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# Rearrange an array such that ‘arr[j]’ becomes ‘i’ if ‘arr[i]’ is ‘j’ | Set 1

• Difficulty Level : Hard
• Last Updated : 09 Dec, 2022

Given an array of size n where all elements are distinct and in the range from 0 to n-1, change the contents of arr[] so that arr[i] = j is changed to arr[j] = i.

Examples:

Example 1:
Input: arr[]  = {1, 3, 0, 2};
Output: arr[] = {2, 0, 3, 1};
Explanation for the above output.
Since arr[0] is 1, arr[1] is changed to 0
Since arr[1] is 3, arr[3] is changed to 1
Since arr[2] is 0, arr[0] is changed to 2
Since arr[3] is 2, arr[2] is changed to 3

Example 2:
Input: arr[]  = {2, 0, 1, 4, 5, 3};
Output: arr[] = {1, 2, 0, 5, 3, 4};

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

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

A Simple Solution is to create a temporary array and one by one copy ‘i’ to ‘temp[arr[i]]’ where i varies from 0 to n-1.

Below is the implementation of the above idea.

## C++

 // A simple C++ program to rearrange contents of arr[] // such that arr[j] becomes j if arr[i] is j #include using namespace std;   // A simple method to rearrange 'arr[0..n-1]' so that 'arr[j]' // becomes 'i' if 'arr[i]' is 'j' void rearrangeNaive(int arr[], int n) {     // Create an auxiliary array of same size     int temp[n], i;       // Store result in temp[]     for (i = 0; i < n; i++)         temp[arr[i]] = i;       // Copy temp back to arr[]     for (i = 0; i < n; i++)         arr[i] = temp[i]; }   // A utility function to print contents of arr[0..n-1] void printArray(int arr[], int n) {     int i;     for (i = 0; i < n; i++)         cout << ("%d ", arr[i]);     cout << ("\n"); }   // Driver code int main() {     int arr[] = { 1, 3, 0, 2 };     int n = sizeof(arr) / sizeof(arr[0]);       cout << ("Given array is \n");     printArray(arr, n);       rearrangeNaive(arr, n);       cout << ("Modified array is \n");     printArray(arr, n);     return 0; }   // This code is contributed by Code_Mech

## C

 // A simple C program to rearrange contents of arr[] // such that arr[j] becomes j if arr[i] is j #include   // A simple method to rearrange 'arr[0..n-1]' so that 'arr[j]' // becomes 'i' if 'arr[i]' is 'j' void rearrangeNaive(int arr[], int n) {     // Create an auxiliary array of same size     int temp[n], i;       // Store result in temp[]     for (i = 0; i < n; i++)         temp[arr[i]] = i;       // Copy temp back to arr[]     for (i = 0; i < n; i++)         arr[i] = temp[i]; }   // A utility function to print contents of arr[0..n-1] void printArray(int arr[], int n) {     int i;     for (i = 0; i < n; i++)         printf("%d ", arr[i]);     printf("\n"); }   // Driver program int main() {     int arr[] = { 1, 3, 0, 2 };     int n = sizeof(arr) / sizeof(arr[0]);       printf("Given array is \n");     printArray(arr, n);       rearrangeNaive(arr, n);       printf("Modified array is \n");     printArray(arr, n);     return 0; }

## Java

 // A simple Java program to rearrange contents of arr[] // such that arr[j] becomes j if arr[i] is j import java.io.*; class RearrangeArray {     // A simple method to rearrange 'arr[0..n-1]' so that 'arr[j]'     // becomes 'i' if 'arr[i]' is 'j'     void rearrangeNaive(int arr[], int n)     {         // Create an auxiliary array of same size         int temp[] = new int[n];         int i;           // Store result in temp[]         for (i = 0; i < n; i++)             temp[arr[i]] = i;           // Copy temp back to arr[]         for (i = 0; i < n; i++)             arr[i] = temp[i];     }       // A utility function to print contents of arr[0..n-1]     void printArray(int arr[], int n)     {         int i;         for (i = 0; i < n; i++) {             System.out.print(arr[i] + " ");         }         System.out.println("");     }       // Driver program to test above functions     public static void main(String[] args)     {         RearrangeArray arrange = new RearrangeArray();         int arr[] = { 1, 3, 0, 2 };         int n = arr.length;           System.out.println("Given array is ");         arrange.printArray(arr, n);           arrange.rearrangeNaive(arr, n);           System.out.println("Modified array is ");         arrange.printArray(arr, n);     } }

