Add solution and test-cases for problem 3405

leetcode/3401-3500/3405.Count-the-Number-of-Arrays-with-K-Matching-Adjacent-Elements/'

@@ -0,0 +1,37 @@
+# [3405.Count the Number of Arrays with K Matching Adjacent Elements][title]
+
+## Description
+
+You are given three integers `n`, `m`, `k`. A **good array** arr of size n is defined as follows:
+
+Each element in arr is in the inclusive range [1, m].
+Exactly k indices i (where 1 <= i < n) satisfy the condition arr[i - 1] == arr[i].
+Return the number of good arrays that can be formed.
+
+Since the answer may be very large, return it modulo 109 + 7.
+
+**Example 1:**
+
+```
+Input: a = "11", b = "1"
+Output: "100"
+```
+
+## 题意
+> ...
+
+## 题解
+
+### 思路1
+> ...
+Count the Number of Arrays with K Matching Adjacent Elements
+```go
+```
+
+
+## 结语
+
+如果你同我一样热爱数据结构、算法、LeetCode，可以关注我 GitHub 上的 LeetCode 题解：[awesome-golang-algorithm][me]
+
+[title]: https://leetcode.com/problems/count-the-number-of-arrays-with-k-matching-adjacent-elements/
+[me]: https://github.com/kylesliu/awesome-golang-algorithm

leetcode/3401-3500/3405.Count-the-Number-of-Arrays-with-K-Matching-Adjacent-Elements/README.md

@@ -1,28 +1,53 @@
 # [3405.Count the Number of Arrays with K Matching Adjacent Elements][title]
 
-> [!WARNING|style:flat]
-> This question is temporarily unanswered if you have good ideas. Welcome to [Create Pull Request PR](https://github.com/kylesliu/awesome-golang-algorithm)
-
 ## Description
 
+You are given three integers `n`, `m`, `k`. A **good array** `arr` of size `n` is defined as follows:
+
+- Each element in `arr` is in the **inclusive** range `[1, m]`.
+- Exactly `k` indices `i` (where `1 <= i < n`) satisfy the condition `arr[i - 1] == arr[i]`.
+
+Return the number of **good arrays** that can be formed.
+
+Since the answer may be very large, return it **modulo** `10^9 + 7`.
+
 **Example 1:**
 
 ```
-Input: a = "11", b = "1"
-Output: "100"
+Input: n = 3, m = 2, k = 1
+
+Output: 4
+
+Explanation:
+
+There are 4 good arrays. They are [1, 1, 2], [1, 2, 2], [2, 1, 1] and [2, 2, 1].
+Hence, the answer is 4.
 ```
 
-## 题意
-> ...
+**Example 2:**
 
-## 题解
+```
+Input: n = 4, m = 2, k = 2
+
+Output: 6
+
+Explanation:
+
+The good arrays are [1, 1, 1, 2], [1, 1, 2, 2], [1, 2, 2, 2], [2, 1, 1, 1], [2, 2, 1, 1] and [2, 2, 2, 1].
+Hence, the answer is 6.
+```
+
+**Example 3:**
 
-### 思路1
-> ...
-Count the Number of Arrays with K Matching Adjacent Elements
-```go
 ```
+Input: n = 5, m = 2, k = 0
+
+Output: 2
 
+Explanation:
+
+The good arrays are [1, 2, 1, 2, 1] and [2, 1, 2, 1, 2]. Hence, the answer is 2.
+```
 
 ## 结语
 

leetcode/3401-3500/3405.Count-the-Number-of-Arrays-with-K-Matching-Adjacent-Elements/Solution.go

@@ -1,5 +1,46 @@
 package Solution
 
-func Solution(x bool) bool {
-	return x
+const (
+	MOD = 1e9 + 7
+	MX  = 100000
+)
+
+var (
+	fact    = make([]int64, MX)
+	invFact = make([]int64, MX)
+)
+
+func qpow(x int64, n int) int64 {
+	res := int64(1)
+	for n > 0 {
+		if n&1 == 1 {
+			res = res * x % MOD
+		}
+		x = x * x % MOD
+		n >>= 1
+	}
+	return res
+}
+
+func initFact() {
+	if fact[0] != 0 {
+		return
+	}
+	fact[0] = 1
+	for i := 1; i < MX; i++ {
+		fact[i] = fact[i-1] * int64(i) % MOD
+	}
+	invFact[MX-1] = qpow(fact[MX-1], MOD-2)
+	for i := MX - 1; i > 0; i-- {
+		invFact[i-1] = invFact[i] * int64(i) % MOD
+	}
+}
+
+func comb(n, m int) int64 {
+	return fact[n] * invFact[m] % MOD * invFact[n-m] % MOD
+}
+
+func Solution(n, m, k int) int {
+	initFact()
+	return int(comb(n-1, k) * int64(m) % MOD * qpow(int64(m-1), n-k-1) % MOD)
 }

leetcode/3401-3500/3405.Count-the-Number-of-Arrays-with-K-Matching-Adjacent-Elements/Solution_test.go

@@ -9,31 +9,31 @@ import (
 func TestSolution(t *testing.T) {
 	//	测试用例
 	cases := []struct {
-		name   string
-		inputs bool
-		expect bool
+		name    string
+		n, m, k int
+		expect  int
 	}{
-		{"TestCase", true, true},
-		{"TestCase", true, true},
-		{"TestCase", false, false},
+		{"TestCase1", 3, 2, 1, 4},
+		{"TestCase2", 4, 2, 2, 6},
+		{"TestCase3", 5, 2, 0, 2},
 	}
 
 	//	开始测试
 	for i, c := range cases {
 		t.Run(c.name+" "+strconv.Itoa(i), func(t *testing.T) {
-			got := Solution(c.inputs)
+			got := Solution(c.n, c.m, c.k)
 			if !reflect.DeepEqual(got, c.expect) {
-				t.Fatalf("expected: %v, but got: %v, with inputs: %v",
-					c.expect, got, c.inputs)
+				t.Fatalf("expected: %v, but got: %v, with inputs: %v %v %v",
+					c.expect, got, c.n, c.m, c.k)
 			}
 		})
 	}
 }
 
-//	压力测试
+// 压力测试
 func BenchmarkSolution(b *testing.B) {
 }
 
-//	使用案列
+// 使用案列
 func ExampleSolution() {
 }