Rank of all elements in a Stream in descending order when they arrive

Given a stream of numbers as arr, the task is to find the rank of each element in the stream in descending order when they arrive.  

Rank is defined as the total number of elements that is greater than the arriving element, where rank 1 defines the maximum value in the stream. Each value in the array is unique.

Examples:

Input: arr = [88, 14, 69, 30, 29, 89] 
Output: 1 2 2 3 4 1 
Explanation:
First 88 arrives, so its rank is 1. 
when 14 arrives, 14 is less than 88 so its rank is 2. 
when 69 arrives, 69 is less than 88 and greater than 14 so its rank is 2. 
when 30 arrives, 30 is less than 88 and 69 so its rank is 3. 
when 29 arrives, 29 is less than 88, 69, 30 than 29 so its rank is 4. 
when 89 arrives, 89 is greater than all values so its rank is 1. 
The rank of elements of array 1 2 2 3 4 1
Input: arr = [100, 110, 80, 85, 88, 89] 
Output: 1 1 3 3 3 3 
Explanation:
First 100 arrive so its rank is 1. 
when 110 arrive, 110 is greater than 100 so its rank is 1. 
when 80 arrive, 80 is less than 110 and 100 so its rank is 3. 
when 85 arrive, 85 is less than 110 and 100 so its rank is 3. 
when 88 arrive, 88 is less than 110 and 100 so its rank is 3. 
when 89 arrive, 89 is less than 110 and 100 so its rank is 3. 
The rank of elements of array 1 1 3 3 3 3 

Naive Approach:

1. The first element of the array will always have rank 1. 
   
2. Iterate over the array, if the element is greatest among previous elements then its rank is 1. 
   
3. If the element is not greatest than previous compared elements. then the rank of this element will be the number of greater elements before it.
   For example, lets say if it is greater than 2 previous elements so its rank is 3. 
   

Below is the implementation of the above approach:  

C++

// C++ program to rank of all elements
// in a Stream in descending order
// when they arrive
#include <iostream>
using namespace std;

    // FindRank function to find rank
        void FindRank(int arr[], int length)
    {
        // Rank of first element is always 1
        cout << "1" <<  " ";

        // Iterate over array
        for (int i = 1; i < length; i++)
        {
            // As element let say its rank is 1
            int rank = 1;

            // Element is compared
            // with previous elements
            for (int j = 0; j < i; j++)
            {
                // If greater than previous
                // than rank is incremented
                if(arr[j] > arr[i])
                    rank++;

            }

            // print rank
            cout <<  rank  << " ";
        }
    }




// Driver code
int main() {

        // array named arr
        int arr[] = {88, 14, 69, 30, 29, 89};

        // length of arr
        int len = sizeof(arr)/sizeof(arr[0]);

        FindRank(arr, len);

    return 0;
}

// This code is contributed by AnkitRai01

Java

// Java program to rank of all elements
// in a Stream in descending order
// when they arrive
import java.util.*;

class GFG{

    // FindRank function to find rank
    static void FindRank(int arr[], int length)
    {
        // Rank of first element is always 1
        System.out.print("1" + " ");

        // Iterate over array
        for (int i = 1; i < arr.length; i++)
        {
            // As element let say its rank is 1
            int rank = 1;

            // Element is compared
            // with previous elements
            for (int j = 0; j < i; j++)
            {
                // If greater than previous
                // than rank is incremented
                if(arr[j] > arr[i])
                    rank++;

            }

            // print rank
            System.out.print(rank + " ");
        }
    }

    // Driver code
    public static void main(String args[]){

        // array named arr
        int arr[] = {88, 14, 69, 30, 29, 89};

        // length of arr
        int len = arr.length;

