# Maximize count of empty water bottles from N filled bottles

Given two integers **N** and **E,** where **N** represents the number of full water bottles and **E** represents the number of empty bottles that can be exchanged for a full water bottle. The task is to find the maximum number of water bottles that can be emptied.

**Examples:**

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Input:N = 9, E= 3Output:13Explanation:

Initially, there are 9 fully filled water bottles.

All of them are emptied to obtain 9 empty bottles. Therefore, count =9

Then exchange 3 bottles at a time for 1 fully filled bottle.

Therefore, 3 fully filled bottles are obtained.

Then those 3 bottles are emptied to get 3 empty bottles. Therefore, count =9 + 3 = 12

Then those 3 bottles are exchanged for 1 full bottle which is emptied.

Therefore, count =9 + 3 + 1=13.

Input:N = 7, E = 5Output:8Explanation:

Empty the 7 fully filled water bottles. Therefore, count =7

Then exchange 5 bottles to obtain 1 fully filled bottle. Then empty that bottle.

Therefore, count =7 + 1=8.

**Approach: **The following steps have to be followed to solve the problem:

- Store the value of
**N**in a temporary variable, say**a.** - Initialize a variable, say
**s,**to store the count of empty bottles and another variable, say**b,**to store the count of bottles remaining after exchange. - Now, iterate until
**a**is not equal to**0**and increment**s**by**a**, as it will be the minimum number of bottles that have been emptied. - Update the following values:
**a**to**(a + b) / e****b**to**N – (a * e)****N**to**(a+b)**

- Return
**s**as the required answer.

Below is the implementation of the above approach:

## C++

`// C++ program for the` `// above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the maximum` `// bottles that can be emptied` `int` `maxBottles(` `int` `n, ` `int` `e)` `{` ` ` `int` `s = 0, b = 0;` ` ` `int` `a = n;` ` ` `// Iterate until a` ` ` `// is non-zero` ` ` `while` `(a != 0) {` ` ` ` ` `// Add the number of` ` ` `// bottles that are emptied` ` ` `s = s + a;` ` ` `// Update a after` ` ` `// exchanging empty bottles` ` ` `a = (a + b) / e;` ` ` `// Stores the number of bottles` ` ` `// left after the exchange` ` ` `b = n - (a * e);` ` ` `n = a + b;` ` ` `}` ` ` `// Return the answer` ` ` `return` `s;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 9, e = 3;` ` ` `// Function call` ` ` `int` `s = maxBottles(n, e);` ` ` `cout << s << endl;` `}` |

## Java

`// Java program for the` `// above approach` `import` `java.util.*;` `class` `GFG{` `// Function to find the maximum` `// bottles that can be emptied` `static` `int` `maxBottles(` `int` `n, ` `int` `e)` `{` ` ` `int` `s = ` `0` `, b = ` `0` `;` ` ` `int` `a = n;` ` ` `// Iterate until a` ` ` `// is non-zero` ` ` `while` `(a != ` `0` `)` ` ` `{` ` ` ` ` `// Add the number of` ` ` `// bottles that are emptied` ` ` `s = s + a;` ` ` `// Update a after` ` ` `// exchanging empty bottles` ` ` `a = (a + b) / e;` ` ` `// Stores the number of bottles` ` ` `// left after the exchange` ` ` `b = n - (a * e);` ` ` `n = a + b;` ` ` `}` ` ` `// Return the answer` ` ` `return` `s;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `n = ` `9` `, e = ` `3` `;` ` ` `// Function call` ` ` `int` `s = maxBottles(n, e);` ` ` ` ` `System.out.print(s + ` `"\n"` `);` `}` `}` `// This code is contributed by 29AjayKumar` |

## Python3

`# Python3 program for the` `# above approach` `# Function to find the maximum` `# bottles that can be emptied` `def` `maxBottles(n, e):` ` ` ` ` `s ` `=` `0` ` ` `b ` `=` `0` ` ` `a ` `=` `n` ` ` `# Iterate until a` ` ` `# is non-zero` ` ` `while` `(a !` `=` `0` `):` ` ` `# Add the number of` ` ` `# bottles that are emptied` ` ` `s ` `=` `s ` `+` `a` ` ` `# Update a after` ` ` `# exchanging empty bottles` ` ` `a ` `=` `(a ` `+` `b) ` `/` `/` `e` ` ` `# Stores the number of bottles` ` ` `# left after the exchange` ` ` `b ` `=` `n ` `-` `(a ` `*` `e)` ` ` `n ` `=` `a ` `+` `b` ` ` `# Return the answer` ` ` `return` `s` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` ` ` `n ` `=` `9` ` ` `e ` `=` `3` ` ` `# Function call` ` ` `s ` `=` `maxBottles(n, e)` ` ` `print` `(s)` `# This code is contributed by mohit kumar 29` |

## C#

`// C# program for the above approach` `using` `System;` `class` `GFG{` `// Function to find the maximum` `// bottles that can be emptied` `static` `int` `maxBottles(` `int` `n, ` `int` `e)` `{` ` ` `int` `s = 0, b = 0;` ` ` `int` `a = n;` ` ` `// Iterate until a` ` ` `// is non-zero` ` ` `while` `(a != 0)` ` ` `{` ` ` ` ` `// Add the number of` ` ` `// bottles that are emptied` ` ` `s = s + a;` ` ` `// Update a after` ` ` `// exchanging empty bottles` ` ` `a = (a + b) / e;` ` ` `// Stores the number of bottles` ` ` `// left after the exchange` ` ` `b = n - (a * e);` ` ` `n = a + b;` ` ` `}` ` ` `// Return the answer` ` ` `return` `s;` `}` `// Driver Code` `public` `static` `void` `Main()` `{` ` ` `int` `n = 9, e = 3;` ` ` `// Function call` ` ` `int` `s = maxBottles(n, e);` ` ` ` ` `Console.Write(s + ` `"\n"` `);` `}` `}` `// This code is contributed by code_hunt` |

## Javascript

`<script>` `// javascript program for the` `// above approach` `// Function to find the maximum` `// bottles that can be emptied` `function` `maxBottles(n, e)` `{` ` ` `var` `s = 0, b = 0;` ` ` `var` `a = n;` ` ` `// Iterate until a` ` ` `// is non-zero` ` ` `while` `(a != 0)` ` ` `{` ` ` ` ` `// Add the number of` ` ` `// bottles that are emptied` ` ` `s = s + a;` ` ` `// Update a after` ` ` `// exchanging empty bottles` ` ` `a = (a + b) / e;` ` ` `// Stores the number of bottles` ` ` `// left after the exchange` ` ` `b = n - (a * e);` ` ` `n = a + b;` ` ` `}` ` ` `// Return the answer` ` ` `return` `s;` `}` `// Driver Code` `var` `n = 9, e = 3;` `// Function call` `var` `s = maxBottles(n, e);` `document.write(parseInt(s) + ` `"\n"` `);` `// This code contributed by Princi Singh` `</script>` |

**Output:**

13

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