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 maxint 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 codeint 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 maximport 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 maxfrom bisect import bisect_left as upper_bound# Function to remove minimum elements from the# array such that 2*min becomes more than maxdef 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 codea = [4, 5, 100, 9, 10, 11, 12, 15, 200]n = len(a)# Function callprint(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 maxusing 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:
4
Time complexity: O(NlogN)
Auxiliary Space: O(1)
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