Merge pull request #898 from 0xff-dev/2318

Add solution and test-cases for problem 2318

Author: 6boris

leetcode/2301-2400/2318.Number-of-Distinct-Roll-Sequences/README.md

@@ -1,32 +1,39 @@
 # [2318.Number of Distinct Roll Sequences][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 an integer `n`. You roll a fair 6-sided dice `n` times. Determine the total number of **distinct** sequences of rolls possible such that the following conditions are satisfied:
+
+1. The **greatest common divisor** of any **adjacent** values in the sequence is equal to `1`.
+2. There is **at least** a gap of 2 rolls between **equal** valued rolls. More formally, if the value of the i<sup>th</sup> roll is **equal** to the value of the j<sup>th</sup> roll, then `abs(i - j) > 2`.
+
+Return the **total number** of distinct sequences possible. Since the answer may be very large, return it **modulo** `10^9 + 7`.
+
+Two sequences are considered distinct if at least one element is different.
 
 **Example 1:**
 
 ```
-Input: a = "11", b = "1"
-Output: "100"
+Input: n = 4
+Output: 184
+Explanation: Some of the possible sequences are (1, 2, 3, 4), (6, 1, 2, 3), (1, 2, 3, 1), etc.
+Some invalid sequences are (1, 2, 1, 3), (1, 2, 3, 6).
+(1, 2, 1, 3) is invalid since the first and third roll have an equal value and abs(1 - 3) = 2 (i and j are 1-indexed).
+(1, 2, 3, 6) is invalid since the greatest common divisor of 3 and 6 = 3.
+There are a total of 184 distinct sequences possible, so we return 184.
 ```
 
-## 题意
-> ...
+**Example 2:**
 
-## 题解
-
-### 思路1
-> ...
-Number of Distinct Roll Sequences
-```go
 ```
-
+Input: n = 2
+Output: 22
+Explanation: Some of the possible sequences are (1, 2), (2, 1), (3, 2).
+Some invalid sequences are (3, 6), (2, 4) since the greatest common divisor is not equal to 1.
+There are a total of 22 distinct sequences possible, so we return 22.
+```
 
 ## 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/number-of-distinct-roll-sequences/
 [me]: https://github.com/kylesliu/awesome-golang-algorithm

leetcode/2301-2400/2318.Number-of-Distinct-Roll-Sequences/Solution.go

@@ -1,5 +1,59 @@
 package Solution
 
-func Solution(x bool) bool {
-	return x
+const mod2318 = 1000000007
+
+func Solution(n int) int {
+	cache := make([]map[int]map[[7]int]int, n+1)
+	for i := 0; i <= n; i++ {
+		cache[i] = map[int]map[[7]int]int{}
+		for j := 1; j < 7; j++ {
+			cache[i][j] = map[[7]int]int{}
+		}
+	}
+	ref := map[int][]int{
+		1: {1, 2, 3, 4, 5, 6},
+		2: {1, 3, 5},
+		3: {1, 2, 4, 5},
+		4: {1, 3, 5},
+		5: {1, 2, 3, 4, 6},
+		6: {1, 5},
+	}
+
+	var dfs func(int, int, [7]int) int
+	dfs = func(nn, selected int, used [7]int) int {
+		if nn <= 1 {
+			return nn
+		}
+		m := cache[nn]
+		if v, ok := m[selected]; ok {
+			if v1, ok1 := v[used]; ok1 {
+				return v1
+			}
+		}
+		ans := 0
+		for _, next := range ref[selected] {
+			x := used
+			if used[next] == 0 {
+				used[next] = 2
+				for j := 1; j < 7; j++ {
+					if j == next || used[j] == 0 {
+						continue
+					}
+					used[j]--
+				}
+				ans = (ans + dfs(nn-1, next, used)) % mod2318
+			}
+			used = x
+		}
+		cache[nn][selected][used] = ans
+		return ans
+	}
+	r := 0
+	for i := 1; i < 7; i++ {
+		// 1:2
+		used := [7]int{}
+		used[i] = 2
+		r = (r + dfs(n, i, used)) % mod2318
+	}
+	return r
 }

leetcode/2301-2400/2318.Number-of-Distinct-Roll-Sequences/Solution_test.go

@@ -10,12 +10,12 @@ func TestSolution(t *testing.T) {
 	//	测试用例
 	cases := []struct {
 		name   string
-		inputs bool
-		expect bool
+		inputs int
+		expect int
 	}{
-		{"TestCase", true, true},
-		{"TestCase", true, true},
-		{"TestCase", false, false},
+		{"TestCase1", 4, 184},
+		{"TestCase2", 2, 22},
+		{"TestCase3", 999, 209513669},
 	}
 
 	//	开始测试
@@ -30,10 +30,10 @@ func TestSolution(t *testing.T) {
 	}
 }
 
-//	压力测试
+// 压力测试
 func BenchmarkSolution(b *testing.B) {
 }
 
-//	使用案列
+// 使用案列
 func ExampleSolution() {
 }