Longest subarray with all even or all odd elements

Given an array A[ ] of N non-negative integers, the task is to find the length of the longest sub-array such that all the elements in that sub-array are odd or even.

Examples:

Input: A[] = {2, 5, 7, 2, 4, 6, 8, 3}
Output: 4
Explanation: Sub-array {2, 4, 6, 8} of length 4 has all even elements

Input: A[] = {2, 3, 2, 5, 7, 3} 
Output: 3
Explanation: Sub-array {5, 7, 3} of length 3 has all odd elements 

Naive Approach: A naive approach to solve this problem is to consider all the contiguous sub-arrays and for each sub-array, check if all the elements are even or odd. The longest of them will be the answer.

Steps to implement:

• Declare a variable “ans” with value 0 because if no such subarray exists then 0 will be the answer
• Run two nested loops to find all subarrays
• Find the length of each subarray
• Make a boolean variable for each subarray that will initially contain false and when that subarray has all elements even or all elements odd then make that boolean variable true.
• If the boolean variable is true for any subarray, it is the required subarray. So update ans as the maximum of ans and the length of that subarray.

Code-

C++

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

// Function to calculate longest substring
// with odd or even elements
int LongestOddEvenSubarray(int arr[], int N)
{
   //Value to store final answer
   int ans=0;

   for(int i=0;i<N;i++){
       //To store length of subarray
       int length=0;
       for(int j=i;j<N;j++){

           //Increment the length
           length++;

           //This will tell that subarray contains all
           //odd or all even
           bool val=false;

           //Check for all elements are even
           int k=i;
           while(k<=j){
               if(arr[k]%2!=0){break;}
               k++;
           }
           //when all elements are even
           if(k==j+1){val=true;}

           //Check for all elements are odd
           k=i;
           while(k<=j){
               if(arr[k]%2!=1){break;}
               k++;
           }
           //when all elements are odd
           if(k==j+1){val=true;}


           //Update answer when all elements are even or odd
           if(val==true){
               ans=max(ans,length);
           }
       }
   }
   return ans;
}

// Driver Code
int main()
{
    // Input
    int arr[] = { 2, 5, 7, 2, 4, 6, 8, 3 };
    int N = sizeof(arr) / sizeof(arr[0]);

    // Function call
    cout << LongestOddEvenSubarray(arr, N);

    return 0;
}

Java

// Nikunj Sonigara

import java.util.*;

class Main {
    // Function to calculate the longest substring with odd or even elements
    static int longestOddEvenSubarray(int[] arr, int N) {
        // Value to store the final answer
        int ans = 0;

        for (int i = 0; i < N; i++) {
            // To store the length of the subarray
            int length = 0;
            for (int j = i; j < N; j++) {
                // Increment the length
                length++;

                // This will tell that the subarray contains all odd or all even
                boolean val = false;

                // Check for all elements are even
                int k = i;
                while (k <= j) {
                    if (arr[k] % 2 != 0) {
                        break;
                    }
                    k++;
                }
                // when all elements are even
                if (k == j + 1) {
                    val = true;
                }

                // Check for all elements are odd
                k = i;
                while (k <= j) {
                    if (arr[k] % 2 != 1) {
                        break;
                    }
                    k++;
                }
                // when all elements are odd
                if (k == j + 1) {
                    val = true;
                }

                // Update the answer when all elements are even or odd
                if (val) {
                    ans = Math.max(ans, length);
                }
            }
        }
        return ans;
    }

    // Driver Code
    public static void main(String[] args) {
        // Input
        int[] arr = { 2, 5, 7, 2, 4, 6, 8, 3 };
        int N = arr.length;

        // Function call
        System.out.println(longestOddEvenSubarray(arr, N));
    }
}

Python3

# Function to calculate the longest substring
# with either all odd or all even elements
def longest_odd_even_subarray(arr, N):
    # Variable to store the final answer
    ans = 0

    for i in range(N):
        # To store the length of the subarray
        length = 0

        for j in range(i, N):
            # Increment the length
            length += 1

            # This will tell us if the subarray contains all
            # odd or all even elements
            val = False

            # Check if all elements are even
            k = i
            while k <= j:
                if arr[k] % 2 != 0:
                    break
                k += 1

