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Articles on Trending Technologies
Technical articles with clear explanations and examples
Golomb sequence
Golomb Sequence − The Golomb Sequence is a non-decreasing sequence of integers where the value of the nth term is the number of times the integer n appeared in the sequence. Some terms of Golomb sequence are, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, … Here as we can see, the 5th term is 3 and 5 also appears 3 times in the sequence. The 6th term is 4 and 6 also appears 4 times in ...
Read MoreFront and Back Search in unsorted array
Unsorted Array − An array is a data structure consisting of a collection of elements of the same type. An unsorted array is such a structure where the order of elements is random, i.e. on insertion, the element is added to the last irrespective of the order of previous elements and searching in such an array is not helped by any search algorithm because of lack of a pattern of the positioning of elements. Searching − Searching in an array means finding a particular element in the array which can be either returning the position of a desired element or ...
Read MoreFind n-th Fortunate Number
Fortunate Numbers − It is the smallest integer m > 1 such that, for a given positive integer n, pn# + m is a prime number, where pn# is the product of the first n prime numbers. For example, for calculating the third fortunate number, first calculate the product of the first 3 prime numbers (2, 3, 5) i.e. 30. Upon adding 2 we get 32 which is an even number, adding 3 gives 33 which is a multiple of 3. One would similarly rule out integers up to 6. Adding 7 gives, 37 which is a prime number. Thus, ...
Read MoreCheck if the given two numbers are friendly pairs or not
Friendly Numbers − According to number theory, friendly numbers are two or more numbers having the same abundancy index. Abundancy Index − Abundancy index of a natural number can be defined as the ratio between the sum of all the divisors of the natural number and the natural number itself. The abundancy of a number n can be expressed as $\mathrm{\frac{\sigma(n)}{n}}$ where $\mathrm{\sigma(n)}$ denotes the divisor function equal to all the divisors of n. For example, the abundancy index of the natural number 30 is, $$\mathrm{\frac{\sigma(30)}{30}=\frac{1+2+3+5+6+10+15+30}{30}=\frac{72}{30}=\frac{12}{5}}$$ A number n is said to be a ‘friendly number’ if there exists a ...
Read MoreCheck if any valid sequence is divisible by M
A sequence is a collection of objects, and in our case, it is a collection of integers. The task is to find if a sequence with the usage of the addition and subtraction operator within the elements is divisible by M or not. Problem Statement Given an integer M and an array of integers. Using only addition and subtraction between elements check if there is a valid sequence whose solution is divisible by M. Sample Example 1 Input: M = 2, arr = {1, 2, 5} Output: TRUE Explanation − For the given array a valid sequence {1 ...
Read MoreMax occurring divisor in an interval
Let x and y be two numbers. In this case, x is said to be a divisor of y if when y is divided by x it returns zero remainder. The maximum occurring divisor in an interval is the number that is a divisor of the maximum number of elements of that interval. Problem Statement Given an interval [a, b]. Find the maximum occurring divisor in the range including both a and b, except ‘1’. In case all divisors have equal occurrence, return 1. Sample Example 1 Input [2, 5] Output 2 Explanation − Divisors of 2 = ...
Read MoreRamanujan–Nagell Conjecture
Ramanujan-Nagell Equation is an example of the exponential Diophantine equation. The diophantine equation is a polynomial equation with integer coefficients of two or more unknowns. Only integral solutions are required for the Diophantine equation. Ramanujan-Nagell Equation is an equation between a square number and a number that is seven less than the power of 2, where the power of 2 can only be a natural number. Ramanujan conjectured that the diophantine equation 2y - 7 = x2 has positive integral solutions and was later proved by Nagell. $$\mathrm{2y−7=x^2\:has\:x\epsilon\:Z_+:x=1, 3, 5, 11, 181}$$ Triangular Number − It counts objects arranged in ...
Read MorePlaceholders in Tensorflow
TensorFlow is a widely-used platform for creating and training machine learning models, when designing a model in TensorFlow, you may need to create placeholders which are like empty containers that will later be filled with data during runtime. These placeholders are important because they allow your model to be more flexible and efficient. In this article, we'll dive into the world of TensorFlow placeholders, what they are, and how they can be used to create better machine learning models. What are placeholders in Tensorflow? In TensorFlow, placeholders are a special type of tensor used to supply real data to ...
Read MoreRandom Forest vs Gradient Boosting Algorithm
Introduction Random forest and gradient boosting are two of the most popular and powerful machine learning algorithms for classification and regression tasks. Both algorithms belong to the family of ensemble learning methods and are used to improve model accuracy by combining the strengths of multiple weak learners. Despite their similarities, random forest and gradient boosting differ in their approach to model building, performance, and interpretability. When you're finished reading, you'll understand when to use each algorithm and how to select the one that's ideal for your unique problem. What is Random Forest? Random Forest, a ...
Read MoreBox-Cox Transformation in Regression Models Explained
Introduction A popular statistical method for comprehending and simulating the connections between variables is regression analysis. The dependent variable is frequently assumed to have a normal distribution, though. The accuracy and dependability of the regression model may be jeopardized if this assumption is broken. The Box−Cox transformation offers a potent method for changing skewed or non−normal dependent variables to resemble a normal distribution in order to overcome this issue. We shall examine the Box−Cox transformation theory and use it in regression models in this post. We'll look at the transformation's justification and how it helps to satisfy the ...
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