diff --git a/solution/3500-3599/3528.Unit Conversion I/README.md b/solution/3500-3599/3528.Unit Conversion I/README.md index dd0c34397aa00..4b9c7e712213b 100644 --- a/solution/3500-3599/3528.Unit Conversion I/README.md +++ b/solution/3500-3599/3528.Unit Conversion I/README.md @@ -34,8 +34,8 @@ tags:

解释：

@@ -49,13 +49,13 @@ tags:

解释：

@@ -64,11 +64,11 @@ tags:

提示：

@@ -77,32 +77,143 @@ tags: -### 方法一 +### 方法一：DFS + +由于题目保证了单位 0 可以通过唯一的转换路径转换为其他单位，因此我们可以使用深度优先搜索（DFS）来遍历所有单位的转换关系。另外，由于 $\textit{conversions}$ 数组的长度为 $n - 1$，表示有 $n - 1$ 条转换关系，因此我们可以将单位转换关系看作一棵树，根节点为单位 0，其他节点为其他单位。 + +我们可以用一个邻接表 $g$ 来表示单位转换关系，其中 $g[i]$ 表示单位 $i$ 可以转换到的单位和对应的转换因子。 + +然后，我们从根节点 $0$ 开始进行深度优先搜索，即调函数 $\textit{dfs}(s, \textit{mul})$，其中 $s$ 表示当前单位，$\textit{mul}$ 表示从单位 $0$ 转换到单位 $s$ 的转换因子。初始时 $s = 0$, $\textit{mul} = 1$。在每次递归中，我们将当前单位 $s$ 的转换因子 $\textit{mul}$ 存储到答案数组中，然后遍历当前单位 $s$ 的所有邻接单位 $t$，递归调用 $\textit{dfs}(t, \textit{mul} \times w \mod (10^9 + 7))$，其中 $w$ 为单位 $s$ 转换到单位 $t$ 的转换因子。 + +最后，我们返回答案数组即可。 + +时间复杂度 $O(n)$，空间复杂度 $O(n)$。其中 $n$ 为单位的数量。 #### Python3 ```python - +class Solution: + def baseUnitConversions(self, conversions: List[List[int]]) -> List[int]: + def dfs(s: int, mul: int) -> None: + ans[s] = mul + for t, w in g[s]: + dfs(t, mul * w % mod) + + mod = 10**9 + 7 + n = len(conversions) + 1 + g = [[] for _ in range(n)] + for s, t, w in conversions: + g[s].append((t, w)) + ans = [0] * n + dfs(0, 1) + return ans ``` #### Java ```java - +class Solution { + private final int mod = (int) 1e9 + 7; + private List[] g; + private int[] ans; + private int n; + + public int[] baseUnitConversions(int[][] conversions) { + n = conversions.length + 1; + g = new List[n]; + Arrays.setAll(g, k -> new ArrayList<>()); + ans = new int[n]; + for (var e : conversions) { + g[e[0]].add(new int[] {e[1], e[2]}); + } + dfs(0, 1); + return ans; + } + + private void dfs(int s, long mul) { + ans[s] = (int) mul; + for (var e : g[s]) { + dfs(e[0], mul * e[1] % mod); + } + } +} ``` #### C++ ```cpp - +class Solution { +public: + vector baseUnitConversions(vector>& conversions) { + const int mod = 1e9 + 7; + int n = conversions.size() + 1; + vector>> g(n); + vector ans(n); + for (const auto& e : conversions) { + g[e[0]].push_back({e[1], e[2]}); + } + auto dfs = [&](this auto&& dfs, int s, long long mul) -> void { + ans[s] = mul; + for (auto [t, w] : g[s]) { + dfs(t, mul * w % mod); + } + }; + dfs(0, 1); + return ans; + } +}; ``` #### Go ```go +func baseUnitConversions(conversions [][]int) []int { + const mod = int(1e9 + 7) + n := len(conversions) + 1 + + g := make([][]struct{ t, w int }, n) + for _, e := range conversions { + s, t, w := e[0], e[1], e[2] + g[s] = append(g[s], struct{ t, w int }{t, w}) + } + + ans := make([]int, n) + + var dfs func(s int, mul int) + dfs = func(s int, mul int) { + ans[s] = mul + for _, e := range g[s] { + dfs(e.t, mul*e.w%mod) + } + } + + dfs(0, 1) + return ans +} +``` +#### TypeScript + +```ts +function baseUnitConversions(conversions: number[][]): number[] { + const mod = BigInt(1e9 + 7); + const n = conversions.length + 1; + const g: { t: number; w: number }[][] = Array.from({ length: n }, () => []); + for (const [s, t, w] of conversions) { + g[s].push({ t, w }); + } + const ans: number[] = Array(n).fill(0); + const dfs = (s: number, mul: number) => { + ans[s] = mul; + for (const { t, w } of g[s]) { + dfs(t, Number((BigInt(mul) * BigInt(w)) % mod)); + } + }; + dfs(0, 1); + return ans; +} ``` diff --git a/solution/3500-3599/3528.Unit Conversion I/README_EN.md b/solution/3500-3599/3528.Unit Conversion I/README_EN.md index bdcd4ab35d682..01b370e3cedcf 100644 --- a/solution/3500-3599/3528.Unit Conversion I/README_EN.md +++ b/solution/3500-3599/3528.Unit Conversion I/README_EN.md @@ -33,8 +33,8 @@ tags:

