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For N to be a stormer number, the highest prime factor of the expression N^2+1 must be greater than or equal to 2*N and it should be a positive integer. For example, 4 is a stormer number. Since 4*4+1=17 has the greatest prime factor 17 itself which is greater than 8 i.e. 2*4. But 3 is not a stormer number because 3*3+1=10. The greatest prime factor of 10 is 5 which is less than 6 i.e. 2*3. In this problem, we are given a positive integer N and our goal is to print the first N stormer. INPUT: 4 ... Read More
In this article, we are going to solve the problem of printing first n Fibonacci Numbers using a direct formula. In mathematics, the fibonacci numbers often denoted by Fn (which indicates nth fibonacci number), form a series in which each number is equal to the sum of the preceding two numbers. The nth fibonacci number can be indicates as below − $$\mathrm{Fn\:=\:F_{n-1}\:+\:F_{n-2}}$$ The series begins with 0 and 1. The first few values in the fibonacci sequence, starting with 0 and 1 are − 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. ... Read More
In this problem, we simply need to print the number of ones in the smallest repunit. A repunit is a positive number like 11, 111, or 1111 in recreational mathematics that only has the digit 1. A repunit is of the form $\mathrm{(10*n-1)/9}$ Example $\mathrm{(10*10-1)/9}$ gives 11. $\mathrm{(10*100-1)/9}$ gives 111. $\mathrm{(10*1000-1)/9}$ gives 1111. The above problem states that we are given any positive integer N with its unit digit 3 and we need to determine the smallest repunit that is divisible by the given number N. For example, If we are given N=13. Output: 6 N i.e. 13 perfectly divides ... Read More
Introduction In a networked computing environment, file systems allow users to access and manage files across different computers and storage devices. Network file systems (NFS) are a type of file system that enables remote file access and sharing between machines over a network. In NFS, a client machine can access files stored on a remote server as if they were on its local file system. One common question that arises regarding network file systems is whether they pre-fetch data to improve performance. In this article, we will explore concept of pre-fetching in network file systems and provide examples of how ... Read More
This problem statement says that we are allowed to perform only one operation i.e. multiply the given number by 2 such that it is divisible by 10. We will be given a number say n. The only operation that we can perform on a given number is that we can multiply the given number by 2 until it is divisible by 10. We need to determine the minimum number of operations required to make the number such that it is divisible by 10 by repeatedly multiplying the given number n by 2. Else, print -1 if it is not possible ... Read More
From the above problem statement, our task is to get the minimum steps in which a given number N can be obtained using addition or subtraction at every step. We can understand that we need to print the minimum number of steps that we can perform and sequence of the steps on any given integer N to reach the number starting from 0 by addition or subtraction of the step number. In this problem set, we can add or subtract the number equal to the step count from the current location at each step. For instance, we can add either ... Read More
In this problem set, we will be given any two distinct positive numbers, let’s say a and b, we need to return the largest of two distinct numbers without using any conditional statements (if-else) or any operators(, ==, !=, etc.) in c++. The main difficulty of the problem includes that we need to determine the largest of any two distinct positive numbers without using any operators or conditional statements. For example, INPUT: x=12, y=20 OUTPUT: 20 INPUT: x=3, y=2 OUTPUT: 3 Below is the algorithm that we will be using to solve this problem. Algorithm We will use type casting ... Read More
Our objective is to find the smallest positive number that is missing from an unsorted array. We will be given an array a[] of both positive and negative numbers, we need to get the smallest positive number that is missing from an unsorted array in this problem. We can modify the array given in this problem to solve it. For example, INPUT : a[] = {5, 8, -13, 0, 18, 1, 3} OUTPUT : 2 INPUT : a[] = {7, 10, -8, 1, 4} OUTPUT : 2 In the above examples, we are given an unsorted array as an input. ... Read More
In this problem, we simply need to divide two integers without using multiplication, division and mod operator. Though we can use addition or multiplication or bit manipulation. The problem statement states that we will be given two integers x and y. Without using multiplication, division or mod operator, we need to determine the quotient after dividing x by y. Example INPUT: x=15 , y=5 OUTPUT: 3 INPUT: x=10 , y=4 OUTPUT: 2 INPUT: x=-20 , y=3 OUTPUT: -6 Approach Approach-1(using simple mathematics) In this approach, we will use a simple mathematics algorithm. Below is the step-by-step illustration of the ... Read More
A figurative number that depicts a dodecagon is called a dodecagonal number. The Centered Dodecagonal number is represented by a dot in the centre and other dots encircling it in the successive dodecagonal (i.e. a 12-sided polygon) layers. Centered Dodecagonal number can be better explained with the below figure. For n=1, only a single dot will be there in the centre. So the output will be 1. For n=2, a single dot in the centre followed by a dodecagon encircling it. Thus, the total number of dots will be 13. So the next centred dodecagonal number ... Read More