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Minimize swaps to rearrange Array such that remainder of any element and its index with 3 are same

  • Difficulty Level : Hard
  • Last Updated : 29 Oct, 2021

Given an array arr[]. The task is to minimize the number of swaps required such that for each i in arr[], arr[i]%3 = i%3. If such rearrangement is not possible, print -1.

Examples: 

Input: arr[ ] = {4, 3, 5, 2, 9, 7}
Output: 3
Explanation: Following are the operations performed in arr[]
Initially, index % 3 = {0, 1, 2, 0, 1, 2} and arr[i] % 3 = {1, 0, 2, 2, 0, 1}.
swap arr[0] and arr[1] updates arr[] to arr[]  % 3 = {0, 1, 2, 2, 0, 1}
swap arr[3] and arr[4] updates arr[] to arr[] % 3 = {0, 1, 2, 0, 2, 1}
swap arr[4] and arr[5] updates arr[] to arr[] % 3 = {0, 1, 2, 0, 1, 2}
Therefore, 3 swaps are required to get the resultant array which is minimum possible. 

Input: arr[] = {0, 1, 2, 3, 4}
Output: 0

 

Approach: This problem is implementation-based and related to modulo properties. Follow the steps below to solve the given problem. 

  • Iterate the array with i from i = 0 to i=n-1
    • if arr[i] % 3 equals 0 then, continue.
    • else, find the index j from i+1 to n-1, where i % 3 = arr[j] % 3 and j % 3 = arr[i] % 3.
    • With above step move two array elements at their wanted positions.
    • If no such j is found, then find an index k form i+1 to n-1, where i % 3 = arr[k] % 3, and swap the elements.
    • The base case will be count of indices such that index%3 = arr[i] % 3.
  • Return the final count as the required answer.

Below is the implementation of the above approach: 

C++




// C++ Program for above approach
#include <iostream>
using namespace std;
 
// Function to swap two array elements.
void swapping(int arr[], int i, int j)
{
    int temp = arr[i];
    arr[i] = arr[j];
    arr[j] = temp;
}
 
// Function to count the Swaps required such that
// for all i in arr[] arr[]% 3 = i % 3
int CountMinSwaps(int arr[], int n)
{
 
    // index_mod_i = count of indexes which
    // give i on modulo 3: index%3==i
    int index_mod_0 = 0,
        index_mod_1 = 0,
        index_mod_2 = 0;
 
    // array_mod_i = count of array elements
    // which give i on modulo 3: arr[i]%3==i
    int array_mod_0 = 0,
        array_mod_1 = 0,
        array_mod_2 = 0;
 
    int i, j, count = 0;
 
    for (i = 0; i < n; i++) {
        if (i % 3 == 0)
            index_mod_0 += 1;
 
        else if (i % 3 == 1)
            index_mod_1 += 1;
 
        else if (i % 3 == 2)
            index_mod_2 += 1;
 
        if (arr[i] % 3 == 0)
            array_mod_0 += 1;
 
        else if (arr[i] % 3 == 1)
            array_mod_1 += 1;
 
        else if (arr[i] % 3 == 2)
            array_mod_2 += 1;
    }
 
    // check for base condition.
    if (index_mod_0 != array_mod_0
        || index_mod_1 != array_mod_1
        || index_mod_2 != array_mod_2)
        return -1;
 
    // count the swaps now.
    for (i = 0; i < n; i++) {
 
        // If already in right format
        // Then goto next index
        if (i % 3 == arr[i] % 3)
            continue;
 
        int index_org = i % 3;
        int array_org = arr[i] % 3;
 
        // Initially set swapped to false
        bool swapped = false;
 
        for (j = i + 1; j < n; j++) {
            int index_exp = j % 3;
            int array_exp = arr[j] % 3;
 
            if (index_org == array_exp
                && array_org == index_exp) {
                swapping(arr, i, j);
 
                // Set swapped to true to make sure
                // any value is swapped
                swapped = true;
 
                // Increment the count
                count += 1;
                break;
            }
        }
 
