BFS algorithm used to find shortest path to solve 2x3 sliding puzzle board with minimum moves.

Create a 2D grid and mark guarded cells by simulating guard vision in four directions. Count unguarded cells after processing all guards.

Take K of Each Character From Left and Right: Use sliding window technique with two pointers to find min minutes needed to take at least k of each char ('a', 'b', 'c') from left & right of string.

Find max sum of distinct subarrays with length K in array nums using sliding window and hash table approach.

Given an array and an integer k, return the length of the shortest subarray with sum at least k. Use prefix sums and a monotonic queue for efficient solution.

Find shortest subarray to remove from array to make it non-decreasing, using two pointers and binary search techniques.

Binary search finds smallest x where all products can be distributed without exceeding x per store.

Count fair pairs in array nums with lower <= nums[i] + nums[j] <= upper. Sort nums, use binary search for bounds & count valid indices.

Integrate Stripe Treasury API with PHP: Install SDK, set up account & keys, create financial accounts, fund & transfer funds, monitor transactions. Follow 8 steps for seamless integration.

Integrate 3rd party APIs in Laravel with step-by-step guide & examples: set up API keys, install Guzzle, create service class, bind service, define routes & build view.

Automate CSV/Excel to MySQL & PostgreSQL using PHP: Connect, load data, & transfer between databases with PDO & PHPExcel.

Can make nums strictly increasing by subtracting primes: loop through nums, find largest prime less than num - prevNum and subtract it if possible.

Find shortest special subarray with OR at least k using sliding window and bit manipulation techniques.

Find largest combination of candidates with bitwise AND > 0. Count numbers with set bits at each position (0-23). Return max count as largest combination size.

Can sort array if adjacent elements with same set bits can be swapped and sorted individually

Make binary string beautiful by partitioning into substrings with even length & only 1's or 0's. Change minority char in each block to match majority. Time complexity: O(n), space complexity: O(1).

Compress string using greedy approach: take longest prefix of repeating chars (up to 9) and append count & char. Example: 'abcde' -> '1a1b1c1d1e', 'aaaaaaaaaaaaaabb' -> '9a5a2b

Rotate string s into goal by checking if goal is a substring of s + s. If lengths match and goal exists in doubleS, return true; otherwise, false. Time complexity: O(n), space complexity: O(n).

Create a simple carousel using Alpine.js: Set up HTML, define data & methods, add CSS transitions for fade effect & auto-play functionality.

Sort robots & factories by position, then use dynamic programming to minimize distance each robot travels to be repaired by a factory.

Given an array nums, return min elements to remove to make it a mountain array. Use dynamic programming to find max mountain subsequence and compute min removals.

Dynamic Programming solution for Maximum Number of Moves in a Grid: Initialize dp array with 0s, traverse grid from last column to first, update dp values based on possible moves, and return max value in first column.

Pattern recognition is key to solving LeetCode problems. Consistently reinforcing algorithmic foundations & optimizing problem-solving approaches helps tackle complex problems with ease.

In Laravel, use `saveQuietly()` to update models silently, bypassing events like logging & notifications, ideal for bulk updates or admin overrides.

Dynamic Programming solution counts square submatrices with all ones in O(m*n) time complexity.

Remove sub-folders from filesystem: Sort folders lexicographically, identify & filter out sub-folders based on parent-child relationships.

We can use recursive DFS to check if two binary trees are flip equivalent by comparing their root values and subtrees with or without flipping.

Find kth largest level sum in binary tree using BFS and sorting.

Split string into max unique substrings using backtracking & set for uniqueness. Recursive function explores all possible substrings, backtracks if repetition occurs.

Evaluates boolean expressions recursively using stack and helper functions for AND, OR, NOT operations.

Find Kth Bit in Nth Binary String: Use recursion & string properties to avoid generating entire string, reducing time complexity to O(n).

Count Number of Maximum Bitwise-OR Subsets: Calculate max bitwise OR, enumerate subsets (2^n), count valid subsets with max OR. PHP solution for arrays up to size 16.

Maximize score by selecting largest nums[i] and updating with ceil(nums[i]/3) in O(k log n) time using Max Heap.

Maximum valued number achieved by swapping digits at most once: swap 2 and 7 in 2736 to get 7236.

