Check if given Array can be reduced to 0 by removing element less than K and adding it to K

Given an array, arr[] of size N and an integer K. If a value in arr[] is less than or equal to K, then that value will be removed from the array and added to K. The task is to check if all the elements in arr[] can be absorbed or not. 

Examples:

Input: K = 10, arr[] = {3, 9, 19, 5, 21}
Output: true
Explanation: The array elements are absorbed in following way.
One way to absorption is {9, 19, 5, 3, 21}
value is 9 and the New k value: 10 + 9 = 19
value is 19 and the New k value: 19 + 19 = 38
value is 5 and the New k value: 38 + 5 = 43
value is 3 and the New k value: 43 + 3 = 46
value is 9 and the New k value: 46 + 21 = 6. 
Hence, All values are absorbed.

Input: K = 5, arr[] = {4, 9, 23, 4}
Output: false

Approach: This problem can be solved by using the Greedy Approach. Follow the steps below to solve the given problem. 

• Any element in arr[] that has the highest probability to be less than or equal to K would be the smallest element.
• So, sort the array in non-decreasing order and try to remove elements from left to right.
• Iterate from left to right while removing values of arr[].
• At any time if it is not possible to remove any element, return false.
• Else return true.

Below is the implementation of the above approach.

// C++ program for above approach
#include <bits/stdc++.h>
using namespace std;

// Function to check if all the elements
// can be absorbed or not
bool absorption(int K, vector<int>& arr)
{

    // Sort the array in non-decreasing order
    sort(arr.begin(), arr.end());

    // Long long  prevent from integer overflow
    long long m = K;

    for (int i = 0; i < arr.size(); i++) {
        int value = arr[i];
        if (m < value) {
            return false;
        }
        else {
            m += arr[i];
        }
    }
    return true;
}

// Driver Code
int main()
{
    vector<int> arr{ 3, 9, 19, 5, 21 };
    int K = 10;

    // Check if all the elements
    // can be removed or not.
    if (absorption(K, arr))
        cout << "true";
    else
        cout << "false";
    return 0;
}

// Java program for the above approach
import java.io.*;
import java.lang.*;
import java.util.*;

class GFG {

  // Function to check if all the elements
  // can be absorbed or not
  static  Boolean absorption(int K, int arr[ ])
  {

    // Sort the array in non-decreasing order
    Arrays.sort(arr);

    // Long long  prevent from integer overflow
    long m = K;

    for (int i = 0; i < arr.length; i++) {
      int value = arr[i];
      if (m < value) {
        return false;
      }
      else {
        m += arr[i];
      }
    }
    return true;
  }

  public static void main (String[] args) {
    int arr[ ] = { 3, 9, 19, 5, 21 };
    int K = 10;

    // Check if all the elements
    // can be removed or not.
    if (absorption(K, arr))
      System.out.print("true");
    else
      System.out.print("false");
  }
}

// This code is contributed by hrithikgarg03188.

# Python 3 program for above approach

# Function to check if all the elements
# can be absorbed or not
def absorption(K, arr):

    # Sort the array in non-decreasing order
    arr.sort()

    # Long long  prevent from integer overflow
    m = K

    for i in range(len(arr)):
        value = arr[i]
        if (m < value):
            return False

        else:
            m += arr[i]

    return True

# Driver Code
if __name__ == "__main__":

    arr = [3, 9, 19, 5, 21]
    K = 10

    # Check if all the elements
    # can be removed or not.
    if (absorption(K, arr)):
        print("true")
    else:
        print("false")

        # This code is contributed by ukasp.

// C# program for the above approach
using System;
class GFG
{

  // Function to check if all the elements
  // can be absorbed or not
  static bool absorption(int K, int []arr)
  {

    // Sort the array in non-decreasing order
    Array.Sort(arr);

    // Long long  prevent from integer overflow
    long m = K;

    for (int i = 0; i < arr.Length; i++) {
      int value = arr[i];
      if (m < value) {
        return false;
      }
      else {
        m += arr[i];
      }
    }
    return true;
  }

  // Driver Code
  public static void Main()
  {
    int []arr = { 3, 9, 19, 5, 21 };
    int K = 10;

    // Check if all the elements
    // can be removed or not.
    if (absorption(K, arr))
      Console.Write("true");
    else
      Console.Write("false");
  }
}

// This code is contributed by Samim Hossain Mondal.

 <script>
        // JavaScript code for the above approach 

        // Function to check if all the elements
        // can be absorbed or not
        function absorption(K, arr) {

            // Sort the array in non-decreasing order
            arr.sort(function (a, b) { return a - b })
            let m = K;

            for (let i = 0; i < arr.length; i++) {
                let value = arr[i];
                if (m < value) {
                    return false;
                }
                else {
                    m += arr[i];
                }
            }
            return true;
        }

        // Driver Code

        let arr = [3, 9, 19, 5, 21];
        let K = 10;

        // Check if all the elements
        // can be removed or not.
        if (absorption(K, arr))
            document.write("true");
        else
            document.write("false");

  // This code is contributed by Potta Lokesh
    </script>

true

Time Complexity: O(N * logN)
Auxiliary Space: O(1)