Find index of the element differing in parity with all other array elements

Given an array arr[] of size N (N > 3), the task is to find the position of the element that differs in parity (odd/even) with respect to all other array elements. 
Note: It is guaranteed that there will always be a number that differs in parity from all other elements.

Examples:

Input: arr[] = {2, 4, 7, 8, 10}
Output: 2
Explanation: The only odd element in the array is 7 (= arr[2]). Therefore, required output is 2.

Input: arr[] = {2, 1, 1}
Output: 0

Naive Approach: The simplest approach to solve this problem is to store all even and odd numbers with their indices in a Multimap and print the index of the element present in the Map having size 1. Follow the steps below to solve the problem:

1. Initialize two Multimap, for even and odd numbers.
2. Traverse the array and store array elements in their respective Multimaps along with their indices.
3. Now find the Multimap with size equal to 1. Print the index of the array element stored in that Multimap.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to print the array
// element which differs in parity
// with the remaining array elements
int OddOneOut(int arr[], int N)
{

    // Multimaps to store even
    // and odd numbers along
    // with their indices
    multimap<int, int> e, o;

    // Traverse the array
    for (int i = 0; i < N; i++) {

        // If array element is even
        if (arr[i] % 2 == 0) {
            e.insert({ arr[i], i });
        }

        // Otherwise
        else {
            o.insert({ arr[i], i });
        }
    }

    // If only one even element
    // is present in the array
    if (e.size() == 1) {
        cout << e.begin()->second;
    }

    // If only one odd element
    // is present in the array
    else {
        cout << o.begin()->second;
    }
}

// Driver Code
int main()
{
    // Given array
    int arr[] = { 2, 4, 7, 8, 10 };

    // Size of the array
    int N = sizeof(arr) / sizeof(arr[0]);

    OddOneOut(arr, N);

    return 0;
}

Java

// Java program for the above approach
import java.util.*;
class GFG {

  // Function to print the array
  // element which differs in parity
  // with the remaining array elements
  static void OddOneOut(int[] arr, int N)
  {

    // Multimaps to store even
    // and odd numbers along
    // with their indices
    HashMap<Integer, Integer> e
      = new LinkedHashMap<Integer, Integer>();
    HashMap<Integer, Integer> o
      = new LinkedHashMap<Integer, Integer>();

    // Traverse the array
    for (int i = 0; i < N; i++) {

      // If array element is even
      if (arr[i] % 2 == 0) {
        e.put(arr[i], i);
      }

      // Otherwise
      else {
        o.put(arr[i], i);
        ;
      }
    }

    // If only one even element
    // is present in the array
    if (e.size() == 1) {
      Map.Entry<Integer, Integer> entry
        = e.entrySet().iterator().next();
      System.out.print(entry.getValue());
    }

    // If only one odd element
    // is present in the array
    else {
      Map.Entry<Integer, Integer> entry
        = o.entrySet().iterator().next();
      System.out.print(entry.getValue());
    }
  }

  // Driver Code
  public static void main(String[] args)
  {

    // Given array
    int[] arr = { 2, 4, 7, 8, 10 };

    // Size of the array
    int N = arr.length;

    OddOneOut(arr, N);
  }
}

// This code is contributed by phasing17.

Python3

# Python3 program for the above approach

# Function to print the array
# element which differs in parity
# with the remaining array elements
def OddOneOut(arr, N) :

    # Multimaps to store even
    # and odd numbers along
    # with their indices
    e, o = {}, {}

    # Traverse the array
    for i in range(N) :

        # If array element is even
        if (arr[i] % 2 == 0) :
            e[arr[i]] = i

        # Otherwise
        else :
            o[arr[i]] = i

    # If only one even element
    # is present in the array
    if (len(e) == 1) :
        print(list(e.values())[0] )

    # If only one odd element
    # is present in the array
    else :
        print(list(o.values())[0] )

# Given array
arr = [ 2, 4, 7, 8, 10 ]

# Size of the array
N = len(arr)

OddOneOut(arr, N)