We can use a greedy algorithm to find the longest happy string by using a Priority Queue (Max Heap) and continuously extracting the character with the highest count while ensuring we don't exceed two consecutive occurrences of the same character.

Solve string s by swapping adjacent balls to group all 1s (black) right and 0s (white) left.

Find smallest range covering elements from k lists: use min-heap & sliding window to track smallest element from each list. Time complexity: O(n * log k), space complexity: O(k).

Divide intervals into min groups: Sort events by time, track ongoing intervals & max overlap, return max count of overlapping intervals at any point.

Maximum width ramp in an array is achieved by maintaining a decreasing stack of indices and traversing from the end, updating maximum width whenever nums[i] <= nums[j]. Time complexity is O(n).

Minimum moves to make parentheses valid: count unmatched '(' and ')' then add min of those two values.

Minimum swaps to balance string: track imbalance & max_imbalance, swap (max_imbalance + 1) / 2 times. Time complexity O(n), space complexity O(1).

Minimum swaps to balance string: track imbalance & max_imbalance, swap (max_imbalance + 1) / 2 times. Time complexity O(n), space complexity O(1).

Minimize string length by removing 'AB' and 'CD' substrings using stack approach. Traverse string, push chars onto stack, pop if top 2 form 'AB' or 'CD'. Resulting length = stack size.

Remove smallest subarray to make sum divisible by p: use prefix sums & hash table for efficient search

Check if array pairs are divisible by k: use frequency count of remainders and check pairing conditions for efficient solution in O(n) time complexity.

Install PHPUnit via Composer, create a sample class & test case, arrange, act, assert, run tests & expand with new methods for robust testing.

Implement MyCalendar class with book method: store events as sorted list of intervals and check for overlaps before booking new events.

Find longest common prefix among pairs of integers in two arrays using HashSet for efficient lookups.

Break string s into non-overlapping substrings from dictionary. Min extra chars = dp[len(s)]. DP[i] = min(dp[i-1]+1, min(dp[j]) if s[j:i] in dict).

Sort people array, then use two pointers to pair heaviest with lightest until limit is reached, counting each person or pair as one boat.

Maximize binary matrix score by flipping rows & columns to ensure most significant bits are 1 and maximize remaining bits. Calculate final score by interpreting each row as a binary number.

Implementing Event-Driven Architecture (EDA) in PHP using Event Sourcing & CQRS for scalable & maintainable systems

Lexicographical Numbers: Sort numbers from 1 to n in lexicographical order using DFS-like strategy. O(n) time complexity and O(1) extra space used.

Set up PostgreSQL with Docker, automate backups & store securely using Docker Compose, pg_dump, cron & cloud storage.

Create Data Transfer Objects (DTOs) with Laravel Data: Install package, define properties & types, use in controllers, transform data & handle collections.

Find shortest palindrome by adding chars in front of given string using KMP algorithm & LPS array for efficient computation.

Arrange non-negative integers to form largest number. Compare concatenated results using custom comparator. Edge case: if largest num is 0, return '0'. Time complexity: O(n log n) + O(n).

Sum of Distances in Tree: Use DFS & dynamic programming to compute sum of distances for each node. Two traversals: first calculates subtree sizes & total distance from root, second adjusts results based on parent's result.

Maximize profit by assigning workers to jobs based on difficulty and ability, sorting jobs and workers for optimal assignment.

Uncommon Words from Two Sentences: Split sentences into words, count occurrences with hash table, filter uncommon words. Time complexity O(n+m), space complexity O(n+m).

Binary Search on Fractions: count valid fractions and track largest fraction smaller than midpoint m, return when count matches k or adjust search range accordingly.

Convert time points to minutes: 23*60+59=1439, sort them, handle circular clock & find min diff between consecutive time points.

BFS is used to find shortest path from '0000' to target while avoiding deadends in 752. Open the Lock problem.

Find longest substring with even vowel counts using bitmask & hash table, O(n) time complexity.

Find max value in array, then longest contiguous subarray of that max value, as other numbers reduce bitwise AND result.

Prevent SQL injection attacks in PHP by using prepared statements with MySQLi or PDO to separate SQL logic from data, ensuring user input is treated as data rather than executable code.

Laravel migrations help manage database schema changes with version control & rollback capabilities.

Compute XOR of subarray elements using prefix XOR array in O(n + q) time complexity.

