20250617 finished.

src/problems/3405-count-the-number-of-arrays-with-k-matching-adjacent-elements.cpp

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+/**
+* [3405] Count the Number of Arrays with K Matching Adjacent Elements
+ */
+#include <bits/stdc++.h>
+#include <gtest/gtest.h>
+using namespace std;
+
+
+// submission codes start here
+
+constexpr long long MOD         = 1e9 + 7;
+constexpr long long UPPER_BOUND = 1e5;
+
+static long long fact[UPPER_BOUND];
+static long long inverseFact[UPPER_BOUND];
+
+class Solution
+{
+    static long long quickPower(long long x, int n)
+    {
+        long long result = 1;
+
+        while (n > 0)
+        {
+            if ((n & 1) == 1)
+            {
+                result = result * x % MOD;
+            }
+
+            x   = x * x % MOD;
+            n >>= 1;
+        }
+
+        return result;
+    }
+
+    static long long combine(int n, int m)
+    {
+        return fact[n] * inverseFact[m] % MOD * inverseFact[n - m] % MOD;
+    }
+
+    static void init()
+    {
+        if (fact[0] != 0)
+        {
+            return;
+        }
+
+        fact[0] = 1;
+        for (int i = 1; i < UPPER_BOUND; ++i)
+        {
+            fact[i] = fact[i - 1] * i % MOD;
+        }
+
+        // Modular Multiplicative Inverse is calculated by  the quick power.
+        inverseFact[UPPER_BOUND - 1] = quickPower(fact[UPPER_BOUND - 1], MOD - 2);
+        for (int i = UPPER_BOUND - 1; i > 0; --i)
+        {
+            inverseFact[i - 1] = inverseFact[i] * i % MOD;
+        }
+    }
+
+public:
+    int countGoodArrays(int n, int m, int k)
+    {
+        init();
+        const long long result = combine(n - 1, k) * m % MOD * quickPower(m - 1, n - k - 1) % MOD;
+        return result;
+    }
+};
+
+// submission codes end
+
+TEST(P3405, Test1)
+{
+    Solution s;
+    ASSERT_EQ(4, s.countGoodArrays(3, 2, 1));
+    ASSERT_EQ(6, s.countGoodArrays(4, 2, 2));
+    ASSERT_EQ(2, s.countGoodArrays(5, 2, 0));
+}