Fizz Buzz in C++

Fizz Buzz problem states that given an integer n, for every integer i <= n, the task is to write a C++ program to print,

• 'FizzBuzz' if i is divisible by 3 and 5,
• 'Fizz' if i is divisible by 3,
• 'Buzz' if i is divisible by 5
• 'i' as a string, if none of the conditions are true.

Example:

Input: n = 3
Output: [1 2 Fizz]

Input: n = 10
Output: [1 2 Fizz 4 Buzz Fizz 7 8 Fizz Buzz]

Input: n = 20
Output: [1 2 Fizz 4 Buzz Fizz 7 8 Fizz Buzz 11 Fizz 13 14 FizzBuzz 16 17 Fizz 19 Buzz]

Naive Approach - By checking every condition individually

A very simple approach to solve this problem is that we can start checking each number from 1 to n to see if it's divisible by 3, 5, or both. Depending on the divisibility:

• If a number is divisible by both 3 and 5, append "FizzBuzz" into result.
• If it's only divisible by 3, append "Fizz" into result.
• If it's only divisible by 5, append "Buzz" into result..
• Otherwise, append the number itself into result.

Below is the implementation of the above approach:

1 2 Fizz 4 Buzz Fizz 7 8 Fizz Buzz 

Time Complexity: O(n), since we need to traverse the numbers from 1 to n in any condition.
Auxiliary Space: O(n), for storing the result

By String Concatenation

While the naive approach works well for the basic FizzBuzz problem, it becomes very complicated if additional mappings comes under picture, such as "Jazz" for multiples of 7. The number of conditions for checking would increases.

Instead of checking every possible combination of divisors, we check each divisor separately and concatenate the corresponding strings if the number is divisible by them.

Let's see the step-by-step approach:

• For each number i <= n, start with an empty word res.
  • Check if i is divisible by 3, append "Fizz" into res.
  • Check if i is divisible by 5, append "Buzz" into res.
  • If we add "Fizz" and "Buzz", the res becomes "FizzBuzz" and we don't need extra comparisons to check divisibility of both.
  • If nothing was added, just use the number.
• Finally, append this res into our result array.

1 2 Fizz 4 Buzz Fizz 7 8 Fizz Buzz 

Time Complexity: O(n), since we need to traverse the numbers from 1 to n in any condition.
Auxiliary Space: O(n), for storing the result

Using Hashing

When we have many words to add like "Fizz", "Buzz", "Jazz" and more, the second method can still get complicated. To make things cleaner, we can use something called a hash table (in C++, it's called unordered_map). Initially, we can store the divisors and their corresponding words into hash table.

For this problem, first we'll map 3 to "Fizz" and 5 to "Buzz" into unordered_map and for each number i <= n, do the following:

• Start with an empty word res
• Checks if it i divisible by 3 or 5,
  • Appends the corresponding string from map to the res.
  • If the number is not divisible by either, simply adds the number itself as a string into res.
• Finally, append res into result.

1 2 Fizz 4 Buzz Fizz 7 8 Fizz Buzz 

Time Complexity: O(n), since we need to traverse the numbers from 1 to n in any condition.
Auxiliary Space: O(n), for storing the result and for hash table