Select K elements from an array whose maximum value is minimized

Given an array arr[] having N integers and an integer K, the task is to select K elements from the given array such that the sum of all the values is positive and the maximum value among K integers is minimum.

Examples:

Input: arr[] = {10, -8, 5, -5, -2, 4, -1, 0, 11}, k = 4 
Output: 4 
Explanation:
Possible array is {0, 4, -1, -2} the maximum element is 4 which is the minimum possible.
Input: arr[] = {-8, -5, -2, -4, -1}, k = 2 
Output: -1 
Explanation:
Selecting K elements is not possible.

Approach: The idea is to use the Two Pointer Technique. Below are the steps:

• Sort the given array.
• Select the least non-negative value from the above array(say at index idx) using lower_bound() in C++.
• If a positive value doesn’t exist in a given array, then the sum is always negative and none of the K element satisfies the given condition.
• If there exist positive integers then there can be a possibility of selecting K elements whose sum is positive.
• By using two pointers technique we can find K integers whose sum is positive as: 
  • Initialize two pointers left and right as (ind – 1) and ind respectively.
  • Add the element at index left(which is negative) if current sum + arr[left] is greater than 0 to minimize the maximum value among K selected elements and decrement the left.
  • Else add an element at index right and update the maximum value and increment right.
  • Decrement K for each of the above steps.
  • Repeat the above till K becomes zero, left is less than zero, or right reaches the end of the array.
• If K becomes zero in any of the above then print the maximum value stored.
• Else print “-1”.

Below is the implementation of the above approach:

C++

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

// Function to  print the maximum from K
// selected elements of the array
pair<int, bool>
kthsmallestelement(vector<int> a,
                   int n, int k)
{
    // Sort the array
    sort(a.begin(), a.end());

    // Apply Binary search for
    // first positive element
    int ind = lower_bound(a.begin(),
                          a.end(), 0)
              - a.begin();

  // Check if no element is positive
    if (ind == n - 1 && a[n - 1] < 0)
        return make_pair(INT_MAX, false);

    // Initialize pointers
    int left = ind - 1, right = ind;
    int sum = 0;

    // Iterate to select exactly K elements
    while (k--) {

        // Check if left pointer
        // is greater than 0
        if (left >= 0 && sum + a[left] > 0) {

            // Update sum
            sum = sum + a[left];
            // Decrement left
            left--;
        }

        else if (right < n) {

            // Update sum
            sum = sum + a[right];

            // Increment right
            right++;
        }

        else
            return make_pair(INT_MAX, false);
    }

    // Return the answer
    return make_pair(a[right - 1], true);
}

// Driver Code
int main()
{
    // Given array arr[]
    vector<int> arr = { -8, -5, -2, -4, -1 };

    int n = arr.size();
    int k = 2;

    // Function Call
    pair<int, bool> ans
        = kthsmallestelement(arr, n, k);

    if (ans.second == false)
        cout << "-1" << endl;

    else
        cout << ans.first << endl;
}

Java

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

class GFG{

// Function to print the maximum from K
// selected elements of the array
static int[] kthsmallestelement(int[] a, int n,
                                int k)
{

    // Sort the array
    Arrays.sort(a);

    // Apply Binary search for
    // first positive element
    int ind = lowerBound(a, 0, a.length, 0);

    // Check if no element is positive
    if (ind == n - 1 && a[n - 1] < 0)
        return new int[] { Integer.MAX_VALUE, 0 };

    // Initialize pointers
    int left = ind - 1, right = ind;
    int sum = 0;

    // Iterate to select exactly K elements
    while (k-- > 0)
    {

        // Check if left pointer
        // is greater than 0
        if (left >= 0 && sum + a[left] > 0)
        {

            // Update sum
            sum = sum + a[left];
            // Decrement left
            left--;
        }

        else if (right < n)
        {

            // Update sum
            sum = sum + a[right];

            // Increment right
            right++;
        }
        else
            return new int[] { Integer.MAX_VALUE, 0 };
    }

    // Return the answer
    return new int[] { a[right - 1], 1 };
}

static int lowerBound(int[] numbers, int start,
                      int length, int searchnum)
{

    // If the number is not in the
    // list it will return -1
    int answer = -1;

    // Starting point of the list
    start = 0;

    // Ending point of the list
    int end = length - 1;

    while (start <= end)
    {

        // Finding the middle point of the list
        int middle = (start + end) / 2;

        if (numbers[middle] == searchnum)
        {
            answer = middle;
            end = middle - 1;
        } else if (numbers[middle] > searchnum)
            end = middle - 1;
        else
            start = middle + 1;
    }
    if (answer == -1)
        answer = length;

    return answer;
}

// Driver Code
public static void main(String[] args)
{

    // Given array arr[]
    int[] arr = { -8, -5, -2, -4, -1 };

    int n = arr.length;
    int k = 2;

    // Function call
    int[] ans = kthsmallestelement(arr, n, k);

    if (ans[1] == 0)
        System.out.print("-1" + "\n");
    else
        System.out.print(ans[0] + "\n");
}
}

// This code is contributed by amal kumar choubey

Python3

# Python3 program for the above approach
import sys

# Function to find lower_bound
def LowerBound(numbers, length, searchnum):

    # If the number is not in the
    # list it will return -1
    answer = -1

    # Starting point of the list
    start = 0

    # Ending point of the list
    end = length - 1

    while start <= end:

