# Remove minimum elements from array so that max <= 2 * min

Given an array **arr**, the task is to remove minimum number of elements such that after their removal, **max(arr) <= 2 * min(arr)**.

**Examples:**

Input:arr[] = {4, 5, 3, 8, 3}

Output:1

Remove 8 from the array.

Input:arr[] = {1, 2, 3, 4}

Output:1

Remove 1 from the array.

**Approach:** Let us fix each value as the minimum value say **x** and find number of terms that are in range **[x, 2*x]**. This can be done using prefix-sums, we can use map (implements self balancing BST) instead of array as the values can be large. The remaining terms which are not in range **[x, 2*x]** will have to be removed. So, across all values of **x**, we choose the one which maximises the number of terms in range **[x, 2*x]**.

Below is the implementation of the above approach:

`// C++ implementation of the approach ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to return the minimum removals from ` `// arr such that max(arr) <= 2 * min(arr) ` `int` `minimumRemovals(` `int` `n, ` `int` `a[]) ` `{ ` ` ` `// Count occurrence of each element ` ` ` `map<` `int` `, ` `int` `> ct; ` ` ` `for` `(` `int` `i = 0; i < n; i++) ` ` ` `ct[a[i]]++; ` ` ` ` ` `// Take prefix sum ` ` ` `int` `sm = 0; ` ` ` `for` `(` `auto` `mn : ct) { ` ` ` `sm += mn.second; ` ` ` `ct[mn.first] = sm; ` ` ` `} ` ` ` ` ` `int` `mx = 0, prev = 0; ` ` ` `for` `(` `auto` `mn : ct) { ` ` ` ` ` `// Chosen minimum ` ` ` `int` `x = mn.first; ` ` ` `int` `y = 2 * x; ` ` ` `auto` `itr = ct.upper_bound(y); ` ` ` `itr--; ` ` ` ` ` `// Number of elements that are in ` ` ` `// range [x, 2x] ` ` ` `int` `cr = (itr->second) - prev; ` ` ` `mx = max(mx, cr); ` ` ` `prev = mn.second; ` ` ` `} ` ` ` ` ` `// Minimum elements to be removed ` ` ` `return` `n - mx; ` `} ` ` ` `// Driver Program to test above function ` `int` `main() ` `{ ` ` ` `int` `arr[] = { 4, 5, 3, 8, 3 }; ` ` ` `int` `n = ` `sizeof` `(arr) / ` `sizeof` `(arr[0]); ` ` ` `cout << minimumRemovals(n, arr); ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

**Output:**

1

## Recommended Posts:

- Remove minimum elements from the array such that 2*min becomes more than max
- Remove minimum elements from array such that no three consecutive element are either increasing or decreasing
- Remove minimum number of elements such that no common element exist in both array
- Remove minimum elements from either side such that 2*min becomes more than max | Set 2
- Remove minimum elements from either side such that 2*min becomes more than max
- Flip minimum signs of array elements to get minimum sum of positive elements possible
- Remove exactly one element from the array such that max - min is minimum
- Minimum operations required to remove an array
- Remove elements from the array which appear more than k times
- Remove duplicate elements in an Array using STL in C++
- Remove elements to make array sorted
- Remove elements to make array satisfy arr[ i+1] < arr[i] for each valid i
- Remove elements from the array whose frequency lies in the range [l, r]
- Find minimum value to assign all array elements so that array product becomes greater
- Minimum value among AND of elements of every subset of an array

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.