            # When all elements are even
            if k == j + 1:
                val = True

            # Check if all elements are odd
            k = i
            while k <= j:
                if arr[k] % 2 != 1:
                    break
                k += 1

            # When all elements are odd
            if k == j + 1:
                val = True

            # Update the answer when all elements are even or odd
            if val:
                ans = max(ans, length)

    return ans

# Driver Code
if __name__ == "__main__":
    # Input
    arr = [2, 5, 7, 2, 4, 6, 8, 3]
    N = len(arr)

    # Function call
    print(longest_odd_even_subarray(arr, N))

C#

using System;

class GFG
{
    // Function to calculate longest substring
    // with odd or even elements
    static int LongestOddEvenSubarray(int[] arr, int N)
    {
        // Value to store the final answer
        int ans = 0;

        for (int i = 0; i < N; i++)
        {
            // To store the length of the subarray
            int length = 0;
            for (int j = i; j < N; j++)
            {
                // Increment the length
                length++;

                // This will tell that subarray contains all
                // odd or all even
                bool val = false;

                // Check for all elements are even
                int k = i;
                while (k <= j)
                {
                    if (arr[k] % 2 != 0)
                    {
                        break;
                    }
                    k++;
                }

                // when all elements are even
                if (k == j + 1)
                {
                    val = true;
                }

                // Check for all elements are odd
                k = i;
                while (k <= j)
                {
                    if (arr[k] % 2 != 1)
                    {
                        break;
                    }
                    k++;
                }

                // when all elements are odd
                if (k == j + 1)
                {
                    val = true;
                }

                // Update answer when all elements are even or odd
                if (val == true)
                {
                    ans = Math.Max(ans, length);
                }
            }
        }
        return ans;
    }

    // Driver Code
    static void Main()
    {
        // Input
        int[] arr = { 2, 5, 7, 2, 4, 6, 8, 3 };
        int N = arr.Length;

        // Function call
        Console.WriteLine(LongestOddEvenSubarray(arr, N));
    }
}

Javascript

// Nikunj Sonigara

// Function to calculate the longest substring with odd or even elements
function longestOddEvenSubarray(arr) {
    // Value to store the final answer
    let ans = 0;

    for (let i = 0; i < arr.length; i++) {
        // To store the length of the subarray
        let length = 0;
        for (let j = i; j < arr.length; j++) {
            // Increment the length
            length++;

            // This will tell that the subarray contains all odd or all even
            let val = false;

            // Check for all elements are even
            let k = i;
            while (k <= j) {
                if (arr[k] % 2 !== 0) {
                    break;
                }
                k++;
            }
            // when all elements are even
            if (k === j + 1) {
                val = true;
            }

            // Check for all elements are odd
            k = i;
            while (k <= j) {
                if (arr[k] % 2 !== 1) {
                    break;
                }
                k++;
            }
            // when all elements are odd
            if (k === j + 1) {
                val = true;
            }

            // Update the answer when all elements are even or odd
            if (val) {
                ans = Math.max(ans, length);
            }
        }
    }
    return ans;
}

// Driver Code
const arr = [2, 5, 7, 2, 4, 6, 8, 3];

// Function call
console.log(longestOddEvenSubarray(arr));

Output

4

Time Complexity: O(N³), because of two nested loops to find all subarray and the third loop is for finding that subarray contains all elements odd or all elements even
Auxiliary Space: O(1), because no extra space has been used

Efficient Approach: The main idea to solve this problem is to use Dynamic Programming(it has both the properties – Optimal Substructure and Overlapping Subproblems) such that if there are some contiguous odd elements, then the very next odd element will increase the length of that contiguous array by one. And this is also true for even elements. Follow the steps below to solve the problem: 

• Initialize an array dp[ ] where dp[i] stores the length of sub-array that ends at A[i].
• Initialize dp[0] with 1.
• Initialize the variable ans as 1 to store the answer.
• Iterate over the range [1, N] using the variable i and perform the following steps:
  • If A[i]%2 is equal to A[i-1]%2, then set the value of dp[i] as dp[i-1]+1.
  • Else, set the value of dp[i] as 1.
• Iterate over the range [0, N] using the variable i and perform the following steps:
  • Set the value of ans as the maximum of ans or dp[i].
• After performing the above steps, print the value of ans as the answer.