        // Check if element is swapped or not
        if (swapped == false) {
            for (j = i + 1; j < n; j++) {
                int array_exp = arr[j] % 3;
                if (index_org == array_exp) {
                    // Swap indices i and j
                    swapping(arr, i, j);
 
                    // Increment the count of swaps
                    count += 1;
                    break;
                }
            }
        }
    }
 
    // Return the final result
    return count;
}
 
// Driver Code
int main()
{
    int arr[6] = { 4, 3, 5, 2, 9, 7 };
    int n = sizeof(arr) / sizeof(arr[0]);
 
    int swaps = CountMinSwaps(arr, n);
 
    cout << swaps << endl;
}

Java




// Java code for the above approach
import java.io.*;
 
class GFG {
   
// Function to swap two array elements.
static void swapping(int arr[], int i, int j)
{
    int temp = arr[i];
    arr[i] = arr[j];
    arr[j] = temp;
}
 
// Function to count the Swaps required such that
// for all i in arr[] arr[]% 3 = i % 3
static int CountMinSwaps(int arr[], int n)
{
 
    // index_mod_i = count of indexes which
    // give i on modulo 3: index%3==i
    int index_mod_0 = 0,
        index_mod_1 = 0,
        index_mod_2 = 0;
 
    // array_mod_i = count of array elements
    // which give i on modulo 3: arr[i]%3==i
    int array_mod_0 = 0,
        array_mod_1 = 0,
        array_mod_2 = 0;
 
    int i, j, count = 0;
 
    for (i = 0; i < n; i++) {
        if (i % 3 == 0)
            index_mod_0 += 1;
 
        else if (i % 3 == 1)
            index_mod_1 += 1;
 
        else if (i % 3 == 2)
            index_mod_2 += 1;
 
        if (arr[i] % 3 == 0)
            array_mod_0 += 1;
 
        else if (arr[i] % 3 == 1)
            array_mod_1 += 1;
 
        else if (arr[i] % 3 == 2)
            array_mod_2 += 1;
    }
 
    // check for base condition.
    if (index_mod_0 != array_mod_0
        || index_mod_1 != array_mod_1
        || index_mod_2 != array_mod_2)
        return -1;
 
    // count the swaps now.
    for (i = 0; i < n; i++) {
 
        // If already in right format
        // Then goto next index
        if (i % 3 == arr[i] % 3)
            continue;
 
        int index_org = i % 3;
        int array_org = arr[i] % 3;
 
        // Initially set swapped to false
        boolean swapped = false;
 
        for (j = i + 1; j < n; j++) {
            int index_exp = j % 3;
            int array_exp = arr[j] % 3;
 
            if (index_org == array_exp
                && array_org == index_exp) {
                swapping(arr, i, j);
 
                // Set swapped to true to make sure
                // any value is swapped
                swapped = true;
 
                // Increment the count
                count += 1;
                break;
            }
        }
 
        // Check if element is swapped or not
        if (swapped == false) {
            for (j = i + 1; j < n; j++) {
                int array_exp = arr[j] % 3;
                if (index_org == array_exp) {
                    // Swap indices i and j
                    swapping(arr, i, j);
 
                    // Increment the count of swaps
                    count += 1;
                    break;
                }
            }
        }
    }
 
    // Return the final result
    return count;
}
 
    public static void main (String[] args) {
      int arr[] = { 4, 3, 5, 2, 9, 7 };
    int n = arr.length;
 
    int swaps = CountMinSwaps(arr, n);
 
        System.out.println(swaps );
    }
}
 
// This code is contributed by Potta Lokesh

Python3




# python Program for above approach
 
# Function to swap two array elements.
def swapping(arr, i, j):
    temp = arr[i]
    arr[i] = arr[j]
    arr[j] = temp
 
# Function to count the Swaps required such that
# for all i in arr[] arr[]% 3 = i % 3
def CountMinSwaps(arr, n):
 
    # index_mod_i = count of indexes which
    # give i on modulo 3: index%3==i
    index_mod_0 = 0
    index_mod_1 = 0
    index_mod_2 = 0
 
