Add solution and test-cases for problem 2338

leetcode/2301-2400/2338.Count-the-Number-of-Ideal-Arrays/README.md

@@ -1,28 +1,43 @@
 # [2338.Count the Number of Ideal Arrays][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 two integers `n` and `maxValue`, which are used to describe an **ideal** array.
+
+A **0-indexed** integer array `arr` of length `n` is considered **ideal** if the following conditions hold:
+
+- Every `arr[i]` is a value from `1` to `maxValue`, for `0 <= i < n`.
+- Every `arr[i]` is divisible by `arr[i - 1]`, for `0 < i < n`.
+
+Return the number of **distinct** ideal arrays of length `n`. Since the answer may be very large, return it modulo `10^9 + 7`.
 
 **Example 1:**
 
 ```
-Input: a = "11", b = "1"
-Output: "100"
+Input: n = 2, maxValue = 5
+Output: 10
+Explanation: The following are the possible ideal arrays:
+- Arrays starting with the value 1 (5 arrays): [1,1], [1,2], [1,3], [1,4], [1,5]
+- Arrays starting with the value 2 (2 arrays): [2,2], [2,4]
+- Arrays starting with the value 3 (1 array): [3,3]
+- Arrays starting with the value 4 (1 array): [4,4]
+- Arrays starting with the value 5 (1 array): [5,5]
+There are a total of 5 + 2 + 1 + 1 + 1 = 10 distinct ideal arrays.
 ```
 
-## 题意
-> ...
+**Example 2:**
 
-## 题解
-
-### 思路1
-> ...
-Count the Number of Ideal Arrays
-```go
 ```
-
+Input: n = 5, maxValue = 3
+Output: 11
+Explanation: The following are the possible ideal arrays:
+- Arrays starting with the value 1 (9 arrays): 
+   - With no other distinct values (1 array): [1,1,1,1,1] 
+   - With 2nd distinct value 2 (4 arrays): [1,1,1,1,2], [1,1,1,2,2], [1,1,2,2,2], [1,2,2,2,2]
+   - With 2nd distinct value 3 (4 arrays): [1,1,1,1,3], [1,1,1,3,3], [1,1,3,3,3], [1,3,3,3,3]
+- Arrays starting with the value 2 (1 array): [2,2,2,2,2]
+- Arrays starting with the value 3 (1 array): [3,3,3,3,3]
+There are a total of 9 + 1 + 1 = 11 distinct ideal arrays.
+```
 
 ## 结语
 

leetcode/2301-2400/2338.Count-the-Number-of-Ideal-Arrays/Solution.go

@@ -1,5 +1,63 @@
 package Solution
 
-func Solution(x bool) bool {
-	return x
+const (
+	MOD   int = 1e9 + 7
+	MAX_N     = 10010
+	MAX_P     = 15 // There are up to 15 prime factors
+)
+
+var (
+	c     [MAX_N + MAX_P][MAX_P + 1]int
+	sieve [MAX_N]int   // Minimum prime factor
+	ps    [MAX_N][]int // List of prime factor counts
+)
+
+func initialize() {
+	if c[0][0] != 0 {
+		return
+	}
+
+	for i := 2; i < MAX_N; i++ {
+		if sieve[i] == 0 {
+			for j := i; j < MAX_N; j += i {
+				if sieve[j] == 0 {
+					sieve[j] = i
+				}
+			}
+		}
+	}
+
+	for i := 2; i < MAX_N; i++ {
+		x := i
+		for x > 1 {
+			p := sieve[x]
+			cnt := 0
+			for x%p == 0 {
+				x /= p
+				cnt++
+			}
+			ps[i] = append(ps[i], cnt)
+		}
+	}
+
+	c[0][0] = 1
+	for i := 1; i < MAX_N+MAX_P; i++ {
+		c[i][0] = 1
+		for j := 1; j <= MAX_P && j <= i; j++ {
+			c[i][j] = (c[i-1][j] + c[i-1][j-1]) % MOD
+		}
+	}
+}
+
+func Solution(n int, maxValue int) int {
+	initialize()
+	ans := 0
+	for x := 1; x <= maxValue; x++ {
+		mul := 1
+		for _, p := range ps[x] {
+			mul = mul * c[n+p-1][p] % MOD
+		}
+		ans = (ans + mul) % MOD
+	}
+	return ans
 }

leetcode/2301-2400/2338.Count-the-Number-of-Ideal-Arrays/Solution_test.go

@@ -9,31 +9,30 @@ import (
 func TestSolution(t *testing.T) {
 	//	测试用例
 	cases := []struct {
-		name   string
-		inputs bool
-		expect bool
+		name        string
+		n, maxValue int
+		expect      int
 	}{
-		{"TestCase", true, true},
-		{"TestCase", true, true},
-		{"TestCase", false, false},
+		{"TestCase1", 2, 5, 10},
+		{"TestCase2", 5, 3, 11},
 	}
 
 	//	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.maxValue)
 			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",
+					c.expect, got, c.n, c.maxValue)
 			}
 		})
 	}
 }
 
-//	压力测试
+// 压力测试
 func BenchmarkSolution(b *testing.B) {
 }
 
-//	使用案列
+// 使用案列
 func ExampleSolution() {
 }