Multi-Dimensional Knapsack Given N items and a knapsack with two constraints: maximum volume capacity V and maximum weight limit M. Each item i has volume c[i], weight w[i], and value v[i]. Find the maximum total value achievable without exceeding either constraint. Unlike basic knapsack problems th...
Extended Euclidean Algorithm The Extended Euclidean Algorithm serves as a enhancement to the classic Euclidean method. While the standard algorithm computes only the greatest common divisor (\gcd(a, b)), this variant simultaneously determines the coefficients that express the GCD as a linear combina...
Problem Description Given two integers n and k, return all possible comibnations of k numbers out of the range [1, n]. You may return the answer in any order. Example 1: Input: n = 4, k = 2 Output: [ [2,4], [3,4], [2,3], [1,2], [1,3], [1,4], ] Example 2: Input: n = 1, k = 1 Output: [[1]] Constraints...
Articulation points (cut vertices) and bridges (cut edges) are fundamental concepts in undirected graph connectivity. An articulation point is a vertex whose removal increases the number of connected components. A bridge is an edge whose removal disconnects the graph. These structures can be efficie...
When processing identification strings composed of uppercase letters, a common pattern involves converting characters to numerical values and aggregating them through multiplication. Consider a scenario where two entities—a celestial object and a team—must be matched based on their respective name e...
Theory Overview Arrays, sets, and maps are all implementations of hash tables Hash tables excel at determining whether an element has been encountered previously Problem 1: Valid Anagram Problem Link: 242. Valid Anagram - LeetCode Difficulty: Easy Solution Approach: When the chaarcter range is small...
Understanding Difference Arrays Given an array arr, its difference array diff is defined as: diff[0] = arr[0] diff[i] = arr[i] - arr[i-1] for i > 0 To reconstruct the original array from the difference array: arr[i] = diff[0] + diff[1] + ... + diff[i] For range updates [l, r] with value x: diff[l...
When everyone is busy posting photos on social media, there are always some people who are too handsome to have friends. This problem asks you to identify those who are too handsome to have friends. Input Format: The first line contains a positive integer ( N ) (≤100), the number of known friend cir...
Maximizing Triples Product Given three integers, you can increment any of them exactly five times. The goal is to maximize their final product. To achieve the maximum product, we should always increment the smallest of the three integers. This minimizes the disparity between the values, which yields...
Minimum Absolute Difference in a Binary Search Tree To compute the minimum absolute difference between values in a binary search tree, leverage the property that an in-order traversal yields a sorted sequence. By tracking the previous node during traversal, differences can be calculatde efficiently....