Explanation:

    -
  • Convert a single unit of type 0 into 2 units of type 1 using conversions[0].
    • -
  • Convert a single unit of type 0 into 6 units of type 2 using conversions[0], then conversions[1].
    • +
  • Convert a single unit of type 0 into 2 units of type 1 using conversions[0].
    • +
  • Convert a single unit of type 0 into 6 units of type 2 using conversions[0], then conversions[1].
@@ -48,13 +48,13 @@ tags:

Explanation:

    -
  • Convert a single unit of type 0 into 2 units of type 1 using conversions[0].
    • -
  • Convert a single unit of type 0 into 3 units of type 2 using conversions[1].
    • -
  • Convert a single unit of type 0 into 8 units of type 3 using conversions[0], then conversions[2].
    • -
  • Convert a single unit of type 0 into 10 units of type 4 using conversions[0], then conversions[3].
    • -
  • Convert a single unit of type 0 into 6 units of type 5 using conversions[1], then conversions[4].
    • -
  • Convert a single unit of type 0 into 30 units of type 6 using conversions[0], conversions[3], then conversions[5].
    • -
  • Convert a single unit of type 0 into 24 units of type 7 using conversions[1], conversions[4], then conversions[6].
    • +
  • Convert a single unit of type 0 into 2 units of type 1 using conversions[0].
    • +
  • Convert a single unit of type 0 into 3 units of type 2 using conversions[1].
    • +
  • Convert a single unit of type 0 into 8 units of type 3 using conversions[0], then conversions[2].
    • +
  • Convert a single unit of type 0 into 10 units of type 4 using conversions[0], then conversions[3].
    • +
  • Convert a single unit of type 0 into 6 units of type 5 using conversions[1], then conversions[4].
    • +
  • Convert a single unit of type 0 into 30 units of type 6 using conversions[0], conversions[3], then conversions[5].
    • +
  • Convert a single unit of type 0 into 24 units of type 7 using conversions[1], conversions[4], then conversions[6].
@@ -62,11 +62,11 @@ tags:

Constraints:

    -
  • 2 <= n <= 105
    • -
  • conversions.length == n - 1
    • -
  • 0 <= sourceUniti, targetUniti < n
    • -
  • 1 <= conversionFactori <= 109
    • -
  • It is guaranteed that unit 0 can be converted into any other unit through a unique combination of conversions without using any conversions in the opposite direction.
    • +
  • 2 <= n <= 105
    • +
  • conversions.length == n - 1
    • +
  • 0 <= sourceUniti, targetUniti < n
    • +
  • 1 <= conversionFactori <= 109
    • +
  • It is guaranteed that unit 0 can be converted into any other unit through a unique combination of conversions without using any conversions in the opposite direction.
@@ -75,32 +75,143 @@ tags: -### Solution 1 +### Solution 1: DFS + +Since the problem guarantees that unit 0 can be converted to any other unit through a unique conversion path, we can use Depth-First Search (DFS) to traverse all unit conversion relationships. Additionally, since the length of the $\textit{conversions}$ array is $n - 1$, representing $n - 1$ conversion relationships, we can treat the unit conversion relationships as a tree, where the root node is unit 0, and the other nodes are the other units. + +We can use an adjacency list $g$ to represent the unit conversion relationships, where $g[i]$ represents the units that unit $i$ can convert to and the corresponding conversion factors. + +Then, we start the DFS from the root node $0$, i.e., call the function $\textit{dfs}(s, \textit{mul})$, where $s$ represents the current unit, and $\textit{mul}$ represents the conversion factor from unit $0$ to unit $s$. Initially, $s = 0$, $\textit{mul} = 1$. In each recursion, we store the conversion factor $\textit{mul}$ of the current unit $s$ into the answer array, then traverse all adjacent units $t$ of the current unit $s$, and recursively call $\textit{dfs}(t, \textit{mul} \times w \mod (10^9 + 7))$, where $w$ is the conversion factor from unit $s$ to unit $t$. + +Finally, we return the answer array. + +The complexity is $O(n)$, and the space complexity is $O(n)$, where $n$ is the number of units. #### Python3 ```python - +class Solution: + def baseUnitConversions(self, conversions: List[List[int]]) -> List[int]: + def dfs(s: int, mul: int) -> None: + ans[s] = mul + for t, w in g[s]: + dfs(t, mul * w % mod) + + mod = 10**9 + 7 + n = len(conversions) + 1 + g = [[] for _ in range(n)] + for s, t, w in conversions: + g[s].append((t, w)) + ans = [0] * n + dfs(0, 1) + return ans ``` #### Java ```java - +class Solution { + private final int mod = (int) 1e9 + 7; + private List[] g; + private int[] ans; + private int n; + + public int[] baseUnitConversions(int[][] conversions) { + n = conversions.length + 1; + g = new List[n]; + Arrays.setAll(g, k -> new ArrayList<>()); + ans = new int[n]; + for (var e : conversions) { + g[e[0]].add(new int[] {e[1], e[2]}); + } + dfs(0, 1); + return ans; + } + + private void dfs(int s, long mul) { + ans[s] = (int) mul; + for (var e : g[s]) { + dfs(e[0], mul * e[1] % mod); + } + } +} ``` #### C++ ```cpp - +class Solution { +public: + vector baseUnitConversions(vector>& conversions) { + const int mod = 1e9 + 7; + int n = conversions.size() + 1; + vector>> g(n); + vector ans(n); + for (const auto& e : conversions) { + g[e[0]].push_back({e[1], e[2]}); + } + auto dfs = [&](this auto&& dfs, int s, long long mul) -> void { + ans[s] = mul; + for (auto [t, w] : g[s]) { + dfs(t, mul * w % mod); + } + }; + dfs(0, 1); + return ans; + } +}; ``` #### Go ```go +func baseUnitConversions(conversions [][]int) []int { + const mod = int(1e9 + 7) + n := len(conversions) + 1 + + g := make([][]struct{ t, w int }, n) + for _, e := range conversions { + s, t, w := e[0], e[1], e[2] + g[s] = append(g[s], struct{ t, w int }{t, w}) + } + + ans := make([]int, n) + + var dfs func(s int, mul int) + dfs = func(s int, mul int) { + ans[s] = mul + for _, e := range g[s] { + dfs(e.t, mul*e.w%mod) + } + } + + dfs(0, 1) + return ans +} +``` +#### TypeScript + +```ts +function baseUnitConversions(conversions: number[][]): number[] { + const mod = BigInt(1e9 + 7); + const n = conversions.length + 1; + const g: { t: number; w: number }[][] = Array.from({ length: n }, () => []); + for (const [s, t, w] of conversions) { + g[s].push({ t, w }); + } + const ans: number[] = Array(n).fill(0); + const dfs = (s: number, mul: number) => { + ans[s] = mul; + for (const { t, w } of g[s]) { + dfs(t, Number((BigInt(mul) * BigInt(w)) % mod)); + } + }; + dfs(0, 1); + return ans; +} ``` diff --git a/solution/3500-3599/3528.Unit Conversion I/Solution.cpp b/solution/3500-3599/3528.Unit Conversion I/Solution.cpp new file mode 100644 index 0000000000000..1c5c52272b45f --- /dev/null +++ b/solution/3500-3599/3528.Unit Conversion I/Solution.cpp @@ -0,0 +1,20 @@ +class Solution { +public: + vector baseUnitConversions(vector>& conversions) { + const int mod = 1e9 + 7; + int n = conversions.size() + 1; + vector>> g