        FindRank(arr, len);
    }
}

// This code is contributed by AbhiThakur

Python3

# Python program to rank of all elements
# in a Stream in descending order
# when they arrive

# FindRank function to find rank
def FindRank(arr, length):

    # Rank of first element is always 1
    print(1, end =" ")

    # Iterate over array
    for i in range(1, length):

        # As element let say its rank is 1
        rank = 1

        # Element is compared
        # with previous elements
        for j in range(0, i):

            # If greater than previous
            # than rank is incremented
            if(arr[j] > arr[i]):
                rank = rank + 1

        # print rank
        print(rank, end =" ")


# Driver code
if __name__ == '__main__':

    # array named arr
    arr = [88, 14, 69, 30, 29, 89]

    # length of arr
    length = len(arr)

    FindRank(arr, length)

C#

// C# program to rank of all elements
// in a Stream in descending order
// when they arrive
using System;

class GFG{

    // FindRank function to find rank
    static void FindRank(int[] arr, int length)
    {
        // Rank of first element is always 1
        Console.Write("1" + " ");

        // Iterate over array
        for (int i = 1; i < arr.Length; i++)
        {
            // As element let say its rank is 1
            int rank = 1;

            // Element is compared
            // with previous elements
            for (int j = 0; j < i; j++)
            {
                // If greater than previous
                // than rank is incremented
                if(arr[j] > arr[i])
                    rank++;

            }

            // print rank
            Console.Write(rank + " ");
        }
    }

    // Driver code
    public static void Main(){

        // array named arr
        int[] arr = {88, 14, 69, 30, 29, 89};

        // length of arr
        int len = arr.Length;

        FindRank(arr, len);
    }
}

// This code is contributed by AbhiThakur

Javascript

<script>
// javascript program to rank of all elements
// in a Stream in descending order
// when they arrive

    // FindRank function to find rank
    function FindRank(arr , length) {
        // Rank of first element is always 1
        document.write("1" + " ");

        // Iterate over array
        for (i = 1; i < arr.length; i++) {
            // As element let say its rank is 1
            var rank = 1;

            // Element is compared
            // with previous elements
            for (j = 0; j < i; j++) {
                // If greater than previous
                // than rank is incremented
                if (arr[j] > arr[i])
                    rank++;

            }

            // print rank
            document.write(rank + " ");
        }
    }

    // Driver code


        // array named arr
        var arr = [ 88, 14, 69, 30, 29, 89 ];

        // length of arr
        var len = arr.length;

        FindRank(arr, len);

// This code contributed by umadevi9616
</script>

Output:

1 2 2 3 4 1

Time complexity: O(N²), where N is length of array. 
Space complexity: O(1)
Efficient Approach: The idea is to use Binary search to find the rank of the number. It will give the count of numbers which are greater than the given number.
Below is the implementation of the above approach:

C++

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

void FindRank(int arr[], int length)
{

  // rank list to store values of
  // array in ascending order
  vector<int> rank;
  int first = arr[0];
  rank.push_back(first);

  // Rank of first element is always 1
  cout << 1 << " ";

  // Iterate over remaining array
  for (int i = 1; i < length; i++)
  {
    int val = arr[i];

    // element inserted in the rank list
    // using the binary method

    int ind = lower_bound(rank.begin(), rank.end(), val) - rank.begin();

    rank.insert(rank.begin() + ind, val);

    // To find rank of that element

    // length of rank array - index of element
    // in rank array
    int eleRank = rank.size() - ind;

    // print of rank of element of array
    cout << eleRank << " ";
  }
}

int main()
{
  int arr[] = {88, 14, 69, 30, 29, 89};
  int length = sizeof(arr) / sizeof(arr[0]);

  FindRank(arr, length);
}

// This code is contributed by akashish__

Java

/*package whatever //do not write package name here */
import java.util.*;

class GFG {

  static void FindRank(int arr[], int length){

    // rank list to store values of
    // array in ascending order
    List<Integer> rank = new ArrayList<>();
    int first = arr[0];
    rank.add(first);

    // Rank of first element is always 1
    System.out.print(1 + " ");

    //Iterate over remaining array
    for(int i=1;i<length;i++){
      int val = arr[i];

