Convert an Array to reduced form using Vector of pairs

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

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

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

We have discussed simple and hashing based solutions. In this post, a new solution is discussed. The idea is to create a vector of pairs. Every element of pair contains element and index. We sort vector by array values. After sorting, we copy indexes to original array. 

C++

#include <bits/stdc++.h>
using namespace std;

// Converts arr[0..n-1] to reduced form.
void convert(int arr[], int n)
{
    // A vector of pairs. Every element of
    // pair contains array element and its
    // index
    vector<pair<int, int> > v;

    // Put all elements and their index in
    // the vector
    for (int i = 0; i < n; i++)
        v.push_back(make_pair(arr[i], i));

    // Sort the vector by array values
    sort(v.begin(), v.end());

    // Put indexes of modified vector in arr[]
    for (int i = 0; i < n; i++)
        arr[v[i].second] = i;
}

// Utility function to print an array.
void printArr(int arr[], int n)
{
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
}

// Driver program to test above method
int main()
{
    int arr[] = { 10, 20, 15, 12, 11, 50 };
    int n = sizeof(arr) / sizeof(arr[0]);

    cout << "Given Array is \n";
    printArr(arr, n);

    convert(arr, n);

    cout << "\n\nConverted Array is \n";
    printArr(arr, n);

    return 0;
}

Java

// Java equivalent of the code
import java.util.*;

public class Main {

    // Converts arr[0..n-1] to reduced form.
    static void convert(int arr[], int n)
    {
        // A vector of pairs. Every element of
        // pair contains array element and its
        // index
        List<Pair> v = new ArrayList<>();

        // Put all elements and their index in
        // the vector
        for (int i = 0; i < n; i++)
            v.add(new Pair(arr[i], i));

        // Sort the vector by array values
        Collections.sort(v, new SortByVal());

        // Put indexes of modified vector in arr[]
        for (int i = 0; i < n; i++)
            arr[v.get(i).getIndex()] = i;
    }

    // Utility function to print an array.
    static void printArr(int arr[], int n)
    {
        for (int i = 0; i < n; i++)
            System.out.print(arr[i] + " ");
    }

    // Driver program to test above method
    public static void main (String[] args)
    {
        int arr[] = { 10, 20, 15, 12, 11, 50 };
        int n = arr.length;

        System.out.println("Given Array is \n");
        printArr(arr, n);

        convert(arr, n);

        System.out.println("\n\nConverted Array is \n");
        printArr(arr, n);
    }

    // class to store array elements and its
    // index.
    static class Pair {

        int val;
        int index;

        public Pair(int val, int index)
        {
            this.val = val;
            this.index = index;
        }

        public int getVal()
        {
            return val;
        }

        public int getIndex()
        {
            return index;
        }
    }

    // Comparator to sort the vector elements
    // according to their values
    static class SortByVal implements Comparator<Pair> {

        public int compare(Pair a, Pair b)
        {
            return a.getVal() - b.getVal();
        }
    }
}

Python3

# Converts arr[0..n-1] to reduced form.
def convert(arr, n):

    # A list of tuples. Every element of
    # tuple contains array element and its
    # index
    v = []

    # Put all elements and their index in
    # the list
    for i in range(n):
        v.append((arr[i], i))

    # Sort the list by array values
    v.sort()

    # Put indexes of modified list in arr[]
    for i in range(n):
        arr[v[i][1]] = i

# Utility function to print an array.
def printArr(arr, n):
    for i in range(n):
        print(arr[i], end=" ")

# Driver program to test above method
arr = [10, 20, 15, 12, 11, 50]
n = len(arr)

print("Given Array is ")
printArr(arr, n)

convert(arr, n)

print("\n\nConverted Array is ")
printArr(arr, n)

# This code is contributed by Prasad Kandekar(prasad264)

C#

using System;
using System.Collections.Generic;

public class Program {
    // Converts arr[0..n-1] to reduced form.
    static void Convert(int[] arr, int n)
    {
        // A list of pairs. Every element of pair contains
        // array element and its index
        List<Pair> v = new List<Pair>();

        // Put all elements and their index in the list
        for (int i = 0; i < n; i++)
            v.Add(new Pair(arr[i], i));

        // Sort the list by array values
        v.Sort(new SortByVal());

        // Put indexes of modified list in arr[]
        for (int i = 0; i < n; i++)
            arr[v[i].GetIndex()] = i;
    }

    // Utility function to print an array.
    static void PrintArr(int[] arr, int n)
    {
        for (int i = 0; i < n; i++)
            Console.Write(arr[i] + " ");
    }

    // Driver program to test above method
    public static void Main()
    {
        int[] arr = { 10, 20, 15, 12, 11, 50 };
        int n = arr.Length;

        Console.WriteLine("Given Array is ");
        PrintArr(arr, n);

        Convert(arr, n);

        Console.WriteLine("\n\nConverted Array is");
        PrintArr(arr, n);
    }

    // class to store array elements and its index.
    class Pair {
        int val;
        int index;

        public Pair(int val, int index)
        {
            this.val = val;
            this.index = index;
        }

        public int GetVal() { return val; }

        public int GetIndex() { return index; }
    }

    // Comparator to sort the list elements
    // according to their values
    class SortByVal : IComparer<Pair> {
        public int Compare(Pair a, Pair b)
        {
            return a.GetVal() - b.GetVal();
        }
    }
}

Javascript

// Converts arr[0..n-1] to reduced form.
function convert(arr, n) {

    // An array of pairs. Every element of
    // pair contains array element and its
    // index
    let v = [];

    // Put all elements and their index in
    // the array
    for (let i = 0; i < n; i++)
        v.push([arr[i], i]);

