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Find the minimum and maximum amount to buy all N candies

  • Difficulty Level : Easy
  • Last Updated : 05 Aug, 2021

In a candy store, there are N different types of candies available and the prices of all the N different types of candies are provided. There is also an attractive offer by the candy store. We can buy a single candy from the store and get at most K other candies (all are different types) for free.

  1. Find the minimum amount of money we have to spend to buy all the N different candies.
  2. Find the maximum amount of money we have to spend to buy all the N different candies.

In both cases, we must utilize the offer and get the maximum possible candies back. If k or more candies are available, we must take k candies for every candy purchase. If less than k candies are available, we must take all candies for a candy purchase.

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Examples: 



Input :  
price[] = {3, 2, 1, 4}
k = 2
Output :  
Min = 3, Max = 7
Explanation :
Since k is 2, if we buy one candy we can take 
atmost two more for free.
So in the first case we buy the candy which 
costs 1 and take candies worth 3 and 4 for 
free, also you buy candy worth 2 as well.
So min cost = 1 + 2 = 3.
In the second case we buy the candy which 
costs 4 and take candies worth 1 and 2 for 
free, also We buy candy worth 3 as well.
So max cost = 3 + 4 = 7.

One important thing to note is, we must use the offer and get maximum candies back for every candy purchase. So if we want to minimize the money, we must buy candies at minimum cost and get candies of maximum costs for free. To maximize the money, we must do the reverse. Below is an algorithm based on this.

First Sort the price array.

For finding minimum amount :
  Start purchasing candies from starting 
  and reduce k free candies from last with
  every single purchase.

For finding maximum amount : 
   Start purchasing candies from the end 
   and reduce k free candies from starting 
   in every single purchase.

Below image is an illustration of the above approach:

Minimum amount : 

Maximum amount : 

Below is the implementation of the above approach: 

C++




// C++ implementation to find the minimum
// and maximum amount
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the minimum amount
// to buy all candies
int findMinimum(int arr[], int n, int k)
{
    int res = 0;
    for (int i = 0; i < n; i++) {
        // Buy current candy
        res += arr[i];
 
        // And take k candies for free
        // from the last
        n = n - k;
    }
    return res;
}
 
// Function to find the maximum amount
// to buy all candies
int findMaximum(int arr[], int n, int k)
{
    int res = 0, index = 0;
 
    for (int i = n - 1; i >= index; i--)
    {
        // Buy candy with maximum amount
        res += arr[i];
 
        // And get k candies for free from
        // the starting
        index += k;
    }
    return res;
}
 
// Driver code
int main()
{
    int arr[] = { 3, 2, 1, 4 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int k = 2;
    sort(arr, arr + n);
 
    // Function call
    cout << findMinimum(arr, n, k) << " "
         << findMaximum(arr, n, k) << endl;
    return 0;
}

Java




// Java implementation to find the
// minimum and maximum amount
import java.util.*;
 
class GFG {
 
    // Function to find the minimum
    // amount to buy all candies
    static int findMinimum(int arr[], int n, int k)
    {
        int res = 0;
        for (int i = 0; i < n; i++) {
            // Buy current candy
            res += arr[i];
 
            // And take k candies for free
            // from the last
            n = n - k;
        }
        return res;
    }
 
    // Function to find the maximum
    // amount to buy all candies
    static int findMaximum(int arr[], int n, int k)
    {
        int res = 0, index = 0;
 
        for (int i = n - 1; i >= index; i--)
        {
            // Buy candy with maximum amount
            res += arr[i];
 
            // And get k candies for free from
            // the starting
            index += k;
        }
        return res;
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int arr[] = { 3, 2, 1, 4 };
        int n = arr.length;
        int k = 2;
        Arrays.sort(arr);
 
        // Function call
        System.out.println(findMinimum(arr, n, k) + " "
                           + findMaximum(arr, n, k));
    }
}
 
// This code is contributed by prerna saini

Python3




# Python implementation
# to find the minimum
# and maximum amount
 
# Function to find
# the minimum amount
# to buy all candies
 
 
def findMinimum(arr, n, k):
 
    res = 0
    i = 0
    while(n):
 
        # Buy current candy
        res += arr[i]
 
        # And take k
        # candies for free
        # from the last
        n = n-k
        i += 1
    return res
 
# Function to find
# the maximum amount
# to buy all candies
 
 
def findMaximum(arr, n, k):
 
    res = 0
    index = 0
    i = n-1
    while(i >= index):
 
