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:
4
Time complexity: O(NlogN)
Auxiliary Space: O(1)