## Python3

 # A simple Python3 program to rearrange # contents of arr[] such that arr[j] # becomes j if arr[i] is j   # A simple method to rearrange # 'arr[0..n-1]' so that 'arr[j]' # becomes 'i' if 'arr[i]' is 'j' def rearrangeNaive(arr, n):       # Create an auxiliary array     # of same size     temp = [0] * n           # Store result in temp[]     for i in range(0, n):         temp[arr[i]] = i       # Copy temp back to arr[]     for i in range(0, n):         arr[i] = temp[i]         # A utility function to print     # contents of arr[0..n-1] def printArray(arr, n):     for i in range(0, n):         print(arr[i], end = " ")   # Driver program arr = [1, 3, 0, 2] n = len(arr) print("Given array is", end = " ") printArray(arr, n)   rearrangeNaive(arr, n) print("\nModified array is", end = " ") printArray(arr, n)   # This code is contributed by Smitha Dinesh Semwal

## C#

 // A simple C# program to rearrange contents of arr[] // such that arr[j] becomes j if arr[i] is j   using System; class RearrangeArray {     // A simple method to rearrange 'arr[0..n-1]' so that 'arr[j]'     // becomes 'i' if 'arr[i]' is 'j'     void rearrangeNaive(int[] arr, int n)     {         // Create an auxiliary array of same size         int[] temp = new int[n];         int i;           // Store result in temp[]         for (i = 0; i < n; i++)             temp[arr[i]] = i;           // Copy temp back to arr[]         for (i = 0; i < n; i++)             arr[i] = temp[i];     }       // A utility function to print contents of arr[0..n-1]     void printArray(int[] arr, int n)     {         int i;         for (i = 0; i < n; i++) {             Console.Write(arr[i] + " ");         }         Console.WriteLine("");     }       // Driver program to test above functions     public static void Main()     {         RearrangeArray arrange = new RearrangeArray();         int[] arr = { 1, 3, 0, 2 };         int n = arr.Length;           Console.WriteLine("Given array is ");         arrange.printArray(arr, n);           arrange.rearrangeNaive(arr, n);           Console.WriteLine("Modified array is ");         arrange.printArray(arr, n);     } }

## Javascript



Output

Given array is
1302
Modified array is
2031

Time complexity: O(n)
Auxiliary space :O(n)

Can we solve this in O(n) time and O(1) auxiliary space?
The idea is based on the fact that the modified array is basically a permutation of the input array. We can find the target permutation by storing the next item before updating it.
Let us consider array ‘{1, 3, 0, 2}’ for example. We start with i = 0, arr[i] is 1. So we go to arr[1] and change it to 0 (because i is 0). Before we make the change, we store the old value of arr[1] as the old value is going to be our new index i. In the next iteration, we have i = 3, arr[3] is 2, so we change arr[2] to 3. Before making the change we store next i as old value of arr[2].

// This function works only when output is a permutation
// with one cycle.
void rearrangeUtil(int arr[], int n)
{
// 'val' is the value to be stored at 'arr[i]'
int val = 0;   // The next value is determined
// using current index
int i = arr[0];  // The next index is determined
// using current value

// While all elements in cycle are not processed
while (i != 0)
{
// Store value at index as it is going to be
// used as next index
int new_i = arr[i];

// Update arr[]
arr[i] = val;

// Update value and index for next iteration
val = i;
i = new_i;
}

arr[0] = val;  // Update the value at arr[0]
}

The above function doesn’t work for inputs like {2, 0, 1, 4, 5, 3}; as there are two cycles. One cycle is (2, 0, 1) and other cycle is (4, 5, 3).
How to handle multiple cycles with the O(1) space constraint?
The idea is to process all cycles one by one. To check whether an element is processed or not, we change the value of processed items arr[i] as -arr[i]. Since 0 can not be made negative, we first change all arr[i] to arr[i] + 1. In the end, we make all values positive and subtract 1 to get old values back.

