Lua Coding Practice

Solve Different Position Combinations using Lua Language

Solve Different Position Combinations using Lua to enhance your skills with lua coding practice , master coding concepts, and prepare for interviews with practical exercises and detailed solutions.

Different Position Combinations

Difficulty : Medium

Categories :

  • Mathematics

Given n types of items where you must choose exactly one item of each type, and each type i has items[i] different items available, find the number of ways to select items such that no two adjacent types have items in the same position (1-based index). Return the answer modulo 10⁹ + 7.

Constraints:

  • 2 ≤ n ≤ 100
  • 1 ≤ items[i] ≤ 10
  • The array length equals n

Examples:

Input: items = [2,3,2]
Output: 8
Explanation:
Valid selections (showing positions):
[1,2,2], [1,3,2], [2,1,1], [2,3,1]
[1,2,1], [1,3,1], [2,1,2], [2,3,2]
Input: items = [2,2]
Output: 2
Explanation:
Valid selections: [1,2], [2,1]

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Choose from the following categories

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.