Convert an Array to reduced form using Vector of pairs
Last Updated :
23 Jul, 2025
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 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();
}
}
}
# 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)
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();
}
}
}
// 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
OutputGiven 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;
}
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
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
using System;
using System.Collections.Generic;
public class GFG {
// Converts arr[0..n-1] to reduced form.
static void Convert(int[] arr, int n)
{
// Make a copy of the input array
int[] sortedArr = new int[n];
Array.Copy(arr, sortedArr, n);
// Sort the copy in ascending order
Array.Sort(sortedArr);
// Map each element of the sorted array to its index
// in the range 0 to n-1
Dictionary<int, int> mp
= new Dictionary<int, int>();
for (int i = 0; i < n; i++) {
mp.Add(sortedArr[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.
static void PrintArr(int[] arr, int n)
{
for (int i = 0; i < n; i++) {
Console.Write(arr[i] + " ");
}
}
// Driver program to test above method
static public 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);
}
}
//This code is contributed by Rohit Singh
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);
OutputGiven 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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