Maximize count of corresponding same elements in given Arrays by Rotation

Given two arrays arr1[] and arr2[] of N integers and array arr1[] has distinct elements. The task is to find the maximum count of corresponding same elements in the given arrays by performing cyclic left or right shift on array arr1[]. 
Examples:

Input: arr1[] = { 6, 7, 3, 9, 5 }, arr2[] = { 7, 3, 9, 5, 6 } 
Output: 5 
Explanation:
By performing cyclic left shift on array arr1[] by 1. 
Updated array arr1[] = {7, 3, 9, 5, 6}. 
This rotation contains a maximum number of equal elements between array arr1[] and arr2[].
Input: arr1[] = {1, 3, 2, 4}, arr2[] = {4, 2, 3, 1} 
Output: 2 
Explanation:
By performing cyclic left shift on array arr1[] by 1. 
Updated array arr1[] = {3, 2, 4, 1} 
This rotation contains a maximum number of equal elements between array arr1[] and arr2[]. 

Approach: This problem can be solved using Greedy Approach. Below are the steps: 

1. Store the position of all the elements of the array arr2[] in an array(say store[]).
2. For each element in the array arr1[], do the following: 
   • Find the difference(say diff) between the position of the current element in arr2[] with the position in arr1[].
   • If diff is less than 0 then update diff to (N – diff).
   • Store the frequency of current difference diff in a map.
3. After the above steps, the maximum frequency stored in map is the maximum number of equal elements after rotation on arr1[].

Below is the implementation of the above approach: 

C++

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

// Function that prints maximum
// equal elements
void maximumEqual(int a[], int b[],
                  int n)
{

    // Vector to store the index
    // of elements of array b
    vector<int> store(1e5);

    // Storing the positions of
    // array B
    for (int i = 0; i < n; i++) {
        store[b[i]] = i + 1;
    }

    // frequency array to keep count
    // of elements with similar
    // difference in distances
    vector<int> ans(1e5);

    // Iterate through all element in arr1[]
    for (int i = 0; i < n; i++) {

        // Calculate number of
        // shift required to
        // make current element
        // equal
        int d = abs(store[a[i]]
                    - (i + 1));

        // If d is less than 0
        if (store[a[i]] < i + 1) {
            d = n - d;
        }

        // Store the frequency
        // of current diff
        ans[d]++;
    }

    int finalans = 0;

    // Compute the maximum frequency
    // stored
    for (int i = 0; i < 1e5; i++)
        finalans = max(finalans,
                       ans[i]);

    // Printing the maximum number
    // of equal elements
    cout << finalans << "\n";
}

// Driver Code
int main()
{
    // Given two arrays
    int A[] = { 6, 7, 3, 9, 5 };
    int B[] = { 7, 3, 9, 5, 6 };

    int size = sizeof(A) / sizeof(A[0]);

    // Function Call
    maximumEqual(A, B, size);
    return 0;
}

Java

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

// Function that prints maximum
// equal elements
static void maximumEqual(int a[],
                         int b[], int n)
{

    // Vector to store the index
    // of elements of array b
    int store[] = new int[(int) 1e5];

    // Storing the positions of
    // array B
    for (int i = 0; i < n; i++)
    {
        store[b[i]] = i + 1;
    }

    // frequency array to keep count
    // of elements with similar
    // difference in distances
    int ans[] = new int[(int) 1e5];

    // Iterate through all element in arr1[]
    for (int i = 0; i < n; i++)
    {

        // Calculate number of
        // shift required to
        // make current element
        // equal
        int d = Math.abs(store[a[i]] - (i + 1));

        // If d is less than 0
        if (store[a[i]] < i + 1)
        {
            d = n - d;
        }

        // Store the frequency
        // of current diff
        ans[d]++;
    }

    int finalans = 0;

    // Compute the maximum frequency
    // stored
    for (int i = 0; i < 1e5; i++)
        finalans = Math.max(finalans,
                            ans[i]);

    // Printing the maximum number
    // of equal elements
    System.out.print(finalans + "\n");
}

// Driver Code
public static void main(String[] args)
{
    // Given two arrays
    int A[] = { 6, 7, 3, 9, 5 };
    int B[] = { 7, 3, 9, 5, 6 };

    int size = A.length;

