Add solution and test-cases for problem 813

Author: 0xff-dev

leetcode/801-900/0813.Largest-Sum-of-Averages/README.md

@@ -1,28 +1,29 @@
 # [813.Largest Sum of Averages][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`. You can partition the array into **at most** k non-empty adjacent subarrays. The **score** of a partition is the sum of the averages of each subarray.
+
+Note that the partition must use every integer in `nums`, and that the score is not necessarily an integer.
+
+Return the maximum **score** you can achieve of all the possible partitions. Answers within `10^-6` of the actual answer will be accepted.
 
 **Example 1:**
 
 ```
-Input: a = "11", b = "1"
-Output: "100"
+Input: nums = [9,1,2,3,9], k = 3
+Output: 20.00000
+Explanation: 
+The best choice is to partition nums into [9], [1, 2, 3], [9]. The answer is 9 + (1 + 2 + 3) / 3 + 9 = 20.
+We could have also partitioned nums into [9, 1], [2], [3, 9], for example.
+That partition would lead to a score of 5 + 2 + 6 = 13, which is worse.
 ```
 
-## 题意
-> ...
+**Example 2:**
 
-## 题解
-
-### 思路1
-> ...
-Largest Sum of Averages
-```go
 ```
-
+Input: nums = [1,2,3,4,5,6,7], k = 4
+Output: 20.50000
+```
 
 ## 结语
 

leetcode/801-900/0813.Largest-Sum-of-Averages/Solution.go

@@ -1,5 +1,42 @@
 package Solution
 
-func Solution(x bool) bool {
-	return x
+func Solution(nums []int, k int) float64 {
+	l := len(nums)
+	cache := make([][]float64, l)
+	sum := 0
+	mm := 0
+	for i := 0; i < l; i++ {
+		sum += nums[i]
+		mm = max(mm, nums[i])
+		cache[i] = make([]float64, k+1)
+		for j := 0; j <= k; j++ {
+			cache[i][j] = -1.0
+		}
+		cache[i][1] = float64(sum) / float64(i+1)
+		if i+1 <= k {
+			cache[i][i+1] = float64(sum)
+		}
+	}
+	var dfs func(int, int) float64
+	dfs = func(index, kk int) float64 {
+		if index < 0 {
+			return 0
+		}
+		if r := cache[index][kk]; r+1.0 > 0.000001 {
+			return r
+		}
+		ans := float64(0)
+		cur := 0
+		for c := index; c >= kk-1; c-- {
+			cur += nums[c]
+			avg := float64(cur) / float64(index-c+1)
+
+			if r := dfs(c-1, kk-1); r+1.0 > 0.000001 {
+				ans = max(ans, avg+r)
+			}
+		}
+		cache[index][kk] = ans
+		return ans
+	}
+	return dfs(l-1, k)
 }

leetcode/801-900/0813.Largest-Sum-of-Averages/Solution_test.go

@@ -10,30 +10,30 @@ func TestSolution(t *testing.T) {
 	//	测试用例
 	cases := []struct {
 		name   string
-		inputs bool
-		expect bool
+		nums   []int
+		k      int
+		expect float64
 	}{
-		{"TestCase", true, true},
-		{"TestCase", true, true},
-		{"TestCase", false, false},
+		{"TestCase1", []int{9, 1, 2, 3, 9}, 3, 20.00000},
+		{"TestCase2", []int{1, 2, 3, 4, 5, 6, 7}, 4, 20.50000},
 	}
 
 	//	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.nums, 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.nums, 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() {
 }