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.
- Find the minimum amount of money we have to spend to buy all the N different candies.
- 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.
Examples:Â
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 :Â
Maximum amount :Â
Below is the implementation of the above approach:Â
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(i<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 = [1,2,3,4,5,6,7,8,9,10] n = len(arr) k = 0  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(nlogn)Â
Auxiliary Space: O(1)
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)
Time Complexity: O(nlog(n))
Auxiliary Space: O(1)
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