Given an array arr[] of N integers, the task is to replace each element of Array with their rank in array.
The rank of an element is defined as the distance between the element with the first element of the array when the array is arranged in ascending order. If two or more are same in the array then their rank is also the same as the rank of the first occurrence of the element.
For Example: Let the given array arr[] = {2, 2, 1, 6}, then rank of elements is given by:
sorted array is:
arr[] = {1, 2, 2, 6}
Rank(1) = 1 (at index 0)
Rank(2) = 2 (at index 1)
Rank(2) = 2 (at index 2)
Rank(6) = 4 (at index 3)
Examples:
Input: arr[] = [100, 5, 70, 2]
Output: [4, 2, 3, 1]
Explanation:
Rank of 2 is 1, 5 is 2, 70 is 3 and 100 is 4.
Input: arr[] = [100, 2, 70, 2]
Output: [3, 1, 2, 1]
Explanation:
Rank of 2 is 1, 70 is 2 and 100 is 3.
Naive Approach: The naive approach is to find the rank of each element is 1 + the count of smaller elements in the array for the current element.
Time Complexity: O(N2)
Auxiliary Space: O(1)
Efficient Approach: To optimize the above naive approach find ranks of elements and then assign the rank to the elements. Below are the steps:
- To compute the rank of the element first make a copy of given arr[] then sort that copied array in ascending order.
- Then traverse in the copied array and put their rank in HashMap by taking a rank variable.
- If the element is already present in HashMap then don’t update rank otherwise update rank of the element in HashMap and increment rank variable as well.
- Traverse the given array arr[] assign the rank of each element using the rank stored in HashMap.
Below is the implementation of the above approach:
// C++ program for the above approach #include <bits/stdc++.h> using namespace std;
// Function to assign rank to // array elements void changeArr( int input[], int N)
{ // Copy input array into newArray
int newArray[N];
copy(input, input + N, newArray);
// Sort newArray[] in ascending order
sort(newArray, newArray + N);
int i;
// Map to store the rank of
// the array element
map< int , int > ranks;
int rank = 1;
for ( int index = 0; index < N; index++)
{
int element = newArray[index];
// Update rank of element
if (ranks[element] == 0)
{
ranks[element] = rank;
rank++;
}
}
// Assign ranks to elements
for ( int index = 0; index < N; index++)
{
int element = input[index];
input[index] = ranks[input[index]];
}
} // Driver code int main()
{ // Given array arr[]
int arr[] = { 100, 2, 70, 2 };
int N = sizeof (arr) / sizeof (arr[0]);
// Function call
changeArr(arr, N);
// Print the array elements
cout << "[" ;
for ( int i = 0; i < N - 1; i++)
{
cout << arr[i] << ", " ;
}
cout << arr[N - 1] << "]" ;
return 0;
} // This code is contributed by divyeshrabadiya07 |
// Java program for the above approach import java.util.*;
class GFG {
// Function to assign rank to
// array elements
static void changeArr( int [] input)
{
// Copy input array into newArray
int newArray[]
= Arrays
.copyOfRange(input,
0 ,
input.length);
// Sort newArray[] in ascending order
Arrays.sort(newArray);
int i;
// Map to store the rank of
// the array element
Map<Integer, Integer> ranks
= new HashMap<>();
int rank = 1 ;
for ( int index = 0 ;
index < newArray.length;
index++) {
int element = newArray[index];
// Update rank of element
if (ranks.get(element) == null ) {
ranks.put(element, rank);
rank++;
}
}
// Assign ranks to elements
for ( int index = 0 ;
index < input.length;
index++) {
int element = input[index];
input[index]
= ranks.get(input[index]);
}
}
// Driver Code
public static void main(String[] args)
{
// Given array arr[]
int [] arr = { 100 , 2 , 70 , 2 };
// Function Call
changeArr(arr);
// Print the array elements
System
.out
.println(Arrays
.toString(arr));
}
} |
# Python3 program for the above approach # Function to assign rank to # array elements def changeArr(input1):
# Copy input array into newArray
newArray = input1.copy()
# Sort newArray[] in ascending order
newArray.sort()
# Dictionary to store the rank of
# the array element
ranks = {}
rank = 1
for index in range ( len (newArray)):
element = newArray[index];
# Update rank of element
if element not in ranks:
ranks[element] = rank
rank + = 1
# Assign ranks to elements
for index in range ( len (input1)):
element = input1[index]
input1[index] = ranks[input1[index]]
# Driver Code if __name__ = = "__main__" :
# Given array arr[]
arr = [ 100 , 2 , 70 , 2 ]
# Function call
changeArr(arr)
# Print the array elements
print (arr)
# This code is contributed by chitranayal |
// C# program for the above approach using System;
using System.Collections.Generic;
using System.Text;
class GFG{
// Function to assign rank to // array elements static void changeArr( int [] input)
{ // Copy input array into newArray
int []newArray = new int [input.Length];
Array.Copy(input, newArray, input.Length);
// Sort newArray[] in ascending order
Array.Sort(newArray);
// To store the rank of
// the array element
Dictionary< int ,
int > ranks= new Dictionary< int ,
int >();
int rank = 1;
for ( int index = 0;
index < newArray.Length;
index++)
{
int element = newArray[index];
// Update rank of element
if (!ranks.ContainsKey(element))
{
ranks[element] = rank;
rank++;
}
}
// Assign ranks to elements
for ( int index = 0;
index < input.Length;
index++)
{
input[index] = ranks[input[index]];
}
} // Driver Code public static void Main( string [] args)
{ // Given array arr[]
int [] arr = { 100, 2, 70, 2 };
// Function call
changeArr(arr);
// Print the array elements
Console.WriteLine( "[{0}]" ,
string .Join( ", " , arr));
} } // This code is contributed by rutvik_56 |
<script> // Javascript program for the above approach // Function to assign rank to // array elements function changeArr(input, N)
{ // Copy input array into newArray
var newArray = JSON.parse(JSON.stringify(input));
// Sort newArray[] in ascending order
newArray.sort((a,b)=> a-b);
var i;
// Map to store the rank of
// the array element
var ranks = new Map();
var rank = 1;
for ( var index = 0; index < N; index++)
{
var element = newArray[index];
// Update rank of element
if (!ranks.has(element))
{
ranks.set(element, rank);
rank++;
}
}
// Assign ranks to elements
for ( var index = 0; index < N; index++)
{
var element = input[index];
input[index] = ranks.get(input[index]);
}
return input;
} // Driver code // Given array arr[] var arr = [100, 2, 70, 2];
var N = arr.length;
// Function call arr = changeArr(arr, N); // Print the array elements document.write( "[" );
for ( var i = 0; i < N - 1; i++)
{ document.write( arr[i] + ", " );
} document.write( arr[N - 1] + "]" );
// This code is contributed by famously. </script> |
[3, 1, 2, 1]
Time Complexity: O(N * log N)
Auxiliary Space: O(N)