    # array_mod_i = count of array elements
    # which give i on modulo 3: arr[i]%3==i
    array_mod_0 = 0
    array_mod_1 = 0
    array_mod_2 = 0
 
    count = 0
 
    for i in range(0, n):
        if (i % 3 == 0):
            index_mod_0 += 1
 
        elif (i % 3 == 1):
            index_mod_1 += 1
 
        elif (i % 3 == 2):
            index_mod_2 += 1
 
        if (arr[i] % 3 == 0):
            array_mod_0 += 1
 
        elif (arr[i] % 3 == 1):
            array_mod_1 += 1
 
        elif (arr[i] % 3 == 2):
            array_mod_2 += 1
 
    # check for base condition.
    if (index_mod_0 != array_mod_0 or index_mod_1 != array_mod_1 or index_mod_2 != array_mod_2):
        return -1
 
        # count the swaps now.
    for i in range(0, n):
 
                # If already in right format
                # Then goto next index
        if (i % 3 == arr[i] % 3):
            continue
 
        index_org = i % 3
        array_org = arr[i] % 3
 
        # Initially set swapped to false
        swapped = False
 
        for j in range(i+1, n):
            index_exp = j % 3
            array_exp = arr[j] % 3
 
            if (index_org == array_exp and array_org == index_exp):
                swapping(arr, i, j)
 
                # Set swapped to true to make sure
                # any value is swapped
                swapped = True
 
                # Increment the count
                count += 1
                break
 
                # Check if element is swapped or not
        if (swapped == False):
            for j in range(i+1, n):
                array_exp = arr[j] % 3
                if (index_org == array_exp):
                                        # Swap indices i and j
                    swapping(arr, i, j)
 
                    # Increment the count of swaps
                    count += 1
                    break
 
        # Return the final result
    return count
 
# Driver Code
if __name__ == "__main__":
 
    arr = [4, 3, 5, 2, 9, 7]
    n = len(arr)
 
    swaps = CountMinSwaps(arr, n)
    print(swaps)
 
    # This code is contributed by rakeshsahni

C#




// C# code for the above approach
using System;
class GFG
{
 
    // Function to swap two array elements.
    static void swapping(int[] arr, int i, int j)
    {
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }
 
    // Function to count the Swaps required such that
    // for all i in arr[] arr[]% 3 = i % 3
    static int CountMinSwaps(int[] arr, int n)
    {
 
        // index_mod_i = count of indexes which
        // give i on modulo 3: index%3==i
        int index_mod_0 = 0,
            index_mod_1 = 0,
            index_mod_2 = 0;
 
        // array_mod_i = count of array elements
        // which give i on modulo 3: arr[i]%3==i
        int array_mod_0 = 0,
            array_mod_1 = 0,
            array_mod_2 = 0;
 
        int i, j, count = 0;
 
        for (i = 0; i < n; i++)
        {
            if (i % 3 == 0)
                index_mod_0 += 1;
 
            else if (i % 3 == 1)
                index_mod_1 += 1;
 
            else if (i % 3 == 2)
                index_mod_2 += 1;
 
            if (arr[i] % 3 == 0)
                array_mod_0 += 1;
 
            else if (arr[i] % 3 == 1)
                array_mod_1 += 1;
 
            else if (arr[i] % 3 == 2)
                array_mod_2 += 1;
        }
 
        // check for base condition.
        if (index_mod_0 != array_mod_0
            || index_mod_1 != array_mod_1
            || index_mod_2 != array_mod_2)
            return -1;
 
        // count the swaps now.
        for (i = 0; i < n; i++)
        {
 
            // If already in right format
            // Then goto next index
            if (i % 3 == arr[i] % 3)
                continue;
 
            int index_org = i % 3;
            int array_org = arr[i] % 3;
 
