Filter valid recipes with ingredients in supplies or other recipes, build dependency graph, and use topological sorting to process recipes in order, ensuring all dependencies are met.

n vertices in an undirected weighted graph, find min cost walk between nodes si and ti using DSU and bitwise AND of edge weights.

Can an array be divided into pairs where each pair has equal elements? Count frequencies, check if all are even. If yes, return true; otherwise, false.

Binary Search used to find min capability of robber stealing from at least k non-consecutive houses with max value not exceeding the current guess.

Binary search finds max candies each child can get with same number from single pile.

Here's the summary of the blog post in 250 characters or less: "Find closest prime numbers within range [left, right]. Use Sieve of Eratosthenes to generate primes up to right value. Collect primes in range and find pair with min difference.

Count Total Number of Colored Cells: Use formula 2n^2 - 2n + 1 to calculate colored cells after n minutes. Each minute adds 4*(k-1) new cells, forming an arithmetic sequence.

n can be sum of distinct powers of 3 if ternary rep only contains 0 & 1. Convert n to base 3, check for digit 2. If found, return false. Otherwise, true.

Apply operations to an array: multiply equal elements by 2, shift zeros to end

Maximum Absolute Sum of Any Subarray: Use Kadane's algorithm to find max & min subarray sums. Result = max(abs(max sum), abs(min sum)). Efficiently computes result in linear time.

Count subarrays with odd sum using prefix sums & parity tracking. For each index, add count of opposite parity prefix sums to result. Update counts & take modulo 10^9 + 7 for large inputs.

Alice's max net income is 6 when she travels towards node 4 in the tree with edges [[0,1],[1,2],[1,3],[3,4]] and amount [-2,4,2,-4,6].

Construct binary tree from preorder and postorder traversal using recursion. Identify root as first element in preorder, split arrays based on left child position in postorder, and recursively construct left and right subtrees.

Recover binary tree from preorder traversal string: parse dashes for depth & build tree with stack-based approach, ensuring left children are prioritized.

Find Unique Binary String: Construct a binary string that differs from every string in nums by flipping each bit. O(n) time complexity. Example inputs and outputs provided.

Generate all happy strings of length n in lexicographical order and return the k-th string. Use backtracking to build strings character by character, ensuring each new char is different from the previous one.

1079. Letter Tile Possibilities: Use backtracking DFS to generate all possible permutations of tiles for lengths 1 to n. Manage counts with frequency map to avoid duplicates. Complexity manageable due to input length constraint.

Construct Lexicographically Largest Valid Sequence: Use backtracking to build sequence with numbers 1-n twice, distance between occurrences equal to value. Reserve positions for subsequent occurrences.

Iterate through integers 1-n, compute square and check if it can be partitioned into substrings that sum up to the integer using recursive helper function.

Iterative removal of substring part from string s until no occurrences remain. Repeatedly find and remove leftmost occurrence of part, checking resulting string for new occurrences. Time complexity: O(n^2) in worst case.

Clear Digits: Remove all digits from a string by deleting each digit and its closest non-digit char to left. Use stack to track non-digits & pop top element when digit encountered.

Count bad pairs in array nums by calculating total pairs (n*(n-1)/2) and subtracting good pairs (sum of m*(m-1)/2 for each group with m elements). Use a frequency map to count occurrences of each value (nums[i] - i).

Design a number container system with O(log n) time complexity for change and find operations using hash maps and min-heaps.

Use two HashMaps: colorMap & colorCount to track ball colors & counts. Update counts after each query, removing colors with 0 balls. Result is size of colorCount after each query.

Return true if two strings can be equal by swapping at most one character in one string. Check if exactly two indices differ and swap would make them equal. Time complexity: O(n).

Check if Array Is Sorted and Rotated: Return true if array is sorted & rotated, false otherwise. Use single loop to count breaks in sorting order.

Special Array I: An array is special if every pair of adjacent elements has different parity (one even, one odd). Check length, iterate through array, and compare parities. Return true if all pairs have different parities.