# This code is contributed by divyesh072019.

C#

// C# program for the above approach
using System;
using System.Collections.Generic;
using System.Linq;
class GFG {

  // Function to print the array
  // element which differs in parity
  // with the remaining array elements
  static void OddOneOut(int[] arr, int N)
  {

    // Multimaps to store even
    // and odd numbers along
    // with their indices
    Dictionary<int, int> e = new Dictionary<int, int>();
    Dictionary<int, int> o = new Dictionary<int, int>();

    // Traverse the array
    for (int i = 0; i < N; i++) {

      // If array element is even
      if (arr[i] % 2 == 0) {
        e[arr[i]] = i;
      }

      // Otherwise
      else {
        o[arr[i]] = i;
      }
    }

    // If only one even element
    // is present in the array
    if (e.Count == 1) {
      Console.Write(e.First().Value);
    }

    // If only one odd element
    // is present in the array
    else {
      Console.Write(o.First().Value);
    }
  }

  // Driver Code
  public static void Main(string[] args)
  {

    // Given array
    int[] arr = { 2, 4, 7, 8, 10 };

    // Size of the array
    int N = arr.Length;

    OddOneOut(arr, N);
  }
}

// This code is contributed by chitranayal.

Javascript

<script>
// Javascript program for the above approach

// Function to print the array
// element which differs in parity
// with the remaining array elements
function OddOneOut(arr,N)
{
    // Multimaps to store even
    // and odd numbers along
    // with their indices
    let e = new Map();
    let o = new Map();

    // Traverse the array
    for (let i = 0; i < N; i++) {

      // If array element is even
      if (arr[i] % 2 == 0) {
        e.set(arr[i] , i);
      }

      // Otherwise
      else {
        o.set(arr[i] , i);
      }
    }

    // If only one even element
    // is present in the array
    if (e.size == 1) {
        document.write(Array.from(e.values())[0])    ;

    }

    // If only one odd element
    // is present in the array
    else {
    document.write(Array.from(o.values())[0])    ;

    }
}

// Driver Code
// Given array
let arr=[2, 4, 7, 8, 10];
// Size of the array
let N = arr.length;
OddOneOut(arr, N);


// This code is contributed by avanitrachhadiya2155
</script>

Output:

2

Time Complexity: O(N*logN)
Auxiliary Space: O(N)

Efficient Approach: To optimize the above approach, the idea is to keep a count of even and odd array elements in two variables and check which count is equal to 1. Follow the steps below to solve the problem:

1. Maintain four variables even, odd, to keep count of even and odd array elements in the array, and lastOdd, lastEven to store the indices of the last odd and even array elements encountered.
2. After traversing the array, if odd is found to be 1, then print lastOdd.
3. Otherwise, print lastEven.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to print the element
// which differs in parity
int oddOneOut(int arr[], int N)
{
    // Stores the count of odd and
    // even array elements encountered
    int odd = 0, even = 0;

    // Stores the indices of the last
    // odd and even array elements encountered
    int lastOdd = 0, lastEven = 0;

    // Traverse the array
    for (int i = 0; i < N; i++) {

        // If array element is even
        if (arr[i] % 2 == 0) {
            even++;
            lastEven = i;
        }

        // Otherwise
        else {
            odd++;
            lastOdd = i;
        }
    }

    // If only one odd element
    // is present in the array
    if (odd == 1) {
        cout << lastOdd << endl;
    }

    // If only one even element
    // is present in the array
    else {
        cout << lastEven << endl;
    }
}

// Driver Code
int main()
{
    // Given array
    int arr[] = { 2, 4, 7, 8, 10 };

    // Size of the array
    int N = sizeof(arr) / sizeof(arr[0]);

    oddOneOut(arr, N);

    return 0;
}

Java

// Java program for the above approach
import java.util.*;
class GFG
{

// Function to print the element
// which differs in parity
static void oddOneOut(int arr[], int N)
{

    // Stores the count of odd and
    // even array elements encountered
    int odd = 0, even = 0;