Convert allowed string to set for O(1) lookups. Iterate through words, check each char in word against allowed set. Increment counter for consistent words.

Given two integers start and goal, return the minimum number of bit flips to convert start to goal using XOR operation and counting 1s in result.

Valid Parenthesis String: Use greedy approach with two counters (minOpen & maxOpen) to track possible open parentheses. If maxOpen < 0 or minOpen > 0 at end, string is invalid.

Replace words in sentence with shortest root from dictionary using Trie data structure for efficient lookup.

We need to insert nodes between every pair of adjacent nodes in a linked list with values equal to the greatest common divisor (GCD) of them. We'll traverse the list, calculate GCD for each pair and insert new nodes accordingly.

WebSockets can be secure if implemented with proper measures such as encrypted communication, authentication, and input validation.

PHP Sessions: Store user-specific data on the server, persist across pages, and enhance security with session_start(), $_SESSION array, and session_destroy().

PHP Metaprogramming: Writing code that generates or manipulates other code using Reflection API, Magic Methods, Eval Function, Anonymous Functions & Closures.

Add one row to binary tree at specified depth using DFS or BFS traversal and insert new nodes with value val as left and right children of each node.

Learn how to implement the Repository Pattern in Laravel for cleaner, more modular code. Abstracts data access logic, promotes separation of concerns & loose coupling, making it easier to switch databases or storage engines.

Dynamic Programming solution for Student Attendance Record II: count valid records with <2 absences & no 3+ late days. Modular arithmetic handles large numbers.

Slow SQL queries impact app performance. Identify common issues like indexing, joins, and sorting, then optimize using techniques like connection pooling and query rewriting.

Remove nodes from linked list with values in array nums using hash set for O(1) lookup and pointer manipulation.

Recursive DFS checks if linked list matches binary tree path, returning true for matching paths and false otherwise.

Check if array has subarray with sum divisible by k using modulo and hashmap in O(n) time complexity.

Solve "Freedom Trail" problem: find min steps to spell keyword in circular ring of characters using dynamic programming and breadth-first search.

Convert string s to integer by replacing each letter with its position in alphabet, then sum digits k times.

Relative Ranks: Sort scores in descending order, assign 'Gold Medal', 'Silver Medal', 'Bronze Medal' ranks, then numeric rank for 4th+ place. PHP solution: arsort(), loop over original array.

Maximize capital by sorting projects by capital and using a max-heap to track profits, selecting k most profitable projects.

Find student who will replace chalk by simulating turns and iterating through array until remaining chalk is insufficient.

Find student who will replace chalk by simulating turns and iterating through array until remaining chalk is insufficient.

Calculate island perimeter: iterate through grid, add 4 for each land cell, subtract 2 for shared edges with neighbors. Example usage: $grid = [[0,1,0,0],[1,1,1,0],[0,1,0,0],[1,1,0,0]]; echo islandPerimeter($grid); // Output: 16

Convert 1D array into 2D array: check if m*n == original.length, then populate 2D array row by row using nested loops and an index tracker.

Add two numbers represented as linked lists without reversing them using stacks for efficient addition and carry handling.

404. Sum of Left Leaves: Given binary tree root, return sum of all left leaves. A leaf is node with no children, left leaf is left child of another node. Example usage and solution provided.

Remove max stones by DFS: iterate over stones, mark connected components with DFS, return total stones - numComponents

Remove K Digits: Use stack-based greedy approach to build smallest possible number by removing k digits from input string num. Handle leading zeros and edge cases.

Maximize path probability in weighted graph using Dijkstra's algorithm with log probabilities and priority queue.

Postorder traversal of n-ary tree: use stack to reverse recursion, push children first then parent node. Example: [5,6,3,2,4,1] for input [1,null,3,2,4,null,5,6]

Reverse String: Use two pointers, one at start & end, swap elements & increment left, decrement right until left < right. Time complexity O(n), space complexity O(1).

Minimize patches required to cover range [1,n] with array nums using greedy algorithm. Initialize miss=1, loop until miss>n: if current num covers miss, add it; else patch miss & double range.

Find minimum height trees (MHTs) by performing two-pass BFS: build graph, find leaf nodes, trim leaves until only 1 or 2 nodes remain. These are MHT roots.