Program for Chocolate and Wrapper Puzzle

Given following three values, the task is to find the total number of maximum chocolates you can eat.

  1. money : Money you have to buy chocolates
  2. price : Price of a chocolate
  3. wrap : Number of wrappers to be returned for getting one extra chocolate.

It may be assumed that all given values are positive integers and greater than 1.

Examples:

Input :   money = 16, price = 2, wrap = 2
Output :   15
Price of a chocolate is 2. You can buy 8 chocolates from
amount 16. You can return 8 wrappers back and get 4 more
chocolates. Then you can return 4 wrappers and get 2 more
chocolates. Finally you can return 2 wrappers to get 1
more chocolate.

Input :   money = 15, price = 1, wrap = 3
Output :   22
We buy and eat 15 chocolates
We return 15 wrappers and get 5 more chocolates.
We return 3 wrappers, get 1 chocolate and eat it
(keep 2 wrappers). Now we have 3 wrappers. Return
3 and get 1 more chocolate.
So total chocolates = 15 + 5 + 1 + 1

Input :  money = 20, price = 3, wrap = 5
Output :   7

Source: Puzzle 22 | (Maximum Chocolates)

A naive method is to continuously count number of chocolates by returning wrappers until wrappers left didn’t become less than required to get a chocolate. Below is the implementation of this method.

C++



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// Recursive C++ program to find maximum
// number of chocolates
#include <iostream>
using namespace std;
  
// Returns number of chocolates we can
// have from given number of chocolates
// and number of wrappers required to
// get a chocolate.
int countRec(int choc, int wrap)
{
    // If number of chocolates is less than
    // number of wrappers required.
    if (choc < wrap)
        return 0;
  
    // We can immediatly get newChoc using
    // wrappers of choc.
    int newChoc = choc/wrap;
  
    // Now we have "newChoc + choc%wrap" wrappers.
    return newChoc + countRec(newChoc + choc%wrap,
                              wrap);
}
  
// Returns maximum number of chocolates we can eat
// with given money, price of chocolate and number
// of wrappers required to get a chocolate.
int countMaxChoco(int money, int price, int wrap)
{
    // We can directly buy below number of chocolates
    int choc = money/price;
  
    // countRec returns number of chocolates we can
    // have from given number of chocolates
    return choc + countRec(choc, wrap);
}
  
// Driver code
int main()
{
    int money = 15 ; // total money
    int price = 1; // cost of each candy
    int wrap = 3 ; // no of wrappers needs to be
    // exchanged for one chocolate.
  
    cout << countMaxChoco(money, price, wrap);
    return 0;
}

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Java

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// Recursive java program to find maximum
// number of chocolates
  
import java.io.*;
  
class GFG {
  
    // Returns number of chocolates we can
    // have from given number of chocolates
    // and number of wrappers required to
    // get a chocolate.
    static int countRec(int choc, int wrap)
    {
          
        // If number of chocolates is less than
        // number of wrappers required.
        if (choc < wrap)
            return 0;
      
        // We can immediatly get newChoc using
        // wrappers of choc.
        int newChoc = choc / wrap;
      
        // Now we have "newChoc + choc%wrap" 
        // wrappers.
        return newChoc + countRec(newChoc + 
                          choc % wrap, wrap);
    }
      
    // Returns maximum number of chocolates
    // we can eat with given money, price of
    // chocolate and number of wrappers 
    // required to get a chocolate.
    static int countMaxChoco(int money, 
                          int price, int wrap)
    {
          
        // We can directly buy below number of
        // chocolates
        int choc = money/price;
      
        // countRec returns number of chocolates
        // we can have from given number of 
        // chocolates
        return choc + countRec(choc, wrap);
    }
      
    // Driver code
    public static void main (String[] args)
    {
        int money = 15 ; // total money
        int price = 1; // cost of each candy
          
        // no of wrappers needs to be
        // exchanged for one chocolate.
        int wrap = 3
        System.out.println( 
            countMaxChoco(money, price, wrap));
    }
}
  
// This code is contributed by anuj_67.

