Add solution and test-cases for proble 3578

leetcode/3501-3600/3578.Count-Partitions-With-Max-Min-Difference-at-Most-K/README.md

@@ -1,28 +1,45 @@
 # [3578.Count Partitions With Max-Min Difference at Most K][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 array `nums` and an integer `k`. Your task is to partition nums into one or more **non-empty** contiguous segments such that in each segment, the difference between its **maximum** and **minimum** elements is **at most** `k`.
+
+Return the total number of ways to partition `nums` under this condition.
+
+Since the answer may be too large, return it **modulo** `10^9 + 7`.
 
 **Example 1:**
 
 ```
-Input: a = "11", b = "1"
-Output: "100"
-```
+Input: nums = [9,4,1,3,7], k = 4
+
+Output: 6
+
+Explanation:
 
-## 题意
-> ...
+There are 6 valid partitions where the difference between the maximum and minimum elements in each segment is at most k = 4:
 
-## 题解
+[[9], [4], [1], [3], [7]]
+[[9], [4], [1], [3, 7]]
+[[9], [4], [1, 3], [7]]
+[[9], [4, 1], [3], [7]]
+[[9], [4, 1], [3, 7]]
+[[9], [4, 1, 3], [7]]
+```
+
+**Example 2:**
 
-### 思路1
-> ...
-Count Partitions With Max-Min Difference at Most K
-```go
 ```
+Input: nums = [3,3,4], k = 0
+
+Output: 2
 
+Explanation:
+
+There are 2 valid partitions that satisfy the given conditions:
+
+[[3], [3], [4]]
+[[3, 3], [4]]
+```
 
 ## 结语
 

leetcode/3501-3600/3578.Count-Partitions-With-Max-Min-Difference-at-Most-K/Solution.go

@@ -1,5 +1,47 @@
 package Solution
 
-func Solution(x bool) bool {
-	return x
+func Solution(nums []int, k int) int {
+	n := len(nums)
+	mod := int64(1e9 + 7)
+	dp := make([]int64, n+1)
+	prefix := make([]int64, n+1)
+	minQ := make([]int, 0)
+	maxQ := make([]int, 0)
+
+	dp[0] = 1
+	prefix[0] = 1
+
+	for i, j := 0, 0; i < n; i++ {
+		// maintain the maximum value queue
+		for len(maxQ) > 0 && nums[maxQ[len(maxQ)-1]] <= nums[i] {
+			maxQ = maxQ[:len(maxQ)-1]
+		}
+		maxQ = append(maxQ, i)
+		// maintain the minimum value queue
+		for len(minQ) > 0 && nums[minQ[len(minQ)-1]] >= nums[i] {
+			minQ = minQ[:len(minQ)-1]
+		}
+		minQ = append(minQ, i)
+
+		// adjust window
+		for len(maxQ) > 0 && len(minQ) > 0 &&
+			nums[maxQ[0]]-nums[minQ[0]] > k {
+			if maxQ[0] == j {
+				maxQ = maxQ[1:]
+			}
+			if minQ[0] == j {
+				minQ = minQ[1:]
+			}
+			j++
+		}
+
+		if j > 0 {
+			dp[i+1] = (prefix[i] - prefix[j-1] + mod) % mod
+		} else {
+			dp[i+1] = prefix[i] % mod
+		}
+		prefix[i+1] = (prefix[i] + dp[i+1]) % mod
+	}
+
+	return int(dp[n])
 }

leetcode/3501-3600/3578.Count-Partitions-With-Max-Min-Difference-at-Most-K/Solution_test.go

@@ -10,30 +10,30 @@ func TestSolution(t *testing.T) {
 	//	测试用例
 	cases := []struct {
 		name   string
-		inputs bool
-		expect bool
+		inputs []int
+		k      int
+		expect int
 	}{
-		{"TestCase", true, true},
-		{"TestCase", true, true},
-		{"TestCase", false, false},
+		{"TestCase1", []int{9, 4, 1, 3, 7}, 4, 6},
+		{"TestCase2", []int{3, 3, 4}, 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.inputs, 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",
+					c.expect, got, c.inputs, 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() {
 }