Merge pull request #847 from 0xff-dev/553

Add solution and test-cases for problem 553

Author: 6boris

leetcode/501-600/0553.Optimal-Division/README.md

@@ -1,28 +1,39 @@
 # [553.Optimal Division][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`. The adjacent integers in `nums` will perform the float division.
+
+- For example, for `nums = [2,3,4]`, we will evaluate the expression `"2/3/4"`.
+
+However, you can add any number of parenthesis at any position to change the priority of operations. You want to add these parentheses such the value of the expression after the evaluation is maximum.
+
+Return the corresponding expression that has the maximum value in string format.
+
+**Note**: your expression should not contain redundant parenthesis.
 
 **Example 1:**
 
 ```
-Input: a = "11", b = "1"
-Output: "100"
+Input: nums = [1000,100,10,2]
+Output: "1000/(100/10/2)"
+Explanation: 1000/(100/10/2) = 1000/((100/10)/2) = 200
+However, the bold parenthesis in "1000/((100/10)/2)" are redundant since they do not influence the operation priority.
+So you should return "1000/(100/10/2)".
+Other cases:
+1000/(100/10)/2 = 50
+1000/(100/(10/2)) = 50
+1000/100/10/2 = 0.5
+1000/100/(10/2) = 2
 ```
 
-## 题意
-> ...
-
-## 题解
+**Example 2:**
 
-### 思路1
-> ...
-Optimal Division
-```go
 ```
-
+Input: nums = [2,3,4]
+Output: "2/(3/4)"
+Explanation: (2/(3/4)) = 8/3 = 2.667
+It can be shown that after trying all possibilities, we cannot get an expression with evaluation greater than 2.667
+```
 
 ## 结语
 

leetcode/501-600/0553.Optimal-Division/Solution.go

@@ -1,5 +1,61 @@
 package Solution
 
-func Solution(x bool) bool {
-	return x
+import "fmt"
+
+type mm struct {
+	max, min float32
+
+	maxStr, minStr string
+}
+
+func Solution(nums []int) string {
+	if len(nums) == 1 {
+		return fmt.Sprintf("%d", nums[0])
+	}
+	n := len(nums)
+	dp := make([][]mm, n)
+	for i := 0; i < n; i++ {
+		dp[i] = make([]mm, n)
+		s := fmt.Sprintf("%d", nums[i])
+		dp[i][i] = mm{max: float32(nums[i]), min: float32(nums[i]), maxStr: s, minStr: s}
+	}
+
+	for l := 2; l <= n; l++ {
+		for end := l - 1; end < n; end++ {
+			start := end - l + 1
+			for pre := end; pre > start; pre-- {
+				m1 := dp[start][pre-1].max
+				m2 := dp[pre][end].min
+				if r := m1 / m2; r > dp[start][end].max {
+					dp[start][end].max = r
+					b := dp[pre][end].minStr
+					if pre != end {
+						b = "(" + b + ")"
+					}
+					dp[start][end].maxStr = dp[start][pre-1].maxStr + "/" + b
+				}
+			}
+
+			for pre := end; pre > start; pre-- {
+				m1 := dp[start][pre-1].min
+				m2 := dp[pre][end].max
+				if r := m1 / m2; dp[start][end].min == 0 || r < dp[start][end].min {
+					dp[start][end].min = r
+					b := dp[pre][end].maxStr
+					if pre != end {
+						b = "(" + b + ")"
+					}
+					dp[start][end].minStr = dp[start][pre-1].minStr + "/" + b
+				}
+			}
+		}
+	}
+	/*
+		for i := 0; i < n; i++ {
+			for j := i; j < n; j++ {
+				fmt.Printf("----- %d - %d, %+v\n", i, j, dp[i][j])
+			}
+		}
+	*/
+	return dp[0][n-1].maxStr
 }

leetcode/501-600/0553.Optimal-Division/Solution_test.go

@@ -10,12 +10,11 @@ func TestSolution(t *testing.T) {
 	//	测试用例
 	cases := []struct {
 		name   string
-		inputs bool
-		expect bool
+		inputs []int
+		expect string
 	}{
-		{"TestCase", true, true},
-		{"TestCase", true, true},
-		{"TestCase", false, false},
+		{"TestCase1", []int{1000, 100, 10, 2}, "1000/(100/10/2)"},
+		{"TestCase2", []int{2, 3, 4}, "2/(3/4)"},
 	}
 
 	//	开始测试
@@ -30,10 +29,10 @@ 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() {
 }