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Hard/3405. Count the Number of Arrays with K Matching Adjacent Elements/README.md

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+# Leetcode 3405: Count the Number of Arrays with K Matching Adjacent Elements
+
+## 🚀 Problem Statement
+
+You are given three integers `n`, `m`, and `k`. A *good array* of size `n` is defined as follows:
+
+- Each element is between `1` and `m` (inclusive).
+- Exactly `k` indices `i` (where `1 <= i < n`) satisfy `arr[i] == arr[i-1]`.
+
+Your task is to return the number of such good arrays. Since the result may be very large, return the answer modulo `10^9 + 7`.
+
+---
+
+## 🧠 Approach
+
+This is a combinatorics problem that requires:
+- Choosing exactly `k` positions out of `n-1` to place equal adjacent elements.
+- Assigning values from `1` to `m` such that:
+  - The first element can be any value from `1` to `m`.
+  - The `k` chosen positions must match the previous element.
+  - The other `n - 1 - k` positions must differ from the previous one (i.e., have `m - 1` choices).
+
+### 💡 Final Formula
+
+```python
+Total = m × (m - 1)^(n - k - 1) × C(n - 1, k)
+```
+---
+## 🧪 Examples
+### Example 1:
+### Input: 
+```python
+n = 3, m = 2, k = 1
+```
+### Output: 
+```python
+4
+```
+### Explanation: 
+[1,1,2], [1,2,2], [2,2,1], [2,1,1]
+
+---
+## 👨‍💻 Author
+Muawiya Amir
+AI Student | Full Stack Developer
+GitHub: Muawiya-contact
+
+---