Sync LeetCode submission Runtime - 16 ms (89.06%), Memory - 25.2 MB (25.00%)

Author: jimit105

3682-count-the-number-of-arrays-with-k-matching-adjacent-elements/README.md

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+<p>You are given three integers <code>n</code>, <code>m</code>, <code>k</code>. A <strong>good array</strong> <code>arr</code> of size <code>n</code> is defined as follows:</p>
+
+<ul>
+	<li>Each element in <code>arr</code> is in the <strong>inclusive</strong> range <code>[1, m]</code>.</li>
+	<li><em>Exactly</em> <code>k</code> indices <code>i</code> (where <code>1 &lt;= i &lt; n</code>) satisfy the condition <code>arr[i - 1] == arr[i]</code>.</li>
+</ul>
+
+<p>Return the number of <strong>good arrays</strong> that can be formed.</p>
+
+<p>Since the answer may be very large, return it <strong>modulo </strong><code>10<sup>9 </sup>+ 7</code>.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<div class="example-block">
+<p><strong>Input:</strong> <span class="example-io">n = 3, m = 2, k = 1</span></p>
+
+<p><strong>Output:</strong> <span class="example-io">4</span></p>
+
+<p><strong>Explanation:</strong></p>
+
+<ul>
+	<li>There are 4 good arrays. They are <code>[1, 1, 2]</code>, <code>[1, 2, 2]</code>, <code>[2, 1, 1]</code> and <code>[2, 2, 1]</code>.</li>
+	<li>Hence, the answer is 4.</li>
+</ul>
+</div>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<div class="example-block">
+<p><strong>Input:</strong> <span class="example-io">n = 4, m = 2, k = 2</span></p>
+
+<p><strong>Output:</strong> <span class="example-io">6</span></p>
+
+<p><strong>Explanation:</strong></p>
+
+<ul>
+	<li>The good arrays are <code>[1, 1, 1, 2]</code>, <code>[1, 1, 2, 2]</code>, <code>[1, 2, 2, 2]</code>, <code>[2, 1, 1, 1]</code>, <code>[2, 2, 1, 1]</code> and <code>[2, 2, 2, 1]</code>.</li>
+	<li>Hence, the answer is 6.</li>
+</ul>
+</div>
+
+<p><strong class="example">Example 3:</strong></p>
+
+<div class="example-block">
+<p><strong>Input:</strong> <span class="example-io">n = 5, m = 2, k = 0</span></p>
+
+<p><strong>Output:</strong> <span class="example-io">2</span></p>
+
+<p><strong>Explanation:</strong></p>
+
+<ul>
+	<li>The good arrays are <code>[1, 2, 1, 2, 1]</code> and <code>[2, 1, 2, 1, 2]</code>. Hence, the answer is 2.</li>
+</ul>
+</div>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
+	<li><code>1 &lt;= m &lt;= 10<sup>5</sup></code></li>
+	<li><code>0 &lt;= k &lt;= n - 1</code></li>
+</ul>

3682-count-the-number-of-arrays-with-k-matching-adjacent-elements/solution.py

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+MOD = 10**9 + 7
+MX = 10**5
+
+fact = [0] * MX
+inv_fact = [0] * MX
+
+
+def qpow(x, n):
+    res = 1
+    while n:
+        if n & 1:
+            res = res * x % MOD
+        x = x * x % MOD
+        n >>= 1
+    return res
+
+
+def init():
+    if fact[0] != 0:
+        return
+    fact[0] = 1
+    for i in range(1, MX):
+        fact[i] = fact[i - 1] * i % MOD
+    inv_fact[MX - 1] = qpow(fact[MX - 1], MOD - 2)
+    for i in range(MX - 1, 0, -1):
+        inv_fact[i - 1] = inv_fact[i] * i % MOD
+
+
+def comb(n, m):
+    return fact[n] * inv_fact[m] % MOD * inv_fact[n - m] % MOD
+
+
+class Solution:
+    def countGoodArrays(self, n: int, m: int, k: int) -> int:
+        init()
+        return comb(n - 1, k) * m % MOD * qpow(m - 1, n - k - 1) % MOD