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🔢 Count the Number of Arrays with K Matching Adjacent Elements LeetCode 3405 (C++ | Python | JavaScript)
- LeetCode 3405 is a hard problem related to combinatorics.
- The problem involves finding the total number of 'good arrays' meeting specific criteria.
- Criteria: Elements in the array lie in the range [1, m] and exactly k adjacent indices have equal values.
- The result needs to be returned modulo 10⁹ + 7 due to large results.
- Approach: Choose k positions to be equal, and for the rest, have m - 1 options.
- Formula: Number of such arrays = C(n - 1, k) x m x (m - 1)^(n - 1 - k)
- C++ and Python code solutions are provided for the problem.
- The C++ solution involves precomputing factorials and inversions, and utilizes combinatorial functions.
- The JavaScript solution also precomputes factorials and inversions, employing modular exponentiation.
- Python code initializes values, calculates modular inverse, and implements combinatorial functions.
- The problem showcases the use of modular combinatorics, fast exponentiation, and factorial precomputation with inverse modulo.
- It requires mathematical insight rather than just raw implementation.
- The problem serves as a good template for combinatorics-based questions with constraints up to 10⁵.
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