            // Initially set swapped to false
            Boolean swapped = false;
 
            for (j = i + 1; j < n; j++)
            {
                int index_exp = j % 3;
                int array_exp = arr[j] % 3;
 
                if (index_org == array_exp
                    && array_org == index_exp)
                {
                    swapping(arr, i, j);
 
                    // Set swapped to true to make sure
                    // any value is swapped
                    swapped = true;
 
                    // Increment the count
                    count += 1;
                    break;
                }
            }
 
            // Check if element is swapped or not
            if (swapped == false)
            {
                for (j = i + 1; j < n; j++)
                {
                    int array_exp = arr[j] % 3;
                    if (index_org == array_exp)
                    {
                        // Swap indices i and j
                        swapping(arr, i, j);
 
                        // Increment the count of swaps
                        count += 1;
                        break;
                    }
                }
            }
        }
 
        // Return the final result
        return count;
    }
 
    public static void Main()
    {
        int[] arr = { 4, 3, 5, 2, 9, 7 };
        int n = arr.Length;
 
        int swaps = CountMinSwaps(arr, n);
 
        Console.Write(swaps);
    }
}
 
// This code is contributed by Saurabh Jaiswal

Javascript




<script>
    // JavaScript Program for above approach
 
    // Function to swap two array elements.
    const swapping = (arr, i, j) => {
        let temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }
 
    // Function to count the Swaps required such that
    // for all i in arr[] arr[]% 3 = i % 3
    const CountMinSwaps = (arr, n) => {
 
        // index_mod_i = count of indexes which
        // give i on modulo 3: index%3==i
        let index_mod_0 = 0,
            index_mod_1 = 0,
            index_mod_2 = 0;
 
        // array_mod_i = count of array elements
        // which give i on modulo 3: arr[i]%3==i
        let array_mod_0 = 0,
            array_mod_1 = 0,
            array_mod_2 = 0;
 
        let i, j, count = 0;
 
        for (i = 0; i < n; i++) {
            if (i % 3 == 0)
                index_mod_0 += 1;
 
            else if (i % 3 == 1)
                index_mod_1 += 1;
 
            else if (i % 3 == 2)
                index_mod_2 += 1;
 
            if (arr[i] % 3 == 0)
                array_mod_0 += 1;
 
            else if (arr[i] % 3 == 1)
                array_mod_1 += 1;
 
            else if (arr[i] % 3 == 2)
                array_mod_2 += 1;
        }
 
        // check for base condition.
        if (index_mod_0 != array_mod_0
            || index_mod_1 != array_mod_1
            || index_mod_2 != array_mod_2)
            return -1;
 
        // count the swaps now.
        for (i = 0; i < n; i++) {
 
            // If already in right format
            // Then goto next index
            if (i % 3 == arr[i] % 3)
                continue;
 
            let index_org = i % 3;
            let array_org = arr[i] % 3;
 
            // Initially set swapped to false
            let swapped = false;
 
            for (j = i + 1; j < n; j++) {
                let index_exp = j % 3;
                let array_exp = arr[j] % 3;
 
                if (index_org == array_exp
                    && array_org == index_exp) {
                    swapping(arr, i, j);
 
                    // Set swapped to true to make sure
                    // any value is swapped
                    swapped = true;
 
                    // Increment the count
                    count += 1;
                    break;
                }
            }
 
            // Check if element is swapped or not
            if (swapped == false) {
                for (j = i + 1; j < n; j++) {
                    let array_exp = arr[j] % 3;
                    if (index_org == array_exp) {
                        // Swap indices i and j
                        swapping(arr, i, j);
 
                        // Increment the count of swaps
                        count += 1;
                        break;
                    }
                }
            }
        }
 
        // Return the final result
        return count;
    }
 
    // Driver Code
    let arr = [4, 3, 5, 2, 9, 7];
    let n = arr.length;
    let swaps = CountMinSwaps(arr, n);
    document.write(swaps);
 
    // This code is contributed by rakeshsahni
 
</script>

 
 

Output: 
3

 

 

Time Complexity: O(N2), Where N is the size of arr[].

 

Auxiliary Space: O(1).

 


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