        # Finding the middle point of the list
        middle = (start + end) // 2

        if numbers[middle] == searchnum:
            answer = middle
            end = middle - 1
        elif numbers[middle] > searchnum:
            end = middle - 1
        else:
            start = middle + 1

    if(answer == -1):
        answer = length

    return answer

# Function to print the maximum from K
# selected elements of the array
def kthsmallestelement(a, n, k):

    # Sort the array
    a.sort()

    # Apply Binary search for
    # first positive element
    ind = LowerBound(a, len(a), 0)

    # Check if no element is positive
    if (ind == n - 1 and a[n - 1] < 0):
        return make_pair(INT_MAX, False)

    # Initialize pointers
    left = ind - 1
    right = ind
    sum = 0

    # Iterate to select exactly K elements
    while (k > 0):
        k -= 1

        # Check if left pointer
        # is greater than 0
        if (left >= 0 and sum + a[left] > 0):

            # Update sum
            sum = sum + a[left]

            # Decrement left
            left -= 1

        elif (right < n):

            # Update sum
            sum = sum + a[right]

            # Increment right
            right += 1
        else:
            return [sys.maxsize, False]

    print(sys.maxsize)

    # Return the answer
    return [a[right - 1], True]

# Driver Code

# Given array arr[]
arr = [ -8, -5, -2, -4, -1 ]

n = len(arr)
k = 2

# Function call
ans = kthsmallestelement(arr, n, k)

if (ans[1] == False):
    print(-1)
else:
    print(ans[0])

# This code is contributed by Sanjit_Prasad

C#

// C# program for the above approach
using System;

class GFG{

// Function to print the maximum from K
// selected elements of the array
static int[] kthsmallestelement(int[] a, int n,
                                int k)
{

    // Sort the array
    Array.Sort(a);

    // Apply Binary search for
    // first positive element
    int ind = lowerBound(a, 0, a.Length, 0);

    // Check if no element is positive
    if (ind == n - 1 && a[n - 1] < 0)
        return new int[] { int.MaxValue, 0 };

    // Initialize pointers
    int left = ind - 1, right = ind;
    int sum = 0;

    // Iterate to select exactly K elements
    while (k-- > 0)
    {

        // Check if left pointer
        // is greater than 0
        if (left >= 0 && sum + a[left] > 0)
        {

            // Update sum
            sum = sum + a[left];

            // Decrement left
            left--;
        }

        else if (right < n)
        {

            // Update sum
            sum = sum + a[right];

            // Increment right
            right++;
        }
        else
            return new int[] { int.MaxValue, 0 };
    }

    // Return the answer
    return new int[] { a[right - 1], 1 };
}

static int lowerBound(int[] numbers, int start,
                      int length, int searchnum)
{

    // If the number is not in the
    // list it will return -1
    int answer = -1;

    // Starting point of the list
    start = 0;

    // Ending point of the list
    int end = length - 1;

    while (start <= end)
    {

        // Finding the middle point of the list
        int middle = (start + end) / 2;

        if (numbers[middle] == searchnum)
        {
            answer = middle;
            end = middle - 1;
        } else if (numbers[middle] > searchnum)
            end = middle - 1;
        else
            start = middle + 1;
    }
    if (answer == -1)
        answer = length;

    return answer;
}

// Driver Code
public static void Main(String[] args)
{

    // Given array []arr
    int[] arr = { -8, -5, -2, -4, -1 };

    int n = arr.Length;
    int k = 2;

    // Function call
    int[] ans = kthsmallestelement(arr, n, k);

    if (ans[1] == 0)
        Console.Write("-1" + "\n");
    else
        Console.Write(ans[0] + "\n");
}
}

// This code is contributed by Amit Katiyar

Javascript

<script>

// Javascript program implementation
// of the approach

// Function to print the maximum from K
// selected elements of the array
function kthsmallestelement(a, n, k)
{

    // Sort the array
    a.sort();

    // Apply Binary search for
    // first positive element
    let ind = lowerBound(a, 0, a.length, 0);

    // Check if no element is positive
    if (ind == n - 1 && a[n - 1] < 0)
        return [ Number.MAX_VALUE, 0 ];

    // Initialize pointers
    let left = ind - 1, right = ind;
    let sum = 0;

    // Iterate to select exactly K elements
    while (k-- > 0)
    {

        // Check if left pointer
        // is greater than 0
        if (left >= 0 && sum + a[left] > 0)
        {

            // Update sum
            sum = sum + a[left];
            // Decrement left
            left--;
        }

        else if (right < n)
        {

            // Update sum
            sum = sum + a[right];

            // Increment right
            right++;
        }
        else
            return [ Number.MAX_VALUE, 0 ];
    }

    // Return the answer
    return [ a[right - 1], 1 ];
}

function lowerBound( numbers, start,
                      length, searchnum)
{

    // If the number is not in the
    // list it will return -1
    let answer = -1;

    // Starting point of the list
    start = 0;

    // Ending point of the list
    let end = length - 1;

    while (start <= end)
    {

        // Finding the middle point of the list
        let middle = (start + end) / 2;

        if (numbers[middle] == searchnum)
        {
            answer = middle;
            end = middle - 1;
        } else if (numbers[middle] > searchnum)
            end = middle - 1;
        else
            start = middle + 1;
    }
    if (answer == -1)
        answer = length;

    return answer;
}

// Driver Code

    // Given array arr[]
    let arr = [ -8, -5, -2, -4, -1 ];

    let n = arr.length;
    let k = 2;

    // Function call
    let ans = kthsmallestelement(arr, n, k);

    if (ans[1] == 0)
        document.write("-1" + "\n");
    else
        document.write(ans[0] + "\n");

</script>

Output:

-1

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