    // Sort the array by array values
    v.sort((a, b) => a[0] - b[0]);

    // Put indexes of modified array in arr[]
    for (let i = 0; i < n; i++)
        arr[v[i][1]] = i;
}

// Utility function to print an array.
function printArr(arr, n) {
    for (let i = 0; i < n; i++)
        console.log(arr[i] + " ");
}

// Driver program to test above method
let arr = [10, 20, 15, 12, 11, 50];
let n = arr.length;

console.log("Given Array is ");
printArr(arr, n);

convert(arr, n);

console.log("\n\nConverted Array is ");
printArr(arr, n);

// This code is contributed by prasad264

Output

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) 

Another Approach:

1) Create a copy of the input array and sort it in non-decreasing order.
2) Create a map where each element of the sorted array is mapped to its corresponding index in the range 0 to n-1.
3) Traverse the input array and for each element, replace it with the value obtained from the map.

C++

#include <bits/stdc++.h>
using namespace std;

// Converts arr[0..n-1] to reduced form.
void convert(int arr[], int n)
{
    // Make a copy of the input array
    int sorted_arr[n];
    copy(arr, arr+n, sorted_arr);

    // Sort the copy in non-decreasing order
    sort(sorted_arr, sorted_arr+n);

    // Map each element of the sorted array to its index in the range 0 to n-1
    unordered_map<int, int> mp;
    for (int i = 0; i < n; i++) {
        mp[sorted_arr[i]] = i;
    }

    // Replace each element of the input array with its corresponding index
    for (int i = 0; i < n; i++) {
        arr[i] = mp[arr[i]];
    }
}

// Utility function to print an array.
void printArr(int arr[], int n)
{
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
}

// Driver program to test above method
int main()
{
    int arr[] = { 10, 20, 15, 12, 11, 50 };
    int n = sizeof(arr) / sizeof(arr[0]);

    cout << "Given Array is \n";
    printArr(arr, n);

    convert(arr, n);

    cout << "\n\nConverted Array is \n";
    printArr(arr, n);

    return 0;
}

Java

import java.util.*;

public class Main {
    // Converts arr[0..n-1] to reduced form.
    public static void convert(int arr[], int n)
    {
        // Make a copy of the input array
        int[] sorted_arr = Arrays.copyOf(arr, n);

        // Sort the copy in non-decreasing order
        Arrays.sort(sorted_arr);

        // Map each element of the sorted array to its index
        // in the range 0 to n-1
        HashMap<Integer, Integer> mp
            = new HashMap<Integer, Integer>();
        for (int i = 0; i < n; i++) {
            mp.put(sorted_arr[i], i);
        }

        // Replace each element of the input array with its
        // corresponding index
        for (int i = 0; i < n; i++) {
            arr[i] = mp.get(arr[i]);
        }
    }

    // Utility function to print an array.
    public static void printArr(int arr[], int n)
    {
        for (int i = 0; i < n; i++) {
            System.out.print(arr[i] + " ");
        }
    }

    // Driver program to test above method
    public static void main(String[] args)
    {
        int arr[] = { 10, 20, 15, 12, 11, 50 };
        int n = arr.length;

        System.out.println("Given Array is ");
        printArr(arr, n);

        convert(arr, n);

        System.out.println("\n\nConverted Array is ");
        printArr(arr, n);
    }
}
// This code is contributed by Prajwal Kandekar

Python3

def convert(arr, n):
    # Make a copy of the input array
    sorted_arr = arr.copy()

    # Sort the copy in non-decreasing order
    sorted_arr.sort()

    # Map each element of the sorted array to its index in the range 0 to n-1
    mp = {}
    for i in range(n):
        mp[sorted_arr[i]] = i

    # Replace each element of the input array with its corresponding index
    for i in range(n):
        arr[i] = mp[arr[i]]


def print_arr(arr, n):
    for i in range(n):
        print(arr[i], end=' ')
    print()


# Driver program to test above method
if __name__ == '__main__':
    arr = [10, 20, 15, 12, 11, 50]
    n = len(arr)

    print("Given Array is ")
    print_arr(arr, n)

    convert(arr, n)

    print("\nConverted Array is ")
    print_arr(arr, n)
# This code is contributed by Prajwal Kandekar

Javascript

function convert(arr, n) {
  // Make a copy of the input array
  let sorted_arr = [...arr];

  // Sort the copy in non-decreasing order
  sorted_arr.sort((a, b) => a - b);

  // Map each element of the sorted array to its index in the range 0 to n-1
  let mp = {};
  for (let i = 0; i < n; i++) {
    mp[sorted_arr[i]] = i;
  }

  // Replace each element of the input array with its corresponding index
  for (let i = 0; i < n; i++) {
    arr[i] = mp[arr[i]];
  }
}

function print_arr(arr, n) {
  for (let i = 0; i < n; i++) {
    process.stdout.write(`${arr[i]} `);
  }
  console.log();
}

// Driver program to test above method
let arr = [10, 20, 15, 12, 11, 50];
let n = arr.length;

process.stdout.write("Given Array is \n");
print_arr(arr, n);

convert(arr, n);

process.stdout.write("\nConverted Array is \n");
print_arr(arr, n);

Output

Given Array is 
10 20 15 12 11 50 

Converted Array is 
0 4 3 2 1 5 

Time Complexity: O(n log n) where n is the size of the input array. This is because the function creates a copy of the input array using the “copy” function, which takes O(n) time, sorts the copy using the “sort” function, which has a time complexity of O(n log n)

Space Complexity: O(n) we are using extra space as a map.

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