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Find K for every Array element such that at least K prefixes are ≥ K

  • Difficulty Level : Hard
  • Last Updated : 27 May, 2021

Given an array arr[] consisting of N non-negative integers, the task is to find an integer K for every index such that at least K integers in the array till that index are greater or equal to K.

Note: Consider 1-based indexing

Examples:

Input: arr[] = {3, 0, 6, 1, 5} 
Output: K = {1, 1, 2, 2, 3} 
Explanation: 
At index 1, there is 1 number greater than or equal to 1 in the array i.e. 3. So the K value for elements up to index 1 is 1. 
At index 2, there is 1 number greater than or equal to 1 in the array i.e. 3. So the K value for elements up to index 2 is 1. 
At index 3, there are 2 numbers greater than or equal to 2 in the array, i.e. 3 and 6. So the K value for elements up to index 3 is 2. 
At index 4, there are 2 numbers greater than or equal to 2 in the array, i.e. 3 and 6. So the K value for elements up to index 4 is 2. 
At index 5, there are 3 numbers greater than or equal to 3 in the array, i.e. 3, 6 and 5. So the K value for elements up to index 5 is 3.

Input: arr[] = {9, 10, 7, 5, 0, 10, 2, 0} 
Output: K = {1, 2, 3, 4, 4, 5, 5, 5}



Naive Approach: 
The simplest approach is to find the value of K for all the elements of the array in the range [0, i], where i is the index of the array arr[], using the efficient approach used in the article link is given here

Time Complexity: O(N2
Space Complexity: O(N)

Efficient Approach: 
The idea is to use Multiset(Red-Black Tree). Multiset stores the values in a sorted order which helps to check if the current minimum value in the multiset is greater than or equal to its size. If yes, then the value of the integer K will be the size of the multiset. 

Below are the steps for the implementation:

  1. Traverse the array from index 0 to N-1.
  2. For each index, insert the element into the multiset and check if the smallest value in the multiset is less than the size of the multiset.
  3. If true, then erase the starting element and print the size of the multiset.
  4. If false, then simply print the size of the multiset.
  5. The size of the multiset is the required K value for every index i.

Below is the implementation of the above approach:

C++




// C++ program for the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the K-value
// for every index in the array
int print_h_index(int arr[], int N)
{
    // Multiset to store the array
    // in the form of red-black tree
    multiset<int> ms;
 
    // Iterating over the array
    for (int i = 0; i < N; i++) {
 
        // Inserting the current
        // value in the multiset
        ms.insert(arr[i]);
 
        // Condition to check if
        // the smallest value
        // in the set is less than
        // it's size
        if (*ms.begin()
            < ms.size()) {
 
            // Erase the smallest
            // value
            ms.erase(ms.begin());
        }
 
        // h-index value will be
        // the size of the multiset
        cout << ms.size() << " ";
    }
}
 
// Driver Code
int main()
{
 
    // array
    int arr[] = { 9, 10, 7, 5, 0,
                10, 2, 0 };
 
    // Size of the array
    int N = sizeof(arr)
            / sizeof(arr[0]);
 
    // function call
    print_h_index(arr, N);
 
    return 0;
}

Java




// Java program for the above approach
import java.util.*;
 
class GFG{
     
// Function to find the K-value
// for every index in the array
static void print_h_index(int arr[], int N)
{
     
    // Multiset to store the array
    // in the form of red-black tree
    List<Integer> ms = new ArrayList<Integer>();
 
    // Iterating over the array
    for(int i = 0; i < N; i++)
    {
         
        // Inserting the current
        // value in the multiset
        ms.add(arr[i]);
 
        // Condition to check if
        // the smallest value
        // in the set is less than
        // it's size
        int t = Collections.min(ms);
        if (t < ms.size())
        {
 
            // Erase the smallest
            // value
            ms.remove(ms.indexOf(t));
        }
 
        // h-index value will be
        // the size of the multiset
        System.out.print(ms.size() + " ");
    }
}
 
// Driver code
public static void main(String[] args)
{
     
    // Array
    int arr[] = { 9, 10, 7, 5, 0,
                10, 2, 0 };
     
    // Size of the array
    int N = arr.length;
     
    // Function call
    print_h_index(arr, N);
}
}
 
// This code is contributed by offbeat

Python3




# Python3 program for the above approach
  
# Function to find the K-value
# for every index in the array
def print_h_index(arr, N):
 
    # Multiset to store the array
    # in the form of red-black tree
    ms = []
  
    # Iterating over the array
    for i in range(N):
  
        # Inserting the current
        # value in the multiset
        ms.append(arr[i])
        ms.sort()
         
        # Condition to check if
        # the smallest value
        # in the set is less than
        # it's size
        if (ms[0] < len(ms)):
  
            # Erase the smallest
            # value
            ms.pop(0)
  
        # h-index value will be
        # the size of the multiset
        print(len(ms), end = ' ')
         
# Driver Code
if __name__=='__main__':
 
    # Array
    arr = [ 9, 10, 7, 5, 0, 10, 2, 0 ]
  
    # Size of the array
    N = len(arr)
  
    # Function call
    print_h_index(arr, N)
 
# This code is contributed by pratham76

C#




// C# program for the above approach
using System;
using System.Collections;
using System.Collections.Generic;
 
class GFG{
     
// Function to find the K-value
// for every index in the array
static void print_h_index(int []arr, int N)
{
     
    // Multiset to store the array
    // in the form of red-black tree
    ArrayList ms = new ArrayList();
 
    // Iterating over the array
    for(int i = 0; i < N; i++)
    {
         
        // Inserting the current
        // value in the multiset
        ms.Add(arr[i]);
 
        // Condition to check if
        // the smallest value
        // in the set is less than
        // it's size
        int t = int.MaxValue;
        foreach(int x in ms)
        {
            if(x < t)
            {
                t = x;
            }
        }
         
        if (t < ms.Count)
        {
             
            // Erase the smallest
            // value
            ms.Remove(t);
        }
 
        // h-index value will be
        // the size of the multiset
        Console.Write(ms.Count + " ");
    }
}
 
// Driver code
public static void Main(string[] args)
{
     
    // Array
    int []arr = { 9, 10, 7, 5, 0,
                  10, 2, 0 };
     
    // Size of the array
    int N = arr.Length;
     
    // Function call
    print_h_index(arr, N);
}
}
 
// This code is contributed by rutvik_56

Javascript




<script>
 
// Javascript program for the above approach
 
// Function to find the K-value
// for every index in the array
function print_h_index(arr, N)
{
    // Multiset to store the array
    // in the form of red-black tree
    var ms = []; 
 
    // Iterating over the array
    for (var i = 0; i < N; i++) {
 
        // Inserting the current
        // value in the multiset
        ms.push(arr[i]);
        ms.sort((a,b)=> a-b)
        // Condition to check if
        // the smallest value
        // in the set is less than
        // it's size
        if (ms[0]
            < ms.length) {
 
            // Erase the smallest
            // value
            ms.shift();
        }
 
        // h-index value will be
        // the size of the multiset
        document.write( ms.length + " ");
    }
}
 
// Driver Code
// array
var arr = [9, 10, 7, 5, 0,
            10, 2, 0 ];
// Size of the array
var N = arr.length;
// function call
print_h_index(arr, N);
 
</script>
Output: 
1 2 3 4 4 5 5 5

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




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