Programming Articles - Page 83 of 2896

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 More

In Python, dictionaries are key-value pairs where each key is associated with a corresponding value. When we want to convert a dictionary to a list by repeating keys, we need to iterate over each key-value pair and repeat the key based on its corresponding value. Input Output Scenarios See the following input-output scenarios to understand the concept of converting a dictionary to a list by repeating keys corresponding to the number present in the values. Input dictionary: {'a': 3, 'b': 2, 'c': 1} Output list: ['a', 'a', 'a', 'b', 'b', 'c'] In the input dictionary the key 'a' has ... Read More

In a dictionary, keys must be unique and immutable, while values can be of any type and can have a list of values. In the case of a dictionary of lists, each key points to a list that can contain multiple elements.  Here's an example of a dictionary of lists − data = {'numbers':[1, 2, 3, 4, 5, 6], 'states':['UP', 'Tamil Nadu', 'Telangana', 'Gujarat', 'UP', 'Tamil Nadu'], 'cities':['Agra', 'Chennai', 'Hyderabad', 'Surat', 'Lucknow', 'Coimbatore']}) In the above dictionary, each key is mapped to a list of values. For instance, the 'states' key maps to the list ['UP', 'Tamil Nadu', 'Telangana', ... Read More

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 More

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

In this article, the user will see how to calculate the maximum and minimum in a set using Python language. The main feature of the python set is that it contains no duplicates elements, store the elements in unordered form and is also difficult to alter the elements presented in the set. In this article, three different methods are illustrated that is Converting the set to a list, using built-in functions, and using the sorted() function. The ‘sorted()’ function retrieves a set’s element in a sorted way. Approach 1: Finding the maximum and minimum in a Python set ... Read More

In this article, we will discuss how to compute the volume, surface area, and space diagonal of a cuboid. A Cuboid is a 3D geometric shape that resembles a rectangular box. It is also called a rectangular prism. A cuboid has six rectangular faces with twelve edges. The length, breadth, and height of a cuboid are different, but in the case of a cube, all sides are equal. Two examples are illustrated in this article. The first example uses the concept of a user-defined function and the second example uses the parameterized constructor of a defined class to calculate the ... Read More

In this article, the user will understand how to get all possible slices of a string for K number of slices in a Python program. Two different examples are depicted in this article. We will employ an iteration approach to accomplish the desired result. In the second example, we will utilize the itertools.combinations approach to obtain the sliced string. Let's take an example to demonstrate the computation. The following examples are provided for understanding purposes, and we will go through the computation process one by one. Example 1: Finding all possible slices of a string for K number of slices ... Read More

Altair is a kind of statistical visualization library in Python. This library is based on vega and vega-lite javascript libraries. Moreover, we can visualize the data distribution in the form of a density plot in Python. These plots are useful whether we need to compare the variable distribution across the different groups or we need to visualize the distribution shape. The useful applications of density plots such as visualizing data shape, outlier detection, comparing distribution and model selection. The density plot is demonstrated in this article with the help of Python code. For better understanding, we are considering an example ... Read More

In this article, we will discuss how to compute the XOR of array elements that are divisible by a given number. The XOR (exclusive OR) is a binary operation that compares the bits of two operands. If the bits are different then it will return 1 whereas it returns 0 if the bits are the same. In this approach, we will use the property of XOR and apply this to this problem. The solution to this problem is shown with a relevant example. Let’s take an example to demonstrate the computation. Consider a simple example for understanding purposes, the array ... Read More