Merge pull request #1285 from 0xff-dev/2787

Add solution and test-cases for problem 2787

Author: 6boris

leetcode/2701-2800/2787.Ways-to-Express-an-Integer-as-Sum-of-Powers/README.md

@@ -0,0 +1,36 @@
+# [2787.Ways to Express an Integer as Sum of Powers][title]
+
+## Description
+Given two **positive** integers `n` and `n`.
+
+Return the number of ways `n` can be expressed as the sum of the `xth` power of **unique** positive integers, in other words, the number of sets of unique integers `[n1, n2, ..., nk]` where `n = n1x + n2x + ... + nkx`.
+
+Since the result can be very large, return it modulo `10^9 + 7`.
+
+For example, if `n = 160` and `x = 3`, one way to express `n` is `n = 2^3 + 3^3 + 5^3`.
+
+**Example 1:**
+
+```
+Input: n = 10, x = 2
+Output: 1
+Explanation: We can express n as the following: n = 32 + 12 = 10.
+It can be shown that it is the only way to express 10 as the sum of the 2nd power of unique integers.
+```
+
+**EXample 2:**
+
+```
+Input: n = 4, x = 1
+Output: 2
+Explanation: We can express n in the following ways:
+- n = 41 = 4.
+- n = 31 + 11 = 4.
+```
+
+## 结语
+
+如果你同我一样热爱数据结构、算法、LeetCode，可以关注我 GitHub 上的 LeetCode 题解：[awesome-golang-algorithm][me]
+
+[title]: https://leetcode.com/problems/ways-to-express-an-integer-as-sum-of-powers
+[me]: https://github.com/kylesliu/awesome-golang-algorithm

leetcode/2701-2800/2787.Ways-to-Express-an-Integer-as-Sum-of-Powers/Solution.go

@@ -1,5 +1,45 @@
 package Solution
 
-func Solution(x bool) bool {
-	return x
+func power(base, n int) int {
+	result := 1
+	for i := 0; i < n; i++ {
+		result *= base
+	}
+	return result
+}
+
+const mod = 1000000007
+
+func Solution(n int, x int) int {
+	candidates := []int{}
+	i := 1
+	for ; ; i++ {
+		p := power(i, x)
+		if p > n {
+			break
+		}
+		candidates = append(candidates, p)
+	}
+
+	var dfs func(index, target int) int
+	cache := make(map[[2]int]int)
+
+	dfs = func(index, target int) int {
+		if target == 0 {
+			return 1
+		}
+		if target < 0 || index == len(candidates) {
+			return 0
+		}
+		key := [2]int{index, target}
+		if val, ok := cache[key]; ok {
+			return val
+		}
+		res := dfs(index+1, target-candidates[index]) % mod
+		res = (res + dfs(index+1, target)) % mod
+		cache[key] = res
+		return res
+	}
+
+	return dfs(0, n)
 }

leetcode/2701-2800/2787.Ways-to-Express-an-Integer-as-Sum-of-Powers/Solution_test.go

@@ -10,30 +10,29 @@ func TestSolution(t *testing.T) {
 	//	测试用例
 	cases := []struct {
 		name   string
-		inputs bool
-		expect bool
+		n, x   int
+		expect int
 	}{
-		{"TestCase", true, true},
-		{"TestCase", true, true},
-		{"TestCase", false, false},
+		{"TestCase1", 10, 2, 1},
+		{"TestCase2", 4, 1, 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.x)
 			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.x)
 			}
 		})
 	}
 }
 
-//	压力测试
+// 压力测试
 func BenchmarkSolution(b *testing.B) {
 }
 
-//	使用案列
+// 使用案列
 func ExampleSolution() {
 }