Identify islands with DFS/BFS, calculate sizes & store in dict/array. For each 0, check neighbors & calc potential new island size. Return max size found or largest island if no 0s.

eventualSafeNodes function returns an array of safe nodes in a directed graph, sorted in ascending order. It uses DFS to detect cycles and classify nodes as safe or unsafe.

eventualSafeNodes function returns an array of safe nodes in a directed graph, sorted in ascending order. It uses DFS to detect cycles and classify nodes as safe or unsafe.

Two servers can communicate if they're in the same row or column. Count servers that can talk to others by counting rows and columns with multiple servers.

We use multi-source BFS to update matrix with distances of nearest 0 for each cell, returning updated matrix.

Built a lightweight web app using OpenWeatherMap API, displaying current weather & 5-day forecast for any city worldwide. GitHub Copilot helped with code autocompletion, debugging assistance & UI integration

Pre-process matrix positions in O(m*n) time. Traverse arr, updating row and column frequencies. Return index where either row or column is fully painted. Time complexity: O(m*n). Space complexity: O(m*n).

Trapping Rain Water II: Compute volume of water trapped after raining on 2D elevation map using BFS and priority queue.

Modify signs in m x n grid to create a valid path from top-left to bottom-right using 0-1 BFS with deque & distance array, achieving min cost of O(m × n) time & space complexity.

The XOR of all elements in derived must equal 0 for a valid original array to exist. If the result is 0, return true; otherwise, return false.

Bitwise XOR of All Pairings: Return the bitwise XOR of all integers in nums3, where nums3 contains the XOR of all pairings between nums1 and nums2.

Minimize XOR: Count set bits in num2, preserve most significant 1s in num1, add extra 1s from least significant bit. Return x with minimal XOR value.

We can solve this problem by iterating over two arrays A and B while keeping track of numbers that have occurred at or before the current index in both arrays using two hash sets (or arrays).

Get started with PHPUnit in Laravel: Install, configure, write & run tests. Integrate into your dev workflow using CI/CD tools like GitHub Actions or Jenkins. Track code coverage with Xdebug.

Delete closest matching chars from left & right to minimize string length. Focus on char freqs: reduce >=3 to <=2, sum remaining counts.

A string is valid if it's empty or can be written as AB where A and B are valid strings, or (A) where A is a valid string. Given a string s and locked string, return true if s can be made valid.

1289. Minimum Falling Path Sum II The minimum falling path sum is 13, which corresponds to the path [1, 5, 7].

Maximizing word scores with bitmasking and letter counts. Code generates all subsets of words, checks validity, and calculates score for each subset. Time complexity is O(2n × w), where n is the number of words and w is max word length.

The maximum length of valid substrings where the total cost is less than or equal to maxCost will be our result.

Remove min parentheses to make valid string: remove unnecessary ( and ) while keeping valid chars. Two-pass approach: first pass removes invalid closing ), second pass removes invalid opening (.

DFS with backtracking finds max gold in grid by exploring all paths, adding current cell's gold to next valid positions' max gold. Time complexity: O(m * n).

The problem requires finding the number of subarrays in an integer array that contain exactly k odd numbers. A sliding window approach with prefix sums efficiently counts these "nice" subarrays.

Construct K Palindrome Strings: Use hash table to count char frequencies & odd counts. If k > len(s) or odd counts > k, return false. Otherwise, true.

Find universal strings in words1 where each string in words2 is a subset. Count max char freq in words2 & check each word in words1. Return universal words.

Iterate through array, check if prefix is part of each word using substr function. Time complexity: O(n * m).

Iterate through all index pairs (i, j) where i < j, check if words[i] is both prefix and suffix of words[j] using PHP's substr() function, return total count of true pairs.

Find all strings in an array that are substrings of another word using brute force or KMP algorithm. PHP solution: loop through words, compare each with others using strpos() function.

Reverse strings between each pair of parentheses: use stack to track chars & nested parens. Pop & reverse substrings when closing parenthesis encountered. Concatenate stack contents for result.

Dynamic programming approach calculates N-th Tribonacci number efficiently with O(n) time and O(1) space complexity.

Delete nodes with values in `to_delete` from binary tree and return forest roots: [[1,2,null,4],[6],[7]] for [1,2,3,4,5,6,7] and {3,5}.

We can use a prefix sum approach to calculate the minimum number of operations needed to move all balls to each box without simulating each operation. The solution runs in O(n) time and has a space complexity of O(n).

