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Articles by Vanshika Sood
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First Occurrence of a Digit in a Given Fraction
The decimal expansion of a fraction is the decimal representation of the fraction's value. In the following article we discuss two approaches to find the first occurrence of c in a/b. Problem Statement Given three integers a, b, c, locate the first instance of c in the fraction a/b after the decimal point. Print-1 if it does not exist. Sample Examples Input a = 5, b = 6, c = 3 Output 2 Explanation $$\mathrm{\frac{a}{b}=\frac{5}{6}=0.83333}$$ So c=3 occurs at the 2nd place after the decimal point. Hence the output is 2. Input a = -10, b = ...
Read MoreMinimize the Absolute Difference of Sum of Two Subsets
To Minimize the Absolute Difference of Sum of Two Subsets, we partition a vector into two subsets i.e. we divide the elements of the vector into two smaller vectors such that each element of the original vector belongs to one of the two smaller vectors, and the two smaller vectors are disjoint. For example, if we have a vector v = {1, 2, 3, 4, 5}, then one possible partitioning of v into two subsets is S1 = {1, 3, 4} and S2 = {2, 5}, where each element of v belongs to either S1 or S2, and the ...
Read MoreNearest power of 2 of frequencies of each digit of a given number
The article describes a method to calculate the closest power of 2 for the frequency of each digit in a given number. The term "frequencies" refers to the count of occurrences of each unique digit in the number. Problem Statement Determine the occurrence count of each digit in a positive integer N. Then, for each digit, find the nearest power of 2 to its frequency. If there are two nearest powers of 2 for any frequency, print the larger one. Example Input n = 677755 Output 5 -> 2 6 -> 1 7 -> 4 ...
Read MoreMaximize count of occurrences of S2 in S1 as a subsequence by concatenating N1 and N2 times respectively
The following article discusses an approach to count the maximum occurrences of a string s2 in another string s1 after they have been concatenated N1 and N2 times respectively. This is an interesting type of pattern searching problem. In this article we have employed a relatively intuitive solution approach. Problem Statement The task is to determine the maximum number of non-overlapping occurrences of string s2 within string s1. The strings are concatenated multiple times: s1 is repeated n1 times, and s2 is repeated n2 times. Example Input s1 = “abc”, s2 = “ac”, n1 = 4, n2 ...
Read MoreLexicographically smallest string with period K possible by replacing ‘?’s from a given string
A string is a period of K if and only if it repeats itself every K characters. For example, the string "abcabcabc" is a period of 3, because it repeats itself every 3 characters. The string "abcabc?abc" is not a period of 3, because the character '?' does not repeat itself every 3 characters. Problem Statement Given a string "str" containing N lowercase characters and a positive integer K, the objective is to replace every occurrence of the character '?' within the string "str" with a lowercase alphabet such that the resulting string forms a period of length ...
Read MoreCount all prime numbers that can be formed using digits of a given number
Any number larger than 1 is said to be prime if it cannot be written as the product of two smaller natural numbers except 1 and the number itself. For instance, 5 is prime since its only product forms, 1 5 and 5 1, both involve 5. Primes play a crucial role in number theory as stated by the prime number theorem, which asserts that any natural number greater than 1 is either a prime itself or can be expressed as a unique product of prime numbers. This theorem highlights the significance of prime numbers in the realm of mathematics. ...
Read MoreCalculate time required to type a word using given single-row keyboard
The following article discusses an efficient approach to compute the total time taken to type out a word using a single-row keyboard. This is an interesting problem and has been asked previously in technical interviews. Problem Statement Consider a hypothetical scenario wherein all the keys on a keyboard are placed in a single row. The first key is indexed 0 and the last key is indexed 25. For a given string ‘s’ calculate the time taken to type all the characters of ‘s’ on a special keyboard with layout specified as ‘keyboard_layout’. The time taken ...
Read MoreFind Mth Eelement after K Right Rotations of an Array
Right rotating an array means shifting its elements to the right by a certain number of positions. In a single right rotation, the last element of the array becomes the first element, and the remaining elements are shifted to the right. Problem Statement The goal is to find the Mth element of an array after performing K right rotations, where K and M are non-negative integers and the array contains N elements. Sample Examples Input arr = [12 34 56 21], K = 2, M = 1 Output 56 Explanation Arr after K right ...
Read MoreToggle First and Last Bits of a Number
The following article provides an in depth explanation of the method used to modify a number by toggling its first and last bit using bitwise operators. A bitwise operator is an operator that can be used to manipulate individual bits in binary numbers or bit patterns. Problem Statement For a given number n, modify the number such that the first and the last bit of the binary expansion of the new number are flipped i.e. if the original bit is 1 then the flipped bit should be 0 and vice versa. All the bits between the first and the last ...
Read MoreThe Sum of the Fifth Powers of the First n Natural Numbers
Natural numbers are numbers that start from 1 and include all the positive integers. The following article discusses two possible approaches to compute the sum of the fifth powers of the first n natural numbers. The article discusses the two approaches in detail and compares them with regards to efficiency and intuitiveness. Problem Statement The purpose of this problem is to compute the arithmetic sum of the first n natural numbers, all raised to their fifth power i.e. $\mathrm{1^5 + 2^5 + 3^5 + 4^5 + 5^5 + … + n^5}$ till the nth term. Examples Since n is a ...
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