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Python3

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# Recursive Python3 program to find
# maximum number of chocolates
import math
  
# Returns number of chocolates we can
# have from given number of chocolates
# and number of wrappers required to
# get a chocolate.
def countRec(choc, wrap):
      
    # If number of chocolates is less 
    # than number of wrappers required.
    if (choc < wrap):
        return 0;
  
    # We can immediatly get newChoc
    # using wrappers of choc.
    newChoc = choc / wrap;
  
    # Now we have "newChoc + choc%wrap" wrappers.
    return newChoc + countRec(newChoc + choc % 
                                  wrap, wrap);
  
# Returns maximum number of chocolates 
# we can eat with given money, price 
# of chocolate and number of wrappers 
# required to get a chocolate.
def countMaxChoco(money, price, wrap):
      
    # We can directly buy below 
    # number of chocolates
    choc = money / price;
  
    # countRec returns number
    # of chocolates we can
    # have from given number 
    # of chocolates
    return math.floor(choc + countRec(choc, wrap));
  
# Driver code
  
# total money
money = 15;
      
# cost of each candy
price = 1
      
# no of wrappers needs to be
wrap = 3
      
# exchanged for one chocolate.
print(countMaxChoco(money, price, wrap));
  
# This code is contributed by mits

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C#

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// Recursive C# program to find maximum
// number of chocolates
  
using System;
  
class GFG {
  
    // Returns number of chocolates we can
    // have from given number of chocolates
    // and number of wrappers required to
    // get a chocolate.
    static int countRec(int choc, int wrap)
    {
          
        // If number of chocolates is less than
        // number of wrappers required.
        if (choc < wrap)
            return 0;
      
        // We can immediatly get newChoc using
        // wrappers of choc.
        int newChoc = choc / wrap;
      
        // Now we have "newChoc + choc%wrap" 
        // wrappers.
        return newChoc + countRec(newChoc + 
                        choc % wrap, wrap);
    }
      
    // Returns maximum number of chocolates
    // we can eat with given money, price of
    // chocolate and number of wrappers 
    // required to get a chocolate.
    static int countMaxChoco(int money, 
                        int price, int wrap)
    {
          
        // We can directly buy below number of
        // chocolates
        int choc = money/price;
      
        // countRec returns number of chocolates
        // we can have from given number of 
        // chocolates
        return choc + countRec(choc, wrap);
    }
      
    // Driver code
    public static void Main ()
    {
        int money = 15 ; // total money
        int price = 1; // cost of each candy
          
        // no of wrappers needs to be
        // exchanged for one chocolate.
        int wrap = 3 ; 
        Console.WriteLine( 
            countMaxChoco(money, price, wrap));
    }
}
  
// This code is contributed by anuj_67.

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PHP

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<?php
// Recursive PHP program to find maximum
// number of chocolates
  
// Returns number of chocolates we can
// have from given number of chocolates
// and number of wrappers required to
// get a chocolate.
function countRec($choc, $wrap)
{
      
    // If number of chocolates is less than
    // number of wrappers required.
    if ($choc < $wrap)
        return 0;
  
    // We can immediatly get newChoc using
    // wrappers of choc.
    $newChoc = $choc/$wrap;
  
    // Now we have "newChoc + choc%wrap" wrappers.
    return $newChoc + countRec($newChoc + $choc % $wrap,
                                                  $wrap);
}
  
// Returns maximum number of chocolates we can eat
// with given money, price of chocolate and number
// of wrappers required to get a chocolate.
function countMaxChoco($money, $price, $wrap)
{
      
    // We can directly buy below 
    // number of chocolates
    $choc = $money/$price;
  
    // countRec returns number
    // of chocolates we can
    // have from given number 
    // of chocolates
    return floor($choc + countRec($choc, $wrap));
}
  
    // Driver code
    // total money
    $money = 15;
      
    // cost of each candy
    $price = 1; 
      
    // no of wrappers needs to be
    $wrap = 3 ; 
      
    // exchanged for one chocolate.
    echo countMaxChoco($money, $price, $wrap);
  
// This code is contributed by anuj_67.
?>

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Output :

22

An efficient solution is to use a direct formula to find the number of chocolates.

Find initial number of chocolates by
dividing the amount with per piece cost.
i.e. choc = money / wrap

then apply below formula
choc += (choc - 1)/(wrap - 1)

In above naive implementation, we noticed that after finding initial number of chocolates, we recursively divide the number of chocolates with the number of wrappers required. until we left with 1 chocolate or wrapper.
We are recomputing the values i.e. ((choc/wrap + choc%wrap)/wrap until we get 1.
It is observed that, we can get the result by just reducing the values of chocolates and wrappers by 1 and then divide them to get the result (choc-1)/(wrap-1)

C++

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// Efficient C++ program to find maximum
// number of chocolates
#include <iostream>
using namespace std;
  
// Returns maximum number of chocolates we can eat
// with given money, price of chocolate and number
// of wrapprices required to get a chocolate.
int countMaxChoco(int money, int price, int wrap)
{
    // Corner case
    if (money < price)
       return 0;
  