We need to avoid shifting characters one by one for each shift, so we use prefix sum to efficiently apply cumulative shifts to each character in the string.

We can use an efficient algorithm that leverages prefix and suffix character tracking to count all valid palindromic subsequences in O(n) time complexity.

Prefix sum and total sum are computed for efficient comparisons. Iterate over array, checking if prefix sum is >= remaining sum (total sum - prefix sum). Time complexity: O(n), space complexity: O(1).

Here is the summary in 250 characters: "Maximize customer satisfaction by making grumpy owners happy for `minutes` minutes. Use sliding window approach to find max possible satisfaction.

heightChecker function efficiently calculates the number of indices where heights are out of place compared to expected order, with time complexity O(n log n) due to sorting.

Find common characters in an array of strings using frequency arrays and minimization logic, handling duplicates and case sensitivity.

Convert BST to Greater Sum Tree: traverse right subtree first, update node value with prefix sum, and recursively process left subtree.

Counting vowel strings in ranges: precompute prefix sum of vowel strings, use unordered_set for vowels, and subtract prefix sum for range [l-1, r] to find count. Complexity: O(n + q).

Precompute prefix sum of ones in string s. Iterate over possible splits, counting zeros in left substring and using prefix sum for right substring. Update max score as the sum of zeros in left part and ones in right part. Return max score found.

Dynamic Programming solution for "Count Ways To Build Good Strings" problem: calculate dp[i] as sum of dp[i-zero] and dp[i-one], with base case dp[0]=1. Return dp[low] + ... + dp[high] modulo 10^9+7.

Dynamic Programming solution for "Number of Ways to Form a Target String Given a Dictionary" implemented in PHP using memoization to efficiently count the number of ways to form the target string.

We use dynamic programming to find 3 non-overlapping subarrays of length k with max sum in an array nums, returning the lexicographically smallest solution if multiple exist.

Maximize sightseeing score: values[i] + values[j] - (j-i). Use single-pass approach with maxI and maxScore. O(n) time complexity, O(1) space complexity.

BFS-based solution efficiently computes largest value in each tree row with linear time complexity, handling large trees and edge cases effectively.

Apply special discount to shop items based on later prices with stack approach for efficient tracking and calculation of final prices.

Find min value in array, multiply by multiplier, repeat k times for final state.

Maximize average pass ratio by distributing extra students among classes using max-heap and greedy approach.

Sort array, apply sliding window technique to maximize subsequence length after applying operation any number of times.

Rotate box 90 degrees clockwise and simulate gravity effect on stones.

Find longest square streak in array: sort nums, use set for quick lookup, iterate through array & track max length. Time complexity O(n log n), space complexity O(n).

Modified Dijkstra's algorithm with priority queue finds shortest time to visit bottom-right cell in grid.

Check if N and its double exist in an array using a hash table. Iterate through the array, checking for each element if its double or half has been encountered. Return true if found, false otherwise.

Split sentence into words, check each word for searchWord prefix, return 1-indexed position if found, -1 otherwise

Add spaces before characters at given indices in string s using two pointers and efficient appending.

Two pointers traverse start and target strings, checking if 'L' moves left and 'R' moves right without crossing each other or changing order.

Preprocess array to mark parity changes, then use prefix sum array to check if all pairs in query have different parity.

Find longest special substring that occurs thrice: iterate over lengths, extract substrings, count occurrences & check if special. Return length or -1 if no special substring found.

Binary search finds min penalty after splitting balls in bags with at most maxOperations splits.

Two pointers i and j are used to check if str2 is a subsequence of str1 with at most one cyclic increment operation. If characters match or can be incremented cyclically, both pointers move forward.

Convert pairs into graph problem, find Eulerian path using Hierholzer's algorithm, return valid arrangement of pairs.

PHP streams efficiently handle large datasets & complex data processing tasks, offering memory efficiency, flexibility & asynchronous processing. Use fopen(), fgetcsv() & stream filters for CSV processing.

Model grid as graph, use 0-1 BFS or Dijkstra's algorithm to minimize obstacles removal from top-left to bottom-right corner.

Automate your Laravel project's code testing & deployment with CI/CD pipelines using GitHub, Jenkins, and Docker. Follow this step-by-step guide to streamline your development process.

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.