Merge pull request #1284 from 0xff-dev/2438

Add solution and test-cases for problem 2438

Author: 6boris

leetcode/2401-2500/2438.Range-Product-Queries-of-Powers/README.md

@@ -1,28 +1,34 @@
 # [2438.Range Product Queries of Powers][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 a positive integer `n`, there exists a **0-indexed** array called `powers`, composed of the **minimum** number of powers of `2` that sum to `n`. The array is sorted in **non-decreasing** order, and there is **only one** way to form the array.
+
+You are also given a **0-indexed** 2D integer array `queries`, where `queries[i] = [lefti, righti]`. Each `queries[i]` represents a query where you have to find the product of all `powers[j]` with `lefti <= j <= righti`.
+
+Return an array `answer`, equal in length to `queries`, where `answers[i]` is the answer to the `ith` query. Since the answer to the `ith` query may be too large, each `answers[i]` should be returned **modulo** `10^9 + 7`.
 
 **Example 1:**
 
 ```
-Input: a = "11", b = "1"
-Output: "100"
+Input: n = 15, queries = [[0,1],[2,2],[0,3]]
+Output: [2,4,64]
+Explanation:
+For n = 15, powers = [1,2,4,8]. It can be shown that powers cannot be a smaller size.
+Answer to 1st query: powers[0] * powers[1] = 1 * 2 = 2.
+Answer to 2nd query: powers[2] = 4.
+Answer to 3rd query: powers[0] * powers[1] * powers[2] * powers[3] = 1 * 2 * 4 * 8 = 64.
+Each answer modulo 109 + 7 yields the same answer, so [2,4,64] is returned.
 ```
 
-## 题意
-> ...
+**Example 2:**
 
-## 题解
-
-### 思路1
-> ...
-Range Product Queries of Powers
-```go
 ```
-
+Input: n = 2, queries = [[0,0]]
+Output: [2]
+Explanation:
+For n = 2, powers = [2].
+The answer to the only query is powers[0] = 2. The answer modulo 109 + 7 is the same, so [2] is returned.
+```
 
 ## 结语
 

leetcode/2401-2500/2438.Range-Product-Queries-of-Powers/Solution.go

@@ -1,5 +1,62 @@
 package Solution
 
-func Solution(x bool) bool {
-	return x
+import "sort"
+
+func construct(n int, powers [33]int) []int {
+	if n&(n-1) == 0 {
+		return []int{n}
+	}
+	index := sort.Search(33, func(i int) bool {
+		return powers[i] > n
+	})
+	set := []int{powers[index-1]}
+	left := construct(n-powers[index-1], powers)
+	set = append(set, left...)
+	return set
+}
+
+func modPow(x int64, n int64, m int64) int64 {
+	result := int64(1)
+	x %= m
+	for n > 0 {
+		if n&1 == 1 {
+			result = (result * x) % m
+		}
+		x = (x * x) % m
+		n >>= 1
+	}
+	return result
+}
+
+func modInverse(x int64, m int64) int64 {
+	return modPow(x, m-2, m)
+}
+
+const mod = 1000000007
+
+func Solution(n int, queries [][]int) []int {
+
+	powers := [33]int{}
+	powers[0] = 1
+	for i := 1; i < 33; i++ {
+		powers[i] = powers[i-1] * 2
+	}
+	arr := construct(n, powers)
+	for s, e := 0, len(arr)-1; s < e; s, e = s+1, e-1 {
+		arr[s], arr[e] = arr[e], arr[s]
+	}
+	ans := make([]int, len(queries))
+	prefix := make([]int64, len(arr)+1)
+	index := 0
+	prefix[index] = 1
+	for i := 0; i < len(arr); i++ {
+		prefix[i+1] = (prefix[index] * int64(arr[i])) % mod
+		index++
+	}
+	for i, q := range queries {
+		l, r := q[0], q[1]
+		res := (prefix[r+1] * modInverse(prefix[l], mod)) % mod
+		ans[i] = int(res)
+	}
+	return ans
 }

leetcode/2401-2500/2438.Range-Product-Queries-of-Powers/Solution_test.go

@@ -9,31 +9,31 @@ import (
 func TestSolution(t *testing.T) {
 	//	测试用例
 	cases := []struct {
-		name   string
-		inputs bool
-		expect bool
+		name    string
+		n       int
+		queries [][]int
+		expect  []int
 	}{
-		{"TestCase", true, true},
-		{"TestCase", true, true},
-		{"TestCase", false, false},
+		{"TestCase1", 15, [][]int{{0, 1}, {2, 2}, {0, 3}}, []int{2, 4, 64}},
+		{"TestCase2", 2, [][]int{{0, 0}}, []int{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.n, c.queries)
 			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.n, c.queries)
 			}
 		})
 	}
 }
 
-//	压力测试
+// 压力测试
 func BenchmarkSolution(b *testing.B) {
 }
 
-//	使用案列
+// 使用案列
 func ExampleSolution() {
 }