Below is the implementation of the above approach:

C++

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

// Function to calculate longest substring
// with odd or even elements
int LongestOddEvenSubarray(int A[], int N)
{
    // Initializing dp[]
    int dp[N];

    // Initializing dp[0] with 1
    dp[0] = 1;

    // ans will store the final answer
    int ans = 1;

    // Traversing the array from index 1 to N - 1
    for (int i = 1; i < N; i++) {

        // Checking both current and previous element
        // is even or odd
        if ((A[i] % 2 == 0 && A[i - 1] % 2 == 0)
            || (A[i] % 2 != 0 && A[i - 1] % 2 != 0)) {

            // Updating dp[i] with dp[i-1] + 1
            dp[i] = dp[i - 1] + 1;
        }
        else
            dp[i] = 1;
    }

    for (int i = 0; i < N; i++)
        // Storing max element to ans
        ans = max(ans, dp[i]);

    // Returning the final answer
    return ans;
}

// Driver Code
int main()
{
    // Input
    int A[] = { 2, 5, 7, 2, 4, 6, 8, 3 };
    int N = sizeof(A) / sizeof(A[0]);

    // Function call
    cout << LongestOddEvenSubarray(A, N);

    return 0;
}

Java

// Java program for the above approach
import java.io.*;

class GFG {

    // Function to calculate longest substring
    // with odd or even elements
    static int LongestOddEvenSubarray(int A[], int N)
    {

        // Initializing dp[]
        int dp[] = new int[N];

        // Initializing dp[0] with 1
        dp[0] = 1;

        // ans will store the final answer
        int ans = 1;

        // Traversing the array from index 1 to N - 1
        for (int i = 1; i < N; i++) {

            // Checking both current and previous element
            // is even or odd
            if ((A[i] % 2 == 0 && A[i - 1] % 2 == 0)
                || (A[i] % 2 != 0 && A[i - 1] % 2 != 0)) {

                // Updating dp[i] with dp[i-1] + 1
                dp[i] = dp[i - 1] + 1;
            }
            else
                dp[i] = 1;
        }

        for (int i = 0; i < N; i++)
            // Storing max element to ans
            ans = Math.max(ans, dp[i]);

        // Returning the final answer
        return ans;
    }

    // Driver Code
    public static void main(String[] args)
    {
        // Input
        int A[] = { 2, 5, 7, 2, 4, 6, 8, 3 };
        int N = A.length;

        // Function call
        System.out.println(LongestOddEvenSubarray(A, N));
    }
}

// This code is contributed by Potta Lokesh

Python3

# Python 3 implementation for the above approach

# Function to calculate longest substring
# with odd or even elements
def LongestOddEvenSubarray(A, N):
    # Initializing dp[]
    dp = [0 for i in range(N)]

    # Initializing dp[0] with 1
    dp[0] = 1

    # ans will store the final answer
    ans = 1

    # Traversing the array from index 1 to N - 1
    for i in range(1, N, 1):

        # Checking both current and previous element
        # is even or odd
        if ((A[i] % 2 == 0 and A[i - 1] % 2 == 0) or (A[i] % 2 != 0 and A[i - 1] % 2 != 0)):

            # Updating dp[i] with dp[i-1] + 1
            dp[i] = dp[i - 1] + 1
        else:
            dp[i] = 1

    for i in range(N):
        # Storing max element to ans
        ans = max(ans, dp[i])

    # Returning the final answer
    return ans

# Driver Code
if __name__ == '__main__':
    # Input
    A = [2, 5, 7, 2, 4, 6, 8, 3]
    N = len(A)

    # Function call
    print(LongestOddEvenSubarray(A, N))

    # This code is contributed by SURENDRA_GANGWAR.

C#

// C# program for the above approach
using System;

class GFG{

    // Function to calculate longest substring
    // with odd or even elements
    static int LongestOddEvenSubarray(int[] A, int N)
    {

        // Initializing dp[]
        int[] dp = new int[N];

