Add solution and test-cases for problem 410

leetcode/401-500/0410.Split-Array-Largest-Sum/README.md

@@ -1,28 +1,29 @@
 # [410.Split Array Largest Sum][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
+Given an integer array `nums` and an integer `k`, split `nums` into `k` non-empty subarrays such that the largest sum of any subarray is **minimized**.
+
+Return the minimized largest sum of the split.
+
+A **subarray** is a contiguous part of the array.
 
 **Example 1:**
 
 ```
-Input: a = "11", b = "1"
-Output: "100"
+Input: nums = [7,2,5,10,8], k = 2
+Output: 18
+Explanation: There are four ways to split nums into two subarrays.
+The best way is to split it into [7,2,5] and [10,8], where the largest sum among the two subarrays is only 18.
 ```
 
-## 题意
-> ...
+**Example 2:**
 
-## 题解
-
-### 思路1
-> ...
-Split Array Largest Sum
-```go
 ```
-
+Input: nums = [1,2,3,4,5], k = 2
+Output: 9
+Explanation: There are four ways to split nums into two subarrays.
+The best way is to split it into [1,2,3] and [4,5], where the largest sum among the two subarrays is only 9.
+```
 
 ## 结语
 

leetcode/401-500/0410.Split-Array-Largest-Sum/Solution.go

@@ -1,5 +1,43 @@
 package Solution
 
-func Solution(x bool) bool {
-	return x
+func Solution(nums []int, k int) int {
+	l := len(nums)
+	sum := 0
+	m := 0
+	cache := make([][]int, l)
+	for i := 0; i < l; i++ {
+		sum += nums[i]
+		m = max(m, nums[i])
+		cache[i] = make([]int, k+1)
+		for j := 0; j <= k; j++ {
+			cache[i][j] = -1
+		}
+		cache[i][1] = sum
+		if i+1 <= k {
+			cache[i][i+1] = m
+		}
+	}
+	var dfs func(int, int) int
+	dfs = func(index, kk int) int {
+		if index < 0 {
+			return -1
+		}
+		if cache[index][kk] != -1 {
+			return cache[index][kk]
+		}
+		cur := 0
+		ans := -1
+		for choose := index; choose >= kk-1; choose-- {
+			cur += nums[choose]
+			if r := dfs(choose-1, kk-1); r != -1 {
+				x := max(cur, r)
+				if ans == -1 || ans > x {
+					ans = x
+				}
+			}
+		}
+		cache[index][kk] = ans
+		return ans
+	}
+	return dfs(l-1, k)
 }

leetcode/401-500/0410.Split-Array-Largest-Sum/Solution_test.go

@@ -10,30 +10,31 @@ func TestSolution(t *testing.T) {
 	//	测试用例
 	cases := []struct {
 		name   string
-		inputs bool
-		expect bool
+		nums   []int
+		k      int
+		expect int
 	}{
-		{"TestCase", true, true},
-		{"TestCase", true, true},
-		{"TestCase", false, false},
+		{"TestCase1", []int{7, 2, 5, 10, 8}, 2, 18},
+		{"TestCase2", []int{1, 2, 3, 4, 5}, 2, 9},
+		{"TestCase3", []int{2, 3, 1, 2, 4, 3}, 5, 4},
 	}
 
 	//	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() {
 }