Undulating Numbers in C++

In this article, we will discuss the Undulating Number in C++ with different examples.

What is the Undulating Number?

"Undulating numbers" are integers that alternate between increasing and decreasing digits. For instance, the number 131 alternates in an increasing decreasing, and increasing sequence, which makes it an undulating number.

Properties:

• There are countless numbers of undulating numbers.
• If an undulating number has odd digits, it is also a Palindrome number.
• For any n ≥3, there are 9 × 9 = 81 non-trivial n-digit undulating numbers because the first digit cannot be zero, it can have nine values and the second digit can also have nine values.
• As ABABAB...AB = 10101...01 × AB, every undulating number with an even number of digits and at least four digits is composite. As an illustration, 282828 = 101010 * 28.
• Every undulating number with an even number of digits and at least four digits is composite because it can be written as,
  XYXYXYXY….XY = 10101010….01 * XY .
  à181818 = 10101 * 18.

Example 1:

Let us take a C++ program to check if the number is an undulating number or not.

Output:

Explanation:

1. A while loop is used by the isUndulating function to loop through the number's digits.
2. It looks for consecutive identical digits and determines if the pattern of the digits is undulating.
3. The first two digits indicate which way the undulation is going.
4. In the main function, the user is asked to enter a number, using the IsUndulating function, which will determine whether the given number is undulating or not

Example 2:

Let us take a C++ program to check if the number is an undulating number or not using Recursion:

Output:

Explanation:

1. In this example, the isUndulating function is invoked recursively to determine whether the number follows the undulating pattern.
2. Two inputs are required: the number to be checked and a boolean increase that indicates whether the pattern is rising or decreasing at the moment.
3. The function returns false when there are fewer than three digits in the number because it cannot be an undulating number.
4. Next, the function determines whether the current set of three numbers continues the undulating pattern. If they do, the program toggles the rising flag and calls itself recursively with the remaining digits.
5. In the main function, the user is asked to enter a number, using the IsUndulating function, it will determine whether the given number is undulating or not