## C++

 // A space efficient C++ program to rearrange contents of // arr[] such that arr[j] becomes j if arr[i] is j #include using namespace std;   // A utility function to rearrange elements in the cycle // starting at arr[i]. This function assumes values in // arr[] be from 1 to n. It changes arr[j-1] to i+1 // if arr[i-1] is j+1 void rearrangeUtil(int arr[], int n, int i) {     // 'val' is the value to be stored at 'arr[i]'     int val = -(i + 1); // The next value is determined     // using current index     i = arr[i] - 1; // The next index is determined     // using current value       // While all elements in cycle are not processed     while (arr[i] > 0)     {                   // Store value at index as it is going to be         // used as next index         int new_i = arr[i] - 1;           // Update arr[]         arr[i] = val;           // Update value and index for next iteration         val = -(i + 1);         i = new_i;     } }   // A space efficient method to rearrange 'arr[0..n-1]' // so that 'arr[j]' becomes 'i' if 'arr[i]' is 'j' void rearrange(int arr[], int n) {     // Increment all values by 1, so that all elements     // can be made negative to mark them as visited     int i;     for (i = 0; i < n; i++)         arr[i]++;       // Process all cycles     for (i = 0; i < n; i++)     {                   // Process cycle starting at arr[i] if this cycle is         // not already processed         if (arr[i] > 0)             rearrangeUtil(arr, n, i);     }       // Change sign and values of arr[] to get the original     // values back, i.e., values in range from 0 to n-1     for (i = 0; i < n; i++)         arr[i] = (-arr[i]) - 1; }   // A utility function to print contents of arr[0..n-1] void printArray(int arr[], int n) {     int i;     for (i = 0; i < n; i++)         cout << arr[i] << " ";     cout << endl; }   // Driver program int main() {     int arr[] = { 2, 0, 1, 4, 5, 3 };     int n = sizeof(arr) / sizeof(arr[0]);       cout << "Given array is " << endl;     printArray(arr, n);       rearrange(arr, n);       cout << "Modified array is " << endl;     printArray(arr, n);     return 0; }   // This code is contributed by shubhamsingh10

## C

 // A space efficient C program to rearrange contents of // arr[] such that arr[j] becomes j if arr[i] is j #include   // A utility function to rearrange elements in the cycle // starting at arr[i]. This function assumes values in // arr[] be from 1 to n.  It changes arr[j-1] to i+1 // if arr[i-1] is j+1 void rearrangeUtil(int arr[], int n, int i) {     // 'val' is the value to be stored at 'arr[i]'     int val = -(i + 1); // The next value is determined     // using current index     i = arr[i] - 1; // The next index is determined     // using current value       // While all elements in cycle are not processed     while (arr[i] > 0) {         // Store value at index as it is going to be         // used as next index         int new_i = arr[i] - 1;           // Update arr[]         arr[i] = val;           // Update value and index for next iteration         val = -(i + 1);         i = new_i;     } }   // A space efficient method to rearrange 'arr[0..n-1]' // so that 'arr[j]' becomes 'i' if 'arr[i]' is 'j' void rearrange(int arr[], int n) {     // Increment all values by 1, so that all elements     // can be made negative to mark them as visited     int i;     for (i = 0; i < n; i++)         arr[i]++;       // Process all cycles     for (i = 0; i < n; i++) {         // Process cycle starting at arr[i] if this cycle is         // not already processed         if (arr[i] > 0)             rearrangeUtil(arr, n, i);     }       // Change sign and values of arr[] to get the original     // values back, i.e., values in range from 0 to n-1     for (i = 0; i < n; i++)         arr[i] = (-arr[i]) - 1; }   // A utility function to print contents of arr[0..n-1] void printArray(int arr[], int n) {     int i;     for (i = 0; i < n; i++)         printf("%d ", arr[i]);     printf("\n"); }   // Driver program int main() {     int arr[] = { 2, 0, 1, 4, 5, 3 };     int n = sizeof(arr) / sizeof(arr[0]);       printf("Given array is \n");     printArray(arr, n);       rearrange(arr, n);       printf("Modified array is \n");     printArray(arr, n);     return 0; }

## Java

 // A space efficient Java program to rearrange contents of // arr[] such that arr[j] becomes j if arr[i] is j import java.io.*; class RearrangeArray {     // A utility function to rearrange elements in the cycle     // starting at arr[i]. This function assumes values in     // arr[] be from 1 to n.  It changes arr[j-1] to i+1     // if arr[i-1] is j+1     void rearrangeUtil(int arr[], int n, int i)     {         // 'val' is the value to be stored at 'arr[i]'           // The next value is determined using current index         int val = -(i + 1);           // The next index is determined         // using current value         i = arr[i] - 1;           // While all elements in cycle are not processed         while (arr[i] > 0) {             // Store value at index as it is going to be             // used as next index             int new_i = arr[i] - 1;               // Update arr[]             arr[i] = val;               // Update value and index for next iteration             val = -(i + 1);             i = new_i;         }     }       // A space efficient method to rearrange 'arr[0..n-1]'     // so that 'arr[j]' becomes 'i' if 'arr[i]' is 'j'     void rearrange(int arr[], int n)     {         // Increment all values by 1, so that all elements         // can be made negative to mark them as visited         int i;         for (i = 0; i < n; i++)             arr[i]++;           // Process all cycles         for (i = 0; i < n; i++) {             // Process cycle starting at arr[i] if this cycle is             // not already processed             if (arr[i] > 0)                 rearrangeUtil(arr, n, i);         }           // Change sign and values of arr[] to get the original         // values back, i.e., values in range from 0 to n-1         for (i = 0; i < n; i++)             arr[i] = (-arr[i]) - 1;     }       // A utility function to print contents of arr[0..n-1]     void printArray(int arr[], int n)     {         int i;         for (i = 0; i < n; i++)             System.out.print(arr[i] + " ");         System.out.println("");     }       // Driver program     public static void main(String[] args)     {         RearrangeArray arrange = new RearrangeArray();         int arr[] = { 2, 0, 1, 4, 5, 3 };         int n = arr.length;           System.out.println("Given array is ");         arrange.printArray(arr, n);           arrange.rearrange(arr, n);           System.out.println("Modified array is ");         arrange.printArray(arr, n);     } }

