ups and downs numbers

In this article, we will learn what a fluctuating number is and introduce our method of checking whether a given number is a fluctuating number, using a Boolean function to check the fluctuating number.

Problem Statement

We will be given a number and our task is to check if the given number is fluctuating.

Let us first understand the fluctuation number;

A fluctuating number is a number that consists of only two types of numbers, and every other number is the same.

We can say that a fluctuating number is of the form "PQPQPQ", where P and Q are two different numbers in the number system.

The first and second digits of the fluctuation number can never be the same, that is, 11111 is not a fluctuation number.

We usually regard non-trivial fluctuating numbers as fluctuating numbers only, which means that fluctuating numbers need to be composed of at least 3 digits. That is, we can't just use two numbers to form a fluctuating number.

Let us now consider some examples of fluctuating numbers -

494, 484, 474, 464, 454, 434, 424, 414, 404, 393, 383, 373, 363, 353, 343, 323, 313, 303, 101, 121, 131, 141, 151, 161 , 171, 181, 191, 202 and more.

Some high value fluctuating numbers are - 1212121212, 3838383838, 57575757575757, etc.

For any d digit number, where d>=3 (d contains at least 3 digits), we can have 9 * 9 = 81 fluctuating digits, since the first (number from 1 to 9) value has 9 options, similarly to the 9 options (numbers from 0 to 9, except for the first digit).

solution

We have a number and our task is to find out whether it fluctuates or not.

There are some restrictions on numbers −

• It contains only two types of numbers.

• Two numbers cannot be the same.

• Contains at least 3 digits

• Adjacent digits in the numbers are not the same.

Example

Given Number : Num = 252
Result: Yes, the number is undulating
Given Number : Num = 64664
Result: =No, the number is not undulating

Example

In the following example, we check if the given number is a fluctuating number. We demonstrated using a number that was not a fluctuating number. You can try different numbers to check if the number is a fluctuating number.

#include <bits/stdc++.h>
using namespace std;

// boolean function that checks
// is the number undulating
bool Is_number_undulating(string num){

   // important to check
   // if first and second digit
   // are equal
   if (num.length() <= 2 || num[0]==num[1])
   return false;
   for (int iterator = 2; iterator < num.length(); iterator++)
   if (num[iterator - 2] != num[iterator])
   false;
   return true;
}
int main(){
   string num = "111111";
   if (Is_number_undulating(num))
   cout << " Yes the number is undulating ";
   else
   cout << " No, the number is not undulating ";
}

Output

When you run the above C program, it will produce the following output -

No, the number is not undulating

Time Complexity - For n digits, the time complexity is O(N).

Space complexity - Since no external space is used, the auxiliary space complexity is O(N).

In this article, we learn in detail what is a fluctuating number and the code solution to check if a given number is fluctuating.

The above is the detailed content of ups and downs numbers. For more information, please follow other related articles on the PHP Chinese website!