        // Initializing dp[0] with 1
        dp[0] = 1;

        // ans will store the final answer
        int ans = 1;

        // Traversing the array from index 1 to N - 1
        for (int i = 1; i < N; i++) {

            // Checking both current and previous element
            // is even or odd
            if ((A[i] % 2 == 0 && A[i - 1] % 2 == 0)
                || (A[i] % 2 != 0 && A[i - 1] % 2 != 0)) {

                // Updating dp[i] with dp[i-1] + 1
                dp[i] = dp[i - 1] + 1;
            }
            else
                dp[i] = 1;
        }

        for (int i = 0; i < N; i++)

            // Storing max element to ans
            ans = Math.Max(ans, dp[i]);

        // Returning the final answer
        return ans;
    }

// Driver Code
public static void Main()
{
    // Input
        int[] A = { 2, 5, 7, 2, 4, 6, 8, 3 };
        int N = A.Length;

        // Function call
        Console.Write(LongestOddEvenSubarray(A, N));
}
}

// This code is contributed by target_2.

Javascript

<script>

// JavaScript implementation for the above approach

// Function to calculate longest substring
// with odd or even elements
function LongestOddEvenSubarray(A, N)
{

  // Initializing dp[]
  let dp = new Array(N);

  // Initializing dp[0] with 1
  dp[0] = 1;

  // ans will store the final answer
  let ans = 1;

  // Traversing the array from index 1 to N - 1
  for (let i = 1; i < N; i++)
  {

    // Checking both current and previous element
    // is even or odd
    if (
      (A[i] % 2 == 0 && A[i - 1] % 2 == 0) ||
      (A[i] % 2 != 0 && A[i - 1] % 2 != 0)
    ) {
      // Updating dp[i] with dp[i-1] + 1
      dp[i] = dp[i - 1] + 1;
    } else dp[i] = 1;
  }

  for (let i = 0; i < N; i++)

    // Storing max element to ans
    ans = Math.max(ans, dp[i]);

  // Returning the final answer
  return ans;
}

// Driver Code
// Input
let A = [2, 5, 7, 2, 4, 6, 8, 3];
let N = A.length;

// Function call
document.write(LongestOddEvenSubarray(A, N));

// This code is contributed by _saurabh_jaiswal.
</script>

Output

4

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

Space Optimization:  It is possible to further optimize the space complexity of the above approach by observing that, for calculating dp[i], only the value of dp[i-1] is relevant. So, store dp[i-1] in a variable and update the variable in each iteration. Also, update the answer in each iteration. Follow the steps below to solve the problem: 

• Initialize the variables dp as 1 to store the length of the sub-array till i-1 and ans as 1 to store the answer.
• Iterate over the range [1, N] using the variable i and perform the following steps:
  • If A[i]%2 is equal to A[i-1]%2, then set the value of dp as dp+1 and set the value of ans as the maximum of ans or dp.
  • Else, set the value of dp as 1.
• After performing the above steps, print the value of ans as the answer.

Below is the implementation of the above approach:

C++

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

// Function to calculate longest substring
// with odd or even elements
int LongestOddEvenSubarray(int A[], int N)
{
    // Initializing dp
    int dp;

    // Initializing dp with 1
    dp = 1;

    // ans will store the final answer
    int ans = 1;

    // Traversing the array from index 1 to N - 1
    for (int i = 1; i < N; i++) {

        // Checking both current and previous element
        // is even or odd
        if ((A[i] % 2 == 0 && A[i - 1] % 2 == 0)
            || (A[i] % 2 != 0 && A[i - 1] % 2 != 0)) {

            // Updating dp with (previous dp value) + 1
            dp = dp + 1;

            // Storing max element so far to ans
            ans = max(ans, dp);
        }
        else
            dp = 1;
    }

    // Returning the final answer
    return ans;
}

// Driver code
int main()
{
    // Input
    int A[] = { 2, 5, 7, 2, 4, 6, 8, 3 };
    int N = sizeof(A) / sizeof(A[0]);

    // Function call
    cout << LongestOddEvenSubarray(A, N);

    return 0;
}

Java

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

// Function to calculate longest subString
// with odd or even elements
static int LongestOddEvenSubarray(int A[], int N)
{

