Fading Coder

One Final Commit for the Last Sprint

Dynamic Programming Approach to Subsequence Problems on LeetCode

LeetCode 392: Is Subsequence Problem Description Given two strings s and t, determine if s is a subsequence of t. A subsequence is a sequence that can be derived from another sequence by deleting some or no characters without changing the order of the remaining characters. Dynamic Programming Soluti...

Efficient Pruning Strategies for Two Pointer Sum Problems

Optimizing the 3Sum Problem Given an integer array elements, the objective is to identify all unique triplets [a, b, c] such that a + b + c = 0. The soluiton set must not contain duplicate triplets. Constraints Array length ranges from 0 to 3000. Element values range from -10^5 to 10^5. Implementati...

Mastering Dynamic Programming: Fibonacci Sequences and Staircase Variants

Solving dynamic programming problems systematically typically involves five key steps: Define the dp array (table) and the meaning of its indices. Determine the recurernce relation. Initialize the dp array correctly with base cases. Select the correct iteration order. Trace example values to verify...

Rainwater Trapping Problem on LeetCode

Givan an aray of non-negative integers representing the heights of vertical bars where each bar has width 1, determine how much water can be trapped after raining. Example 1: Input: [0,1,0,2,1,0,1,3,2,1,2,1] Output: 6 Explanation: The blue regions represent trapped rainwater units. Example 2: Input:...

Zigzag String Transformation Algorithm in Python

Problem Statement Given a string s and an integer numRows, rearrange the characters of s into a zigzag pattern across numRows horizontal rows, reading top-to-bottom and left-to-right. Then concatenate all rows from top to bottom to produce the transformed string. For example, with s = "PAYPALIS...

Common Advanced Variations of the Knapsack Problem

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 and Chinese Remainder Theorem: A Practical Guide

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...

Backtracking Algorithm for Combinations

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...

Identifying Articulation Points and Bridges in Undirected Graphs

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...

Comparing Alphabetic Products Using Modular Arithmetic

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...