    // Stores the indices of the last
    // odd and even array elements encountered
    int lastOdd = 0, lastEven = 0;

    // Traverse the array
    for (int i = 0; i < N; i++) {

        // If array element is even
        if (arr[i] % 2 == 0) {
            even++;
            lastEven = i;
        }

        // Otherwise
        else {
            odd++;
            lastOdd = i;
        }
    }

    // If only one odd element
    // is present in the array
    if (odd == 1) {
        System.out.println(lastOdd);
    }

    // If only one even element
    // is present in the array
    else {
       System.out.println(lastEven);
    }
}

// Driver Code
public static void main(String args[])
{

    // Given array
    int arr[] = { 2, 4, 7, 8, 10 };

    // Size of the array
    int N = arr.length;
    oddOneOut(arr, N);
}
}

// This code is contributed by jana_sayantan.

Python3

# Python program for the above approach

# Function to print the element
# which differs in parity
def oddOneOut(arr, N) :

    # Stores the count of odd and
    # even array elements encountered
    odd = 0
    even = 0

    # Stores the indices of the last
    # odd and even array elements encountered
    lastOdd = 0
    lastEven = 0

    # Traverse the array
    for i in range(N):

        # If array element is even
        if (arr[i] % 2 == 0) :
            even += 1
            lastEven = i

        # Otherwise
        else :
            odd += 1
            lastOdd = i

    # If only one odd element
    # is present in the array
    if (odd == 1) :
        print(lastOdd)

    # If only one even element
    # is present in the array
    else :
        print(lastEven)

# Driver Code

# Given array
arr = [ 2, 4, 7, 8, 10 ]

# Size of the array
N = len(arr)

oddOneOut(arr, N)

# This code is contributed by susmitakundugoaldanga.

C#

// C# program for the above approach
using System;
class GFG
{

    // Function to print the element
    // which differs in parity
    static void oddOneOut(int[] arr, int N)
    {

        // Stores the count of odd and
        // even array elements encountered
        int odd = 0, even = 0;

        // Stores the indices of the last
        // odd and even array elements encountered
        int lastOdd = 0, lastEven = 0;

        // Traverse the array
        for (int i = 0; i < N; i++)
        {

            // If array element is even
            if (arr[i] % 2 == 0)
            {
                even++;
                lastEven = i;
            }

            // Otherwise
            else
            {
                odd++;
                lastOdd = i;
            }
        }

        // If only one odd element
        // is present in the array
        if (odd == 1)
        {
            Console.WriteLine(lastOdd);
        }

        // If only one even element
        // is present in the array
        else
        {
            Console.WriteLine(lastEven);
        }
    }

  // Driver code
  static void Main()
  {

    // Given array
    int[] arr = { 2, 4, 7, 8, 10 };

    // Size of the array
    int N = arr.Length;
    oddOneOut(arr, N);
  }
}

// This code is contributed by divyeshrabadiya07.

Javascript

<script>

// Javascript program for the above approach

// Function to print the element
// which differs in parity
function oddOneOut(arr, N)
{

    // Stores the count of odd and
    // even array elements encountered
    let odd = 0, even = 0;

    // Stores the indices of the last
    // odd and even array elements encountered
    let lastOdd = 0, lastEven = 0;

    // Traverse the array
    for(let i = 0; i < N; i++)
    {

        // If array element is even
        if (arr[i] % 2 == 0)
        {
            even++;
            lastEven = i;
        }

        // Otherwise
        else
        {
            odd++;
            lastOdd = i;
        }
    }

    // If only one odd element
    // is present in the array
    if (odd == 1)
    {
        document.write(lastOdd);
    }

    // If only one even element
    // is present in the array
    else
    {
        document.write(lastEven);
    }
}

// Driver code

// Given array
let arr = [ 2, 4, 7, 8, 10 ];

// Size of the array
let N = arr.length;

oddOneOut(arr, N);

// This code is contributed by suresh07

</script>

Output:

2

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