💡 Problem Formulation: Given a threshold value x, the challenge is to identify the highest natural number n such that when you sum the squares of natural numbers from 1 to n, the result is not greater than x. For example, if x is 100, the maximum n is 4 since 1² + 2² + … Read more

💡 Problem Formulation: The challenge is to compute the maximum number of operations required to reduce a given number n to 1. An operation is defined as either subtracting 1 from the number, or dividing it by 2 if it is even. For instance, given the input 8, the desired output is 4, correlating with … Read more

💡 Problem Formulation: You’re given an array of integers where each element represents points you can earn. The challenge is to find the maximum number of points you can obtain by deleting elements. Each time you delete an element, points equal to the value of the deleted element are added to your total, but adjacent … Read more

💡 Problem Formulation: Given an array of integers, our goal is to find the maximum sum of triplets (i, j, k) in such a manner that the elements at those indices follow the constraint i < j < k and the values are distinct (a[i] < a[j] < a[k]). For example, given the array [1, … Read more

💡 Problem Formulation: Finding the median of a Binary Search Tree (BST) in linear time and constant space is a significant challenge, as the median is the middle element when the elements are sorted, and a BST allows in-order traversal, which naturally orders the elements. The task is to find the median value without consuming … Read more

💡 Problem Formulation: Finding the minimum adjustment cost of an array involves altering each element so that the absolute difference between any two consecutive elements is less than or equal to a target value. The objective is to determine the minimum total cost of adjusting the array’s values. For instance, given an array [1, 4, … Read more

💡 Problem Formulation: You have a set of jobs with individual times to completion and constraints that dictate the order of execution. The challenge is to figure out the minimal time needed to complete all jobs while respecting the constraints. For instance, given an array of job durations [4, 2, 5], and a set of … Read more

💡 Problem Formulation: Imagine you are given a sorted array of consecutive numbers, but one number is missing. Your task is to efficiently find this missing element. For example, if the input is [1, 2, 4, 5], the desired output is 3 because it is the missing number in the sequence. Method 1: Summation Formula … Read more

💡 Problem Formulation: Given a target value K, the challenge is to find N distinct integers such that the result of their bitwise OR operation equals K. Consider the case where K is 15 (0b1111 in binary), and N is 4. The desired output is a list of four distinct integers, for example, [1, 2, … Read more

💡 Problem Formulation: Finding the n-th lexicographically permutation of a string involves generating the string sequence that would appear at position n if all permutations were ordered alphabetically. For example, given the string “ABC” and n = 2, the desired output is “ACB”, which is the second permutation when listed in lexicographic order. Method 1: … Read more

💡 Problem Formulation: Recurrence relations are equations that define sequences of values using recursion and initial terms. Given a recurrence relation and the initial values, the challenge is to find the nth term of this sequence in Python. For instance, for the Fibonacci sequence defined as F(n) = F(n-1) + F(n-2) with F(0) = 0 … Read more

💡 Problem Formulation: Given a sequence of integers which represents the Greatest Common Divisor (GCD) of every possible pair of a set of original numbers, the challenge lies in determining the original set of numbers. For instance, if the input array is [2, 4, 4, 2, 4, 8], a possible set of original numbers that … Read more