new` `pair(odd, even)); ` `        ``for` `(``int` `i = n - 1; i > 0; i--) ` `        ``{ ` `            ``if` `(arr[i] % 2 == 0) ` `            ``{ ` `                ``even++; ` `            ``}  ` `            ``else` `            ``{ ` `                ``odd++; ` `            ``} ` ` `  `            ``v_right.Add(``new` `pair(odd, even)); ` `        ``} ` `        ``v_right.Reverse(); ` ` `  `        ``for` `(``int` `i = 0; i < v_left.Count; i++) ` `        ``{ ` ` `  `            ``// To check even or odd of Both sides are  ` `            ``// equal or not ` `            ``if` `(v_left[i].first == v_right[i].first ||  ` `                ``v_left[i].second == v_right[i].second) ` `            ``{ ` `                ``return` `i; ` `            ``} ` `        ``} ` `        ``return` `-1; ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main(String[] args)  ` `    ``{ ` `        ``int` `[]arr = {4, 3, 2, 1, 2}; ` `        ``int` `n = arr.Length; ` `        ``int` `index = Find_Index(n, arr); ` `        ``if` `(index == -1) ` `        ``{ ` `            ``Console.WriteLine(``"-1"``); ` `        ``} ` `        ``else` `        ``{ ` `            ``Console.WriteLine(``"index = "` `+ index); ` `        ``} ` `    ``} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```index = 2
```

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

Further optimization : We can optimize the space used in the program. Instead of making vectors of pairs, we can make vectors of integers. We can use the fact that number of odd elements is equal total elements minus total number of even elements. Similarly number of even elements is equal total elements minus total number of odd elements.

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