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Solve Longest Alternating Path Search using Lua Language

Solve Longest Alternating Path Search using Lua to enhance your skills with lua coding practice , master coding concepts, and prepare for interviews with practical exercises and detailed solutions.

Longest Alternating Path Search

Difficulty : Hard

Categories :

  • Searching algorithms

You are given a 2D matrix where each cell is either 0 or 1. A path in the matrix is called a 'zigzag path' if:

  • The path starts from any cell in the first row
  • The path ends at any cell in the last row
  • The path only moves down or diagonally down-left/down-right
  • The path should contain an alternating sequence of ones and zeros

Find the length of the longest possible zigzag path. If no such path exists, return -1.

Constraints:

  • 2 ≤ matrix.length, matrix[i].length ≤ 1000
  • matrix[i][j] is either 0 or 1
  • Solution should be optimal in both time and space complexity

Examples:

Input: matrix = [
  [1,0,1,0],
  [0,1,1,0],
  [1,0,1,1],
  [0,1,0,1]
]
Output: 4
Explanation: One possible path is (0,1) -> (1,1) -> (2,2) -> (3,1)
Values along path: 0 -> 1 -> 0 -> 1
Input: matrix = [
  [1,1],
  [1,1],
  [0,1]
]
Output: 2
Explanation: Path can be (0,0) -> (1,1)

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Choose from the following categories

Strings A sequence of characters used to represent text, with problems focused on manipulation, searching, and pattern matching.

Arrays A collection of elements stored in contiguous memory locations, allowing efficient random access and manipulation.

Linked Lists A linear data structure where each element (node) points to the next, offering dynamic memory allocation and efficient insertions/deletions.

Trees A hierarchical data structure with nodes connected by edges, used in applications like databases, file systems, and parsing.

Graphs A collection of nodes (vertices) connected by edges, representing relationships, widely used in networking, routing, and social networks.

Dynamic Programming An optimization technique that solves problems by breaking them into overlapping subproblems and storing their results.

Backtracking A problem-solving method that explores all possibilities recursively, backtracking when a solution is not feasible.

Sorting Algorithms Techniques for arranging elements in a specific order, such as quicksort, mergesort, and bubble sort, essential for data organization.

Searching Algorithms Methods for finding elements in a dataset, such as binary search, linear search, and graph traversal techniques.

Mathematics A field of study involving numbers, calculations, and logical reasoning, forming the foundation for algorithms and problem-solving.

Recursion A programming technique where a function calls itself to solve smaller instances of the same problem, often used in divide-and-conquer approaches.

Bit Manipulation Operations performed directly on binary representations of data, used for efficient computations and optimization tasks.