Convert an Array to reduced form using Hashing

Given an array with N distinct elements, convert the given array to a form where all elements are in the range from 0 to N-1. The order of elements is the same, i.e., 0 is placed in the place of the smallest element, 1 is placed for the second smallest element, ... N-1 is placed for the largest element. 

Examples:

Input:  arr[] = {10, 40, 20}
Output: arr[] = {0, 2, 1}

Input:  arr[] = {5, 10, 40, 30, 20}
Output: arr[] = {0, 1, 4, 3, 2}

Naive Approach:

A simple solution is to first find the minimum element, replace it with 0, consider the remaining array and find the minimum in the remaining array and replace it with 1, and so on.

• Iterate over the array
  • Find the minimum element and keep its position of occurrence.
  • Update the result at the minimum index element with the new Position
  • Increment the new position by 1.
  • Update the original element at the current minimum element with the maximum value possible, so that it won't be minimum in a further iteration
• Return the result

Below is the implementation of the above approach:

Given Array is 
10 20 15 12 11 50 

Converted Array is 
0 4 3 2 1 5 

Time complexity: O(N²)
Auxiliary space: O(N)

Efficient Approach:

The idea is to sort the given array and use an unordered map to store the reduced form of each value of array then update the whole array to its reduced form using values from unordered map.

Follow the below steps to implement the idea: 

• Create a temp array and copy the contents of the given array to temp[]. 
• Sort temp[] in ascending order. 
• Create an empty hash table.  
• Traverse temp[] from left to right and store mapping of numbers and their values (in converted array) in the hash table. 
• Traverse given array and change elements to their positions using a hash table. 

Below are implementations of the above idea. 

Given Array is 
10 20 15 12 11 50 

Converted Array is 
0 4 3 2 1 5 

Time complexity: O(N * log N)
Auxiliary Space: O(N)

Using priority_queue and hashmap:

The idea is to sort the given array using priority_queue instead of calling sort stl and use an unordered map to store the reduced form of each value of array then update the whole array to its reduced form using values from unordered map.

Algorithm:

1. Create a priority_queue pq to get the sorted version of arr in increasing order.
2. Push the values of arr in the priority queue.
3. Create a temp array and copy the contents of the priority_queue to temp[]. 
4. Create an empty hash table.  
5. Traverse temp[] from left to right and store mapping of numbers and their values (in converted array) in the hash table. 
6. Traverse given array and change elements to their positions using a hash table.

Below is the implementation of the approach:

Given Array is 
10 20 15 12 11 50 

Converted Array is 
0 4 3 2 1 5 

Time Complexity: O(N * log N) as insertion of N elements in priority_queue takes N*logN time. Here, N is size of the input array.

Space Complexity: O(N) as priority_queue pq and temp array has been created.

Convert an array to reduced form | Set 2 (Using vector of pairs)