## Python3

 # A space efficient Python3 program to # rearrange contents of arr such that # arr[j] becomes j if arr[i] is j   # A utility function to rearrange elements # in the cycle starting at arr[i]. This # function assumes values in arr be from # 1 to n. It changes arr[j-1] to i+1 if # arr[i-1] is j+1 def rearrangeUtil(arr, n, i):           # 'val' is the value to be stored at      # 'arr[i]'     # The next value is determined using     # current index      val = -(i + 1)           # The next index is determined using     # current index     i = arr[i] - 1        # While all elements in cycle are     # not processed     while (arr[i] > 0):                   # Store value at index as it is         # going to be used as next index         new_i = arr[i] - 1                   # Update arr         arr[i] = val                   # Update value and index for         # next iteration         val = -(i + 1)         i = new_i   # A space efficient method to rearrange # 'arr[0..n-1]' so that 'arr[j]' becomes # 'i' if 'arr[i]' is 'j' def rearrange(arr, n):           # Increment all values by 1, so that     # all elements can be made negative to     # mark them as visited     for i in range(n):         arr[i] += 1               # Process all cycles     for i in range(n):                   # Process cycle starting at arr[i] if          # this cycle is not already processed         if (arr[i] > 0):             rearrangeUtil(arr, n, i)           # Change sign and values of arr to     # get the original values back, i.e.,      # values in range from 0 to n-1     for i in range(n):         arr[i] = (-arr[i]) - 1   # A utility function to print contents o # f arr[0..n-1] def printArray(arr, n):           for i in range(n):         print(arr[i], end = " ")     print()   # Driver code arr = [ 2, 0, 1, 4, 5, 3 ] n = len(arr)   print("Given array is ") printArray(arr, n)   rearrange(arr, n)   print("Modified array is ") printArray(arr, n)   # This code is contributed by shubhamsingh10

## C#

 // A simple C# program to // rearrange contents of arr[] // such that arr[j] becomes // j if arr[i] is j using System;   class GFG {     // A simple method to rearrange     // 'arr[0..n-1]' so that 'arr[j]'     // becomes 'i' if 'arr[i]' is 'j'     void rearrangeNaive(int[] arr,                         int n)     {         // Create an auxiliary         // array of same size         int[] temp = new int[n];         int i;           // Store result in temp[]         for (i = 0; i < n; i++)             temp[arr[i]] = i;           // Copy temp back to arr[]         for (i = 0; i < n; i++)             arr[i] = temp[i];     }       // A utility function to     // print contents of arr[0..n-1]     void printArray(int[] arr, int n)     {         int i;         for (i = 0; i < n; i++) {             Console.Write(arr[i] + " ");         }         Console.WriteLine("");     }       // Driver Code     public static void Main()     {         GFG arrange = new GFG();         int[] arr = { 2, 0, 1, 4, 5, 3 };         int n = arr.Length;           Console.WriteLine("Given array is ");         arrange.printArray(arr, n);           arrange.rearrangeNaive(arr, n);           Console.WriteLine("Modified array is ");         arrange.printArray(arr, n);     } }   // This code is contributed by anuj_67.

## Javascript



Output

Given array is
2 0 1 4 5 3
Modified array is
1 2 0 5 3 4

The time complexity of this method seems to be more than O(n) at first look. If we take a closer look, we can notice that no element is processed more than a constant number of times.

