Remove minimum elements from the array such that 2*min becomes more than max

0 0 4 minutes read

Given an array of size N. The task is to remove minimum elements from the array such that twice of minimum number is greater than the maximum number in the modified array. Print the minimum number of elements removed.
Examples:

Input: arr[] = {4, 5, 100, 9, 10, 11, 12, 15, 200}
Output: 4
Remove 4 elements (4, 5, 100, 200)
so that 2*min becomes more than max.
Input: arr[] = {4, 7, 5, 6}
Output: 0

Approach:

sort the given array
Traverse from left to right in the array and for each element chosen (let it be x) with the index i, find the upper_bound of (2*x). let that index be j. Then, update our required answer by (n-j+i) if (n-j+i) is less than current value of our answer.

Below is the implementation of the above approach :

C++

// CPP program to remove minimum elements from the
// array such that 2*min becomes more than max
#include <bits/stdc++.h>
using namespace std;
 
// Function to remove minimum elements from the
// array such that 2*min becomes more than max
int Removal(vector<int> v, int n)
{
    // Sort the array
    sort(v.begin(), v.end());
 
    // To store the required answer
    int ans = INT_MAX;
 
    // Traverse from left to right
    for (vector<int>::iterator i = v.begin(); i != v.end(); 
                                                     i++) {
 
        vector<int>::iterator j = upper_bound(v.begin(), 
                                    v.end(), (2 * (*i)));
 
        // Update the answer
        ans = min(ans, n - (int)(j - i));
    }
 
    // Return the required answer
    return ans;
}
 
// Driver code
int main()
{
    vector<int> a = { 4, 5, 100, 9, 10, 11, 12, 15, 200 };
 
    int n = a.size();
 
    // Function call
    cout << Removal(a, n);
 
    return 0;
}

Java

// Java program to remove minimum elements from the 
// array such that 2*min becomes more than max
import java.util.Arrays;
 
class GFG 
{
 
    // Function to calculate upper bound
    public static int upperBound(int[] array,
                                 int value)
    {
        int low = 0;
        int high = array.length;
        while (low < high) 
        {
            final int mid = (low + high) / 2;
            if (value >= array[mid]) 
            {
                low = mid + 1;
            } 
            else
            {
                high = mid;
            }
        }
        return low;
    }
 
    // Function to remove minimum elements from the
    // array such that 2*min becomes more than max
    public static int Removal(int[] v, int n) 
    {
 
        // Sort the array
        Arrays.sort(v);
 
        // To store the required answer
        int ans = Integer.MAX_VALUE;
        int k = 0;
 
        // Traverse from left to right
        for (int i : v) 
        {
            int j = upperBound(v, (2 * i));
 
            // Update the answer
            ans = Math.min(ans, n - (j - k));
            k++;
        }
 
        // Return the required answer
        return ans;
    }
 
    // Driver code
    public static void main(String[] args) 
    {
        int[] a = { 4, 5, 100, 9, 10, 
                    11, 12, 15, 200 };
        int n = a.length;
 
        // Function call
        System.out.println(Removal(a, n));
    }
}
 
// This code is contributed by
// sanjeev2552

Python3

# Python3 program to remove minimum elements from the
# array such that 2*min becomes more than max
from bisect import bisect_left as upper_bound
 
# Function to remove minimum elements from the
# array such that 2*min becomes more than max
def Removal(v, n):
     
    # Sort the array
    v = sorted(v)
 
    # To store the required answer
    ans = 10**9
 
    # Traverse from left to right
    for i in range(len(v)):
        j = upper_bound(v, (2 * (a[i])))
 
        # Update the answer
        ans = min(ans, n - (j - i - 1))
 
    # Return the required answer
    return ans
 
# Driver code
a = [4, 5, 100, 9, 10, 11, 12, 15, 200]
 
n = len(a)
 
# Function call
print(Removal(a, n))
 
# This code is contributed by Mohit Kumar

C#

// C# program to remove minimum elements 
// from the array such that 2*min becomes
// more than max
using System;
 
class GFG 
{
 
    // Function to calculate upper bound
    public static int upperBound(int[] array,
                                 int value)
    {
        int low = 0;
        int high = array.Length;
        while (low < high) 
        {
            int mid = (low + high) / 2;
            if (value >= array[mid]) 
            {
                low = mid + 1;
            } 
            else
            {
                high = mid;
            }
        }
        return low;
    }
 
    // Function to remove minimum elements from the
    // array such that 2*min becomes more than max
    public static int Removal(int[] v, int n) 
    {
 
        // Sort the array
        Array.Sort(v);
 
        // To store the required answer
        int ans = int.MaxValue;
        int k = 0;
 
        // Traverse from left to right
        foreach (int i in v) 
        {
            int j = upperBound(v, (2 * i));
 
            // Update the answer
            ans = Math.Min(ans, n - (j - k));
            k++;
        }
 
        // Return the required answer
        return ans;
    }
 
    // Driver code
    public static void Main(String[] args) 
    {
        int[] a = { 4, 5, 100, 9, 10, 
                    11, 12, 15, 200 };
        int n = a.Length;
 
        // Function call
        Console.WriteLine(Removal(a, n));
    }
}
 
// This code is contributed by Rajput-Ji

Javascript

<script>
 
      // JavaScript program to remove minimum elements
      // from the array such that 2*min becomes
      // more than max
 
      // Function to calculate upper bound
      function upperBound(array, value) {
        var low = 0;
        var high = array.length;
        while (low < high) {
          var mid = parseInt((low + high) / 2);
          if (value >= array[mid]) {
            low = mid + 1;
          } else {
            high = mid;
          }
        }
        return low;
      }
 
      // Function to remove minimum elements from the
      // array such that 2*min becomes more than max
      function Removal(v, n) {
        // Sort the array
        v.sort((a, b) => a - b);
 
        // To store the required answer
        var ans = 2147483648;
        var k = 0;
 
        // Traverse from left to right
        for (const i of v) {
          var j = upperBound(v, 2 * i);
 
          // Update the answer
          ans = Math.min(ans, n - (j - k));
          k++;
        }
 
        // Return the required answer
        return ans;
      }
 
      // Driver code
      var a = [4, 5, 100, 9, 10, 11, 12, 15, 200];
      var n = a.length;
 
      // Function call
      document.write(Removal(a, n));
       
</script>

Output:

Time complexity: O(NlogN)

Auxiliary Space: O(1)

Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 zambiatek!