    // First find number of chocolates that
    // can be purchased with the given amount
    int choc = money / price;
  
    // Now just add number of chocolates with the
    // chocolates gained by wrapprices
    choc = choc + (choc - 1) / (wrap - 1);
    return choc;
}
  
// Driver code
int main()
{
    int money = 15 ; // total money
    int price = 1; // cost of each candy
    int wrap = 3 ; // no of wrappers needs to be
    // exchanged for one chocolate.
  
    cout << countMaxChoco(money, price, wrap);
    return 0;
}

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Java

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// Efficient Java program to find maximum
// number of chocolates
import java.io.*;
  
class GFG {
  
    // Returns maximum number of chocolates 
    // we can eat with given money, price 
    // of chocolate and number of wrapprices
    // required to get a chocolate.
    static int countMaxChoco(int money, 
                        int price, int wrap)
    {
          
        // Corner case
        if (money < price)
            return 0;
      
        // First find number of chocolates 
        // that can be purchased with the
        // given amount
        int choc = money / price;
      
        // Now just add number of chocolates
        // with the chocolates gained by
        // wrapprices
        choc = choc + (choc - 1) / (wrap - 1);
        return choc;
    }
      
    // Driver code
    public static void main (String[] args) 
    {
          
        // total money
        int money = 15;
          
        // cost of each candy
        int price = 1
          
        // no of wrappers needs to be
        int wrap = 3
          
        // exchanged for one chocolate.
        System.out.println(
           countMaxChoco(money, price, wrap));
    }
}
  
// This code is contributed by anuj_67.

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Python3

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# Efficient Python3 program to find 
# maximum number of chocolates 
  
# Returns maximum number of 
# chocolates we can eat with 
# given money, price of chocolate
# and number of wrapprices
# required to get a chocolate. 
def countMaxChoco(money, price, wrap) :
  
    # Corner case 
    if (money < price) :
        return 0
  
    # First find number of chocolates 
    # that can be purchased with the
    # given amount 
    choc = int(money / price) 
  
    # Now just add number of
    # chocolates with the chocolates 
    # gained by wrapprices 
    choc = choc + (choc - 1) / (wrap - 1
    return int(choc )
  
# Driver code 
money = 15 # total money 
price = 1 # cost of each candy 
wrap = 3 # no of wrappers needs to be 
         # exchanged for one chocolate. 
  
print(countMaxChoco(money, price, wrap))
  
# This code is contributed by Smitha

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C#

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// Efficient C# program to find maximum
// number of chocolates
using System;
  
class GFG {
  
    // Returns maximum number of chocolates 
    // we can eat with given money, price 
    // of chocolate and number of wrapprices
    // required to get a chocolate.
    static int countMaxChoco(int money, 
                        int price, int wrap)
    {
          
        // Corner case
        if (money < price)
            return 0;
      
        // First find number of chocolates 
        // that can be purchased with the
        // given amount
        int choc = money / price;
      
        // Now just add number of chocolates
        // with the chocolates gained by
        // wrapprices
        choc = choc + (choc - 1) / (wrap - 1);
        return choc;
    }
      
    // Driver code
    public static void Main () 
    {
          
        // total money
        int money = 15;
          
        // cost of each candy
        int price = 1; 
          
        // no of wrappers needs to be
        int wrap = 3 ; 
          
        // exchanged for one chocolate.
        Console.WriteLine(
        countMaxChoco(money, price, wrap));
    }
}
  
// This code is contributed by anuj_67.

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PHP

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<?php
// Efficient PHP program to find maximum
// number of chocolates
  
// Returns maximum number 
// of chocolates we can eat
// with given money, price 
// of chocolate and number
// of wrapprices required 
// to get a chocolate.
function countMaxChoco($money, $price, $wrap)
{
    // Corner case
    if ($money < $price)
    return 0;
  
    // First find number 
    // of chocolates that
    // can be purchased 
    // with the given amount
    $choc = $money / $price;
  
    // Now just add number 
    // of chocolates with the
    // chocolates gained by wrapprices
    $choc = $choc + ($choc - 1) / 
                    ($wrap - 1);
    return $choc;
}
  
    // Driver code
      
     // total money
    $money = 15 ;
      
    // cost of each candy
    $price = 1; 
      
    // no of wrappers needs to be
    // exchanged for one chocolate.
    $wrap = 3 ; 
    echo countMaxChoco($money, $price, $wrap);
      
// This code is contributed by ajit
?>

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Output :

22

This article is contributed by Sahil Chhabra (akku). 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.

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