Another Method: The idea is to store each elementâ€™s new and old value as quotient and remainder of n, respectively (n being the size of the array).
For example, Suppose an elementâ€™s new value is 2, the old value is 1 and n is 3, then the elementâ€™s value is stored as 1 + 2*3 = 7. We can retrieve its old value by 7%3 = 1 and its new value by 7/3 = 2.
Thanks, Prateek Oraon for suggesting this method.

## C++

 // A simple C++ program to rearrange // contents of arr[] such that arr[j] // becomes j if arr[i] is j #include using namespace std;   // A simple method to rearrange // 'arr[0..n-1]' so that 'arr[j]' // becomes 'i' if 'arr[i]' is 'j' void rearrange(int arr[], int n) {     for (int i = 0; i < n; i++) {           // retrieving old value and         // storing with the new one         arr[arr[i] % n] += i * n;     }       for (int i = 0; i < n; i++) {           // retrieving new value         arr[i] /= n;     } }   // A utility function to print // contents of arr[0..n-1] void printArray(int arr[], int n) {     for (int i = 0; i < n; i++)         cout << arr[i] << " ";       cout << endl; }   // Driver program int main() {     int arr[] = { 2, 0, 1, 4, 5, 3 };     int n = sizeof(arr) / sizeof(arr[0]);       cout << "Given array is : " << endl;     printArray(arr, n);       rearrange(arr, n);       cout << "Modified array is :" << endl;     printArray(arr, n);       return 0; }

## Java

 // A simple JAVA program to rearrange // contents of arr[] such that arr[j] // becomes j if arr[i] is j import java.io.*; class GFG {       // A simple method to rearrange     // 'arr[0..n-1]' so that 'arr[j]'     // becomes 'i' if 'arr[i]' is 'j'     static void rearrange(int arr[], int n)     {         for (int i = 0; i < n; i++) {               // retrieving old value and             // storing with the new one             arr[arr[i] % n] += i * n;         }           for (int i = 0; i < n; i++) {               // retrieving new value             arr[i] /= n;         }     }       // A utility function to print     // contents of arr[0..n-1]     static void printArray(int arr[], int n)     {         for (int i = 0; i < n; i++) {             System.out.print(arr[i] + " ");         }           System.out.println();     }       // Driver code     public static void main(String[] args)     {         int arr[] = { 2, 0, 1, 4, 5, 3 };         int n = arr.length;           System.out.println("Given array is : ");         printArray(arr, n);           rearrange(arr, n);           System.out.println("Modified array is :");         printArray(arr, n);     } }   // This code has been contributed by 29AjayKumar

## Python3

 # A simple Python3 program to rearrange # contents of arr[] such that arr[j] # becomes j if arr[i] is j   # A simple method to rearrange # 'arr[0..n-1]' so that 'arr[j]' # becomes 'i' if 'arr[i]' is 'j' def rearrange(arr, n):           for i in range(n):                   # Retrieving old value and         # storing with the new one         arr[arr[i] % n] += i * n           for i in range(n):                   # Retrieving new value         arr[i] //= n       # A utility function to pr # contents of arr[0..n-1] def printArray(arr, n):           for i in range(n):         print(arr[i], end = " ")     print()   # Driver code arr = [2, 0, 1, 4, 5, 3] n = len(arr)   print("Given array is : ") printArray(arr, n)   rearrange(arr, n)   print("Modified array is :") printArray(arr, n)   # This code is contributed by shubhamsingh10

## C#

 // A simple C# program to rearrange // contents of arr[] such that arr[j] // becomes j if arr[i] is j using System;   class GFG{       // A simple method to rearrange     // 'arr[0..n-1]' so that 'arr[j]'     // becomes 'i' if 'arr[i]' is 'j'     static void rearrange(int[] arr, int n)     {         for (int i = 0; i < n; i++) {                   // retrieving old value and             // storing with the new one             arr[arr[i] % n] += i * n;         }               for (int i = 0; i < n; i++) {                   // retrieving new value             arr[i] /= n;         }     }           // A utility function to print     // contents of arr[0..n-1]     static void printArray(int[] arr, int n)     {         for (int i = 0; i < n; i++)             Console.Write(arr[i] + " ");               Console.WriteLine();     }           // Driver program     static public void Main ()     {         int[] arr = { 2, 0, 1, 4, 5, 3 };         int n = arr.Length;               Console.WriteLine("Given array is : ");         printArray(arr, n);               rearrange(arr, n);               Console.WriteLine("Modified array is :");         printArray(arr, n);     } }   // This code is contributed by shubhamsingh10

## Javascript



Output

Given array is :
2 0 1 4 5 3
Modified array is :
1 2 0 5 3 4

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