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Articles by Divya Sahni
Page 3 of 4
Sum of Fourth Powers of first N natural numbers
The fourth power of a number x is x raised to the power 4 or x4. Natural numbers are all positive integers excluding zero. Thus, the sum of the fourth powers of the first N natural numbers is − $\mathrm{Sum = 1^4 + 2^4 + 3^4 + 4^4 + … + N^4}$ This article describes some approaches for finding the sum using minimum time and space complexity. Problem Statement Given the number N, find the sum $\mathrm{1^4 + 2^4 + 3^4 + 4^4 + … + N^4}$. Example 1 Input: 3 Output: 98 Explanation $\mathrm{Sum = 1^4 + ...
Read MoreProgram to print binomial expansion series
Binomial expansion is a mathematical formula used to expand the expressions of the form (a+b)^n, where n is a positive integer and a and b can be any real or complex numbers. The expansion gives the coefficients of the terms in the expansion. A binomial expansion can be represented as $$\mathrm{(a+b)^n= ^nC_0a^nb^0+ ^nC_1a^{n-1}b^1 + ^nCa^{n-2}b^2+...+ ^nC_ra^{n-r}b^r+...+ ^nC_na^0b^n}$$ where $\mathrm{^nC_r}$ are the binomial coefficients and is given by $\mathrm{^nC_r=\frac{n!}{r!\times(n−r)!}}$ where n! is the factorial of n The expansion can be used for calculating all the binomial terms using the formula above and putting it into the expansion equation. Problem ...
Read MorePython program to print words from a sentence with highest and lowest ASCII value of characters
ASCII (American Standard Code for Information Interchange), is a character encoding system that represents every character as a unique 7-bit binary code i.e. ASCII values are a numerical representation of characters. The ASCII values are 7-bit binary codes that range from 0 to 127. For Example, the ASCII code for a space character is 32, and for digit ‘1’ ASCII code is 49 and similarly ASCII codes are assigned to each character which is represented in an ASCII table. In Python, the ASCII code of a character can be computed using a predefined function ord(), which takes a character as ...
Read MoreModify array of strings by replacing characters repeating in the same or remaining strings
Modifying an array of strings by replacing characters repeating in the same or remaining strings is a common problem in programming. It can be solved using hash tables, sets, arrays etc. The aim is to improve the time and space requirements while providing the same functionality. This problem can be encountered in many real-life scenarios, such as processing large text or cleaning up datasets with duplicates. Problem Statement Given an input string array arr[] containing lowercase and uppercase characters. The goal is to modify the array by removing characters from the strings which are repeating in the same string or ...
Read MoreMinimum number of basic logic gates required to realize given Boolean expression`
Logic gates are the basic building block of a digital circuit. They take in one or two binary inputs and return a binary output. Since, using the term binary, the output and input can either be 0 or 1 or it can be said as “false” and “true” or “low” and “high”. There are 3 basic logic gates − AND Gate AND gate has two or more inputs and one output. It produces a high output if all inputs are high. The truth table for a two-input AND gate is given below − Input 1 Input 2 Output ...
Read MoreCheck if it is possible to reach any point on the circumference of a given circle from origin
The circumference of a circle can be defined as the outer boundary of the circle. It is the perimeter of a circle. Each point around a circle follows certain properties as follows − Point (x, y) lying inside the circle such that, $\mathrm{x^2 + y^2 < R^2}$ Point (x, y) lying on the circle such that, $\mathrm{x^2 + y^2 = R^2}$ Point (x, y) lying outside the circle such that, $\mathrm{x^2 + y^2 > R^2}$ where R = radius of the circle. Problem Statement Given a string S representing a sequence of moves (L, R, U, D) and ...
Read MoreCheck if a given string is a comment or not
In computer programming, comments are text written with the source code but ignored by the compiler or interpreter. They are used to provide readability of code by describing the code and its functionality for someone who is reading the code other than a compiler or interpreter. They are not executed and do not affect the functionality of the overall program, they are just for programmer guidance. Each programming language has a different syntax to represent comments. Here are a few examples − C/C++ − In C or C++, single-lined comments begin with ‘//’ and multi-liner comments are enclosed in ...
Read MoreTotal area of two overlapping rectangles
An overlapping area is an area that is shared by two objects. In the case of rectangles, it is the area of the rectangles that belong to both rectangles. In order to find the total areas of two overlapping rectangles, first er need to add the area of both rectangles respectively but in this total, the overlapping area is counted twice. Thus we need to subtract the overlapping area too. Problem Statement Given the bottom left and top right vertices of two rectangles. Find the total area covered by the two rectangles. Sample Example 1 Input bl_x1 = 0 bl_y1 ...
Read MoreSum of Pairwise Products
The pairwise product of a set X = {a, b, c} can be defined as the sum of the product of all possible set pairs. The pairs of the set are, Y = {a * a, a * b, a *c, b * b, b * c, c * c}, where the product is commutative. Thus, the pairwise product of set X is the summation of elements of set Y i.e. aa + ab + ac + bb + bc + cc. In mathematical terms, the sum of possible pair products can be depicted as, $$\mathrm{\displaystyle\sum\limits_{i=1, j=i}^{i\leq n, j\leq n}\:(i, ...
Read MoreGolomb 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 ...
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