    // Initializing dp
    int dp;

    // Initializing dp with 1
    dp = 1;

    // ans will store the final answer
    int ans = 1;

    // Traversing the array from index 1 to N - 1
    for (int i = 1; i < N; i++) {

        // Checking both current and previous element
        // is even or odd
        if ((A[i] % 2 == 0 && A[i - 1] % 2 == 0)
            || (A[i] % 2 != 0 && A[i - 1] % 2 != 0)) {

            // Updating dp with (previous dp value) + 1
            dp = dp + 1;

            // Storing max element so far to ans
            ans = Math.max(ans, dp);
        }
        else
            dp = 1;
    }

    // Returning the final answer
    return ans;
}

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

    // Input
    int A[] = { 2, 5, 7, 2, 4, 6, 8, 3 };
    int N = A.length;

    // Function call
    System.out.print(LongestOddEvenSubarray(A, N));
}
}

// This code is contributed by Amit Katiyar

Python3

# Python implementation for the above approach

# Function to calculate longest substring
# with odd or even elements
def LongestOddEvenSubarray(A, N):

    # Initializing dp
    # Initializing dp with 1
    dp = 1

    # ans will store the final answer
    ans = 1

    # Traversing the array from index 1 to N - 1
    for i in range(1, N):

        # Checking both current and previous element
        # is even or odd
        if ((A[i] % 2 == 0 and A[i - 1] % 2 == 0) or (A[i] % 2 != 0 and A[i - 1] % 2 != 0)):

            # Updating dp with (previous dp value) + 1
            dp = dp + 1

            # Storing max element so far to ans
            ans = max(ans, dp)
        else:
            dp = 1

    # Returning the final answer
    return ans

# Driver code

# Input
A =  [2, 5, 7, 2, 4, 6, 8, 3 ]
N = len(A)

# Function call
print(LongestOddEvenSubarray(A, N))

# This code is contributed by shivani

C#

// C# implementation for the above approach
using System;

public class GFG
{

// Function to calculate longest subString
// with odd or even elements
static int longestOddEvenSubarray(int []A, int N)
{

    // Initializing dp
    int dp;

    // Initializing dp with 1
    dp = 1;

    // ans will store the readonly answer
    int ans = 1;

    // Traversing the array from index 1 to N - 1
    for (int i = 1; i < N; i++) {

        // Checking both current and previous element
        // is even or odd
        if ((A[i] % 2 == 0 && A[i - 1] % 2 == 0)
            || (A[i] % 2 != 0 && A[i - 1] % 2 != 0)) {

            // Updating dp with (previous dp value) + 1
            dp = dp + 1;

            // Storing max element so far to ans
            ans = Math.Max(ans, dp);
        }
        else
            dp = 1;
    }

    // Returning the readonly answer
    return ans;
}

// Driver code
public static void Main(String[] args)
{

    // Input
    int []A = { 2, 5, 7, 2, 4, 6, 8, 3 };
    int N = A.Length;

    // Function call
    Console.Write(longestOddEvenSubarray(A, N));
}
}

// This code is contributed by shikhasingrajput

Javascript

<script>
// Javascript implementation for the above approach

// Function to calculate longest substring
// with odd or even elements
function LongestOddEvenSubarray(A, N) {
  // Initializing dp
  let dp;

  // Initializing dp with 1
  dp = 1;

  // ans will store the final answer
  let ans = 1;

  // Traversing the array from index 1 to N - 1
  for (let i = 1; i < N; i++) {
    // Checking both current and previous element
    // is even or odd
    if (
      (A[i] % 2 == 0 && A[i - 1] % 2 == 0) ||
      (A[i] % 2 != 0 && A[i - 1] % 2 != 0)
    ) {
      // Updating dp with (previous dp value) + 1
      dp = dp + 1;

      // Storing max element so far to ans
      ans = Math.max(ans, dp);
    } else dp = 1;
  }

  // Returning the final answer
  return ans;
}

// Driver code
// Input
let A = [2, 5, 7, 2, 4, 6, 8, 3];
let N = A.length;

// Function call
document.write(LongestOddEvenSubarray(A, N));

</script>

Output

4

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