Add solution and test-cases for problem 2040

leetcode/2001-2100/2040.Kth-Smallest-Product-of-Two-Sorted-Arrays/README.md

@@ -1,28 +1,46 @@
 # [2040.Kth Smallest Product of Two Sorted Arrays][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 two **sorted 0-indexed** integer arrays `nums1` and `nums2` as well as an integer `k`, return the `kth` **(1-based)** smallest product of `nums1[i] * nums2[j]` where `0 <= i < nums1.length` and `0 <= j < nums2.length`.
+
 **Example 1:**
 
 ```
-Input: a = "11", b = "1"
-Output: "100"
+Input: nums1 = [2,5], nums2 = [3,4], k = 2
+Output: 8
+Explanation: The 2 smallest products are:
+- nums1[0] * nums2[0] = 2 * 3 = 6
+- nums1[0] * nums2[1] = 2 * 4 = 8
+The 2nd smallest product is 8.
 ```
 
-## 题意
-> ...
+**Example 2:**
 
-## 题解
-
-### 思路1
-> ...
-Kth Smallest Product of Two Sorted Arrays
-```go
+```
+Input: nums1 = [-4,-2,0,3], nums2 = [2,4], k = 6
+Output: 0
+Explanation: The 6 smallest products are:
+- nums1[0] * nums2[1] = (-4) * 4 = -16
+- nums1[0] * nums2[0] = (-4) * 2 = -8
+- nums1[1] * nums2[1] = (-2) * 4 = -8
+- nums1[1] * nums2[0] = (-2) * 2 = -4
+- nums1[2] * nums2[0] = 0 * 2 = 0
+- nums1[2] * nums2[1] = 0 * 4 = 0
+The 6th smallest product is 0.
 ```
 
+**Example 3:**
+
+```
+Input: nums1 = [-2,-1,0,1,2], nums2 = [-3,-1,2,4,5], k = 3
+Output: -6
+Explanation: The 3 smallest products are:
+- nums1[0] * nums2[4] = (-2) * 5 = -10
+- nums1[0] * nums2[3] = (-2) * 4 = -8
+- nums1[4] * nums2[0] = 2 * (-3) = -6
+The 3rd smallest product is -6.
+```
 
 ## 结语
 

leetcode/2001-2100/2040.Kth-Smallest-Product-of-Two-Sorted-Arrays/Solution.go

@@ -1,5 +1,55 @@
 package Solution
 
-func Solution(x bool) bool {
-	return x
+import (
+	"math"
+	"sort"
+)
+
+func Solution(nums1, nums2 []int, k int64) int64 {
+	// 保证nums1更短，减少遍历次数
+	if len(nums1) > len(nums2) {
+		return Solution(nums2, nums1, k)
+	}
+
+	left, right := int64(-1e10), int64(1e10)
+	for left < right {
+		mid := left + (right-left)/2
+		count := checkNums(mid, nums1, nums2)
+		if count >= k {
+			right = mid
+		} else {
+			left = mid + 1
+		}
+	}
+	return left
+}
+
+func checkNums(mid int64, nums1, nums2 []int) int64 {
+	var ret int64 = 0
+	for _, x := range nums1 {
+		if x == 0 {
+			if mid >= 0 {
+				ret += int64(len(nums2))
+			}
+			// 如果mid<0，乘积都>=0，不计入
+		} else if x > 0 {
+			// 计算上界：mid / x
+			yy := int64(math.Floor(float64(mid) / float64(x)))
+			// upper_bound
+			idx := sort.Search(len(nums2), func(i int) bool {
+				return int64(nums2[i]) > yy
+			})
+			ret += int64(idx)
+		} else {
+			// x < 0
+			// 计算下界：ceil(mid / x)
+			yy := int64(math.Ceil(float64(mid) / float64(x)))
+			// lower_bound
+			idx := sort.Search(len(nums2), func(i int) bool {
+				return int64(nums2[i]) >= yy
+			})
+			ret += int64(len(nums2) - idx)
+		}
+	}
+	return ret
 }

leetcode/2001-2100/2040.Kth-Smallest-Product-of-Two-Sorted-Arrays/Solution_test.go

@@ -10,30 +10,30 @@ func TestSolution(t *testing.T) {
 	//	测试用例
 	cases := []struct {
 		name   string
-		inputs bool
-		expect bool
+		n1, n2 []int
+		k      int64
+		expect int64
 	}{
-		{"TestCase", true, true},
-		{"TestCase", true, true},
-		{"TestCase", false, false},
+		{"TestCase1", []int{2, 5}, []int{3, 4}, 2, 8},
+		{"TestCase2", []int{-2, -1, 0, 1, 2}, []int{-3, -1, 2, 4, 5}, 3, -6},
 	}
 
 	//	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.n1, c.n2, 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 %v",
+					c.expect, got, c.n1, c.n2, 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() {
 }