      // element inserted in the rank list
      // using the binary method

      int ind = Collections.binarySearch(rank,val);
      if(ind<0){
        ind = -ind-1;
      }else{
        ind++;
      }
      rank.add(ind,val);
      // To find rank of that element

      // length of rank array - index of element
      // in rank array
      int eleRank = rank.size()-rank.indexOf(val);

      // print of rank of element of array
      System.out.print(eleRank + " ");
    }
  }

  public static void main (String[] args)
  {

    int []arr = {88, 14, 69, 30, 29, 89};
    int length = arr.length;

    FindRank(arr, length);

  }
}

// This code is contributed by aadityaburujwale.

Python3

# Python program to rank of all elements
# in a Stream in descending order
# when they arrive

# import of bisect to use bisect.insort()
import bisect

# FindRank function to find rank
def FindRank(arr, length):
    # rank list to store values of
    # array in ascending order
    rank = []

    first = arr[0]
    rank.append(first)
    # Rank of first element is always 1
    print(1, end =" ")

    # Iterate over remaining array
    for i in range(1, length):
        val = arr[i]

        # element inserted in the rank list
        # using the binary method

        bisect.insort(rank, val)

        # To find rank of that element

        # length of rank array - index of element
        # in rank array
        eleRank = len(rank)-rank.index(val)

        # print of rank of element of array
        print(eleRank, end =" ")

# Driver code
if __name__ == '__main__':

    # array named arr
    arr = [88, 14, 69, 30, 29, 89]

    # length of arr
    length = len(arr)

    FindRank(arr, length)

C#

// Include namespace system
using System;
using System.Collections.Generic;

using System.Linq;

using System.Collections;

public class GFG
{
  public static void FindRank(int[] arr, int length)
  {

    // rank list to store values of
    // array in ascending order
    var rank = new List<int>();
    var first = arr[0];
    rank.Add(first);

    // Rank of first element is always 1
    Console.Write(1.ToString() + " ");

    // Iterate over remaining array
    for (int i = 1; i < length; i++)
    {
      var val = arr[i];

      // element inserted in the rank list
      // using the binary method
      var ind = rank.BinarySearch(val);
      if (ind < 0)
      {
        ind = -ind - 1;
      }
      else
      {
        ind++;
      }
      rank.Insert(ind,val);

      // To find rank of that element
      // length of rank array - index of element
      // in rank array
      var eleRank = rank.Count - rank.IndexOf(val);

      // print of rank of element of array
      Console.Write(eleRank.ToString() + " ");
    }
  }
  public static void Main(String[] args)
  {
    int[] arr = {88, 14, 69, 30, 29, 89};
    var length = arr.Length;
    GFG.FindRank(arr, length);
  }
}

// This code is contributed by aadityaburujwale.

Javascript

function lower_bound(arr, target){
    for(let i = 0; i < arr.length; i++)
    {
        if(arr[i] >= target)
            return i;
     }
     return arr.length;
 }

function findRank(arr, length) {
  // rank list to store values of
  // array in ascending order
  const rank = [];
  const first = arr[0];
  rank.push(first);

  // Rank of first element is always 1
  // console.log(1);
  let ans = "1 ";
  // Iterate over remaining array
  for (let i = 1; i < length; i++) {
    const val = arr[i];

    // element inserted in the rank list
    // using the binary method
    const ind = lower_bound(rank, val);

    rank.splice(ind, 0, val);

    // To find rank of that element

    // length of rank array - index of element
    // in rank array
    const eleRank = rank.length - ind;

    // print of rank of element of array
    // console.log(eleRank);
    ans+=eleRank.toString()+" ";
  }
  console.log(ans);
}

const arr = [88, 14, 69, 30, 29, 89];
const length = arr.length;

findRank(arr, length);
// This code is contributed by akashish__

Output:

1 2 2 3 4 1

Time complexity: O(N * log N), where N is length of array. 
Space complexity: O(N)