💡 Problem Formulation: Imagine you’re given a set of items, each with a weight and a value, and a knapsack with a limited capacity. How can you maximize the total value of the items you take without exceeding the capacity? This problem, better known as the 0/1 Knapsack Problem, is a classic example in combinatorial … Read more
💡 Problem Formulation: Given a two-dimensional matrix (a list of lists), the task is to compute the sum of elements forming a Z shape. For instance, in a 3×3 matrix [[1,2,3], [4,5,6], [7,8,9]], the Z-shaped sum would include elements 1, 2, 3, 5, and 7, 8, 9, thus the desired output is 35. Method 1: … Read more
💡 Problem Formulation: We often encounter situations where we need to construct words from a given set of letters, for example in games like Scrabble. Given a string of letters, the goal is to find the length of the longest word that can be made. For instance, with the input “pythonista”, we might discover that … Read more
💡 Problem Formulation: Investors often aim to maximize their profits through the buying and selling stocks multiple times based on fluctuating market prices. The goal is to identify the best days to buy and sell within a given list of daily stock prices to achieve the highest possible profit. For instance, given a list of … Read more
💡 Problem Formulation: In the stock market, the goal is to maximize profit by choosing the best time to buy and sell a stock within a given period. The challenge lies in determining the optimal buying day when prices are low, and selling day when prices peak. For example, if we’re given a list of … Read more
💡 Problem Formulation: You need to determine if a graph is bipartite, where a bipartite graph can be separated into two disjoint vertex sets such that no two vertices within the same set are adjacent. An input example might be an adjacency list representing the graph, and the desired output would be a boolean value … Read more
💡 Problem Formulation: In a circular array, for each element, we aim to find the next greater element located to its right. A circular array means the end of the array wraps around to the beginning, forming a circle. For instance, given the input array [2, 1, 3, 4], a desired output would be [3, … Read more
💡 Problem Formulation: Given a singly linked list, the challenge is to find the middle node — the node that is equidistant from both the start and the end, when you have an odd number of nodes, or one of the two middle nodes when there are an even number of nodes. For instance, if … Read more
💡 Problem Formulation: In this article, we tackle the challenge of determining the minimum number of buses needed to cover all bus stops in a route. Given a list of bus stops where each stop has a certain capacity of passengers it can handle, we aim to find the least number of buses required so … Read more
💡 Problem Formulation: Imagine you have a deck of cards with different values and you want to write a Python program to sort these cards so they’re revealed in ascending order. This article will guide you through various methods of achieving this, from basic sorting techniques to more advanced methods. For instance, if the input … Read more
💡 Problem Formulation: We aim to partition two given strings into substrings such that each corresponding pair of substrings forms an anagram of each other. For instance, taking the strings ‘abcde’ and ‘eadcb’, we can partition them into [‘a’, ‘b’, ‘cd’, ‘e’] and [‘e’, ‘a’, ‘dc’, ‘b’], forming anagrams for each partition respectively. Method 1: … Read more
💡 Problem Formulation: We aim to compute the cumulative sum of all possible contiguous subarrays within a given list of numbers. For instance, given the list [1, 2, 3], the desired output would be the sum of [1], [2], [3], [1, 2], [2, 3], and [1, 2, 3], which equals to 20. Method 1: Brute … Read more