Article Categories
- All Categories
-
Data Structure
-
Networking
-
RDBMS
-
Operating System
-
Java
-
MS Excel
-
iOS
-
HTML
-
CSS
-
Android
-
Python
-
C Programming
-
C++
-
C#
-
MongoDB
-
MySQL
-
Javascript
-
PHP
Articles by Rinish Patidar
Page 2 of 6
Sum of product of Consecutive Binomial Coefficients
The problem statement includes printing the sum of product of consecutive binomial coefficients for any positive number, N which will be the user input. The positive coefficients in the binomial expansion of any term are called binomial coefficients. These binomial coefficients can be found out using Pascal's triangle or a direct formula. The formula to calculate the binomial coefficient: $$\mathrm{^nC_{r}=\frac{n!}{(n-r)!r!}}$$ where, n and r can be any positive numbers and r should never be greater than n. Note : The value of 0! is always equal to 1. In this problem, we will be given a positive number N and ...
Read MoreSum of digits written in different bases from 2 to n-1
The problem statement includes printing the sum of digits of N, which will be the user input, when written in different bases from 2 to N−1. In this problem, we will be provided any positive integer N and we need to represent that number in a different base numeral system from 2 to N−1 and find the sum of the digit of each different base numeral system. In the base−n numeral system, every digit of the representation of any number in that numeral system from right represents the number of times power of n from 0 to 31. For example, ...
Read MoreProgram to print the sum of the given nth term
The problem statement includes printing the sum of the series whose Nth term is given. The value of N will be given in the input. We need to find the sum of the sequence up to N where the Nth term of the sequence is given by: $$\mathrm{N^{2}−(N−1)^{2}}$$ Let’s understand the problem with the below examples: Input N=5 Output 25 Explanation − The value of N given is 5.The first 5 terms of the sequence are: $\mathrm{N=1, 1^{2}−(1−1)^{2}=1}$ $\mathrm{N=2, 2^{2}−(2−1)^{2}=3}$ $\mathrm{N=3, 3^{2}−(3−1)^{2}=5}$ $\mathrm{N=4, 4^{2}−(4−1)^{2}=7}$ $\mathrm{N=5, 5^{2}−(5−1)^{2}=9}$ The sum of the terms of the sequence until 5th ...
Read MoreNumbers within a range that can be expressed as power of two numbers
The problem statement includes printing the count of numbers within a range given that can be expressed as power of two numbers i.e. numbers which are perfect powers. The numbers which are known as perfect powers is the number which can be expressed as $\mathrm{x^{y}}$, where x>0 and y>1 for all integers. For example, 8 is a perfect power because it can be expressed as $\mathrm{2^{3}}$, which is equal to 8 hence it is considered as a perfect power. In this problem, we will be given a range as two positive integers in the input i.e. a and b ...
Read MoreMinimum digits to remove to make a number Perfect Square
The problem statement includes finding the minimum number of digits to remove from a number to make a number perfect square. A perfect square denoted as $\mathrm{x^{2}}$ is a positive integer which is a product of an integer with itself. We will be given a positive number N and we need to find the minimum number of digits we can remove from the number N to make it a perfect square i.e. such that it is a product of some integer with itself. For example, N=42 We can remove 1 digit from N i.e. 2 to make it a perfect ...
Read MoreMaking zero array by decrementing pairs of adjacent
The problem statement includes making an array zero array by decrementing pairs of adjacent. The array will be given in the input and we can perform the operation on the array i.e. subtract 1 from ith and (i+1)th index where 0
Read MoreHoax Number
The problem statement includes checking if the given number N, which will be the user input, is a hoax number or not. A Hoax number is a composite number whose sum of digits of its distinct prime factors is equal to the sum of the digits of the composite number itself. Since 1 is not a prime number, we don’t consider 1 as a sum of digits of distinct prime numbers. If a prime number is a factor of the composite number more than once, it is just considered once while taking the sum of digits of prime factors. In ...
Read MoreHardy-Ramanujan Theorem
The Hardy−Ramanujan Theorem states that the number of distinct prime factors of any natural number N will be approximately equal to the value of $\mathrm{\log(\log N)}$ for most of the cases. For example, let’s consider N to be 1000. The number of distinct prime factors of 15 are 2 and 5 i.e. 2 distinct prime factors. The value of $\mathrm{\log_{e}(\log_{e}(1000))}$ is equal to 1.932 which is approximately equal to 2. The Hardy−Ramanujan theorem is proved in the above case. Since the theorem states that the number of distinct prime factors will be approximately equal to $\mathrm{\log(\log(N))}$ for most of ...
Read MoreGiven a Number N in Decimal Base, find Number of its Digits in any Base (base b)
The problem statement includes finding the number of digits in N when represented in any base b numeral system. Initially, N is given in the base−10 numeral system. In the problem, we will be provided with a positive integer N in the input which will be in the base−10 numeral system and a positive integer b greater than 1. Our task will be to find the number of digits when N is being represented in the base−b numeral system. Any number represented in any base number, every digit from right represents the number of times power of that base number ...
Read MoreCount Numbers formed by given two Digit with Sum having given Digits
The problem statement includes counting the numbers formed by the given two digits, x and y of size N with sum having given digits only i.e. x and y. We need to count the distinct numbers which can be formed by the digits, x and y which will be the user input of size N where N ranges from 1 to 10^6. The N will also be provided in the input. The numbers formed using the digits, x and y of size N must be such that the sum of digits of the numbers formed should have only digits ...
Read More