    // Function Call
    maximumEqual(A, B, size);
}
}

// This code is contributed by sapnasingh4991

Python3

# Python3 program for the above approach

# Function that prints maximum
# equal elements
def maximumEqual(a, b, n):

    # List to store the index
    # of elements of array b
    store = [0] * 10 ** 5

    # Storing the positions of
    # array B
    for i in range(n):
        store[b[i]] = i + 1

    # Frequency array to keep count
    # of elements with similar
    # difference in distances
    ans = [0] * 10 ** 5

    # Iterate through all element
    # in arr1[]
    for i in range(n):

        # Calculate number of shift
        # required to make current
        # element equal
        d = abs(store[a[i]] - (i + 1))

        # If d is less than 0
        if (store[a[i]] < i + 1):
            d = n - d

        # Store the frequency
        # of current diff
        ans[d] += 1

    finalans = 0

    # Compute the maximum frequency
    # stored
    for i in range(10 ** 5):
        finalans = max(finalans, ans[i])

    # Printing the maximum number
    # of equal elements
    print(finalans)

# Driver Code
if __name__ == '__main__':

    # Given two arrays
    A = [ 6, 7, 3, 9, 5 ]
    B = [ 7, 3, 9, 5, 6 ]

    size = len(A)

    # Function Call
    maximumEqual(A, B, size)


# This code is contributed by Shivam Singh

C#

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

// Function that prints maximum
// equal elements
static void maximumEqual(int[] a,
                         int[] b, int n)
{

    // Vector to store the index
    // of elements of array b
    int[] store = new int[(int) 1e5];

    // Storing the positions of
    // array B
    for(int i = 0; i < n; i++)
    {
       store[b[i]] = i + 1;
    }

    // Frequency array to keep count
    // of elements with similar
    // difference in distances
    int[] ans = new int[(int) 1e5];

    // Iterate through all element in arr1[]
    for(int i = 0; i < n; i++)
    {

       // Calculate number of
       // shift required to
       // make current element
       // equal
       int d = Math.Abs(store[a[i]] - (i + 1));

       // If d is less than 0
       if (store[a[i]] < i + 1)
       {
           d = n - d;
       }

       // Store the frequency
       // of current diff
       ans[d]++;
    }

    int finalans = 0;

    // Compute the maximum frequency
    // stored
    for(int i = 0; i < 1e5; i++)
       finalans = Math.Max(finalans, ans[i]);

    // Printing the maximum number
    // of equal elements
    Console.Write(finalans + "\n");
}

// Driver Code
public static void Main()
{

    // Given two arrays
    int[]A = { 6, 7, 3, 9, 5 };
    int[]B = { 7, 3, 9, 5, 6 };

    int size = A.Length;

    // Function Call
    maximumEqual(A, B, size);
}
}

// This code is contributed by chitranayal

Javascript

<script>

// JavaScript program of the above approach

// Function that prints maximum
// equal elements
function maximumEqual(a, b, n)
{

    // Vector to store the index
    // of elements of array b
    let store = Array.from({length: 1e5}, (_, i) => 0);

    // Storing the positions of
    // array B
    for (let i = 0; i < n; i++)
    {
        store[b[i]] = i + 1;
    }

    // frequency array to keep count
    // of elements with similar
    // difference in distances
    let ans = Array.from({length: 1e5}, (_, i) => 0);

    // Iterate through all element in arr1[]
    for (let i = 0; i < n; i++)
    {

        // Calculate number of
        // shift required to
        // make current element
        // equal
        let d = Math.abs(store[a[i]] - (i + 1));

        // If d is less than 0
        if (store[a[i]] < i + 1)
        {
            d = n - d;
        }

        // Store the frequency
        // of current diff
        ans[d]++;
    }

    let finalans = 0;

    // Compute the maximum frequency
    // stored
    for (let i = 0; i < 1e5; i++)
        finalans = Math.max(finalans,
                            ans[i]);

    // Printing the maximum number
    // of equal elements
    document.write(finalans + "\n");
}

// Driver Code

    // Given two arrays
    let A = [ 6, 7, 3, 9, 5 ];
    let B = [ 7, 3, 9, 5, 6 ];

    let size = A.length;

    // Function Call
    maximumEqual(A, B, size);

</script>

Output:

5

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