        # Buy candy with
        # maximum amount
        res += arr[i]
 
        # And get k candies
        # for free from
        # the starting
        index += k
        i -= 1
 
    return res
 
# Driver code
arr = [3, 2, 1, 4]
n = len(arr)
k = 2
 
arr.sort()
 
# Function call
print(findMinimum(arr, n, k), " ",
      findMaximum(arr, n, k))
 
# This code is contributed
# by Anant Agarwal.

C#




// C# implementation to find the
// minimum and maximum amount
using System;
 
public class GFG {
 
    // Function to find the minimum
    // amount to buy all candies
    static int findMinimum(int[] arr, int n, int k)
    {
        int res = 0;
        for (int i = 0; i < n; i++)
        {
 
            // Buy current candy
            res += arr[i];
 
            // And take k candies for
            // free from the last
            n = n - k;
        }
 
        return res;
    }
 
    // Function to find the maximum
    // amount to buy all candies
    static int findMaximum(int[] arr, int n, int k)
    {
        int res = 0, index = 0;
 
        for (int i = n - 1; i >= index; i--)
        {
            // Buy candy with maximum
            // amount
            res += arr[i];
 
            // And get k candies for free
            // from the starting
            index += k;
        }
 
        return res;
    }
 
    // Driver code
    public static void Main()
    {
        int[] arr = { 3, 2, 1, 4 };
        int n = arr.Length;
        int k = 2;
        Array.Sort(arr);
 
        // Function call
        Console.WriteLine(findMinimum(arr, n, k) + " "
                          + findMaximum(arr, n, k));
    }
}
 
// This code is contributed by Sam007.

PHP




<?php
// PHP implementation to find the minimum
// and maximum amount
 
// Function to find the minimum amount
// to buy all candies
function findMinimum($arr, $n,$k)
{
    $res = 0;
    for ($i = 0; $i < $n ; $i++)
    {
         
        // Buy current candy
        $res += $arr[$i];
 
        // And take k candies for free
        // from the last
        $n = $n - $k;
    }
    return $res;
}
 
// Function to find the maximum amount
// to buy all candies
function findMaximum($arr, $n, $k)
{
    $res = 0;
    $index = 0;
 
    for ($i = $n - 1; $i >= $index; $i--)
    {
         
        // Buy candy with maximum amount
        $res += $arr[$i];
 
        // And get k candies
        // for free from
        // the starting
        $index += $k;
    }
    return $res;
}
 
    // Driver Code
    $arr = array(3, 2, 1, 4);
    $n = sizeof($arr);
    $k = 2;
    sort($arr); sort($arr,$n);
 
    // Function call
    echo findMinimum($arr, $n, $k)," "
            ,findMaximum($arr, $n, $k);
    return 0;
 
// This code is contributed by nitin mittal.
?>

Javascript




<script>
 
// Javascript implementation to find the
// minimum and maximum amount
     
// Function to find the minimum
// amount to buy all candies
function findMinimum(arr,n,k)
{
    let res = 0;
     
    for(let i = 0; i < n; i++)
    {
         
        // Buy current candy
        res += arr[i];
 
        // And take k candies for free
        // from the last
        n = n - k;
    }
    return res;
}
 
// Function to find the maximum
// amount to buy all candies
function findMaximum(arr,n,k)
{
    let res = 0, index = 0;
 
    for(let i = n - 1; i >= index; i--)
    {
         
        // Buy candy with maximum amount
        res += arr[i];
 
        // And get k candies for free from
        // the starting
        index += k;
    }
    return res;
}
 
// Driver code
let arr = [ 3, 2, 1, 4 ];
let  n = arr.length;
let  k = 2;
arr.sort(function(a, b){return a - b;});
 
// Function call
document.write(findMinimum(arr, n, k) + " " +
               findMaximum(arr, n, k));
 
// This code is contributed by patel2127
 
</script>
Output
3 7

Time Complexity: O(n log n)

Another Implementation:
We can use the help of The Least integer function (Ceiling function) using built-in ceil() function to implement:

Below is the implementation in Python:

C++




// C++ implementation
// to find the minimum
// and maximum amount
#include <bits/stdc++.h>
using namespace std;
 
// function to find the maximum
// and the minimum cost required
void find(vector<int> arr, int n, int k)
{
 
    // Sort the array
    sort(arr.begin(), arr.end());
    int b = ceil(n / k * 1.0);
    int min_sum = 0, max_sum = 0;
 
    for(int i = 0; i < b; i++)
      min_sum += arr[i];
    for(int i = 2; i < arr.size(); i++)
      max_sum += arr[i];
 
    // print the minimum cost
    cout << "minimum " << min_sum << endl;
 
    // print the maximum cost
    cout << "maximum " << max_sum << endl;
 
}
 
 
// Driver code
int main()
{
  vector<int> arr = {3, 2, 1, 4};
  int n = arr.size();
  int k = 2;
 
  // Function call
  find(arr,n,k);
}
 
// This code is contributed by mohit kumar 29.

Java




// Java implementation to find the minimum
// and maximum amount
import java.io.*;
import java.util.Arrays;
import java.lang.Math;
 
class GFG{
 
// Function to find the maximum
// and the minimum cost required
static void find(int[] arr, int n, int k)
{
     
    // Sort the array
    Arrays.sort(arr);
    int b = (int)Math.ceil(n / k * 1.0);
    int min_sum = 0, max_sum = 0;
 
    for(int i = 0; i < b; i++)
        min_sum += arr[i];
    for(int i = 2; i < arr.length; i++)
        max_sum += arr[i];
 
    // Print the minimum cost
    System.out.println("minimum " + min_sum);
 
    // Print the maximum cost
    System.out.println("maximum " + max_sum);
}
 
// Driver code
public static void main (String[] args)
{
    int[] arr = { 3, 2, 1, 4 };
    int n = arr.length;
    int k = 2;
 
    // Function call
    find(arr, n, k);
}
}
 
// This code is contributed by shivanisinghss2110

Python3




# Python implementation
# to find the minimum
# and maximum amount
 
#import ceil function
from math import ceil
 
# function to find the maximum
# and the minimum cost required
def find(arr,n,k):
     
    # Sort the array
    arr.sort()
    b = int(ceil(n/k))
     
    # print the minimum cost
    print("minimum ",sum(arr[:b]))
     
    # print the maximum cost
    print("maximum ", sum(arr[-b:]))
     
     
# Driver Code
arr = [3, 2, 1, 4]
n = len(arr)
k = 2
 
# Function call
find(arr,n,k)

C#




// C# implementation to find the minimum
// and maximum amount
using System;
 
class GFG{
 
// Function to find the maximum
// and the minimum cost required
static void find(int[] arr, int n, int k)
{
     
    // Sort the array
    Array.Sort(arr);
    int b = (int)Math.Ceiling(n / k * 1.0);
    int min_sum = 0, max_sum = 0;
 
    for(int i = 0; i < b; i++)
        min_sum += arr[i];
    for(int i = 2; i < arr.Length; i++)
        max_sum += arr[i];
 
    // Print the minimum cost
    Console.WriteLine("minimum " + min_sum);
 
    // Print the maximum cost
    Console.WriteLine("maximum " + max_sum);
}
 
// Driver code
public static void Main()
{
    int[] arr = { 3, 2, 1, 4 };
    int n = arr.Length;
    int k = 2;
 
    // Function call
    find(arr, n, k);
}
}
 
// This code is contributed by ukasp

Javascript




<script>
 
// JavaScript implementation
// to find the minimum
// and maximum amount
     
    // function to find the maximum
// and the minimum cost required
    function find(arr,n,k)
    {
        // Sort the array
    arr.sort(function(a,b){return a-b;});
    let b = Math.floor(Math.ceil(n/k));
     
    let min_sum = 0, max_sum = 0;
  
    for(let i = 0; i < b; i++)
      min_sum += arr[i];
    for(let i = 2; i < arr.length; i++)
      max_sum += arr[i];
      
    // print the minimum cost
    document.write("minimum "+min_sum+"<br>");
      
    // print the maximum cost
    document.write("maximum "+ max_sum+"<br>");
    }
     
    // Driver Code
let arr = [3, 2, 1, 4];
let n = arr.length;
let k = 2;
  
// Function call
find(arr,n,k);
     
 
// This code is contributed by unknown2108
 
</script>
Output
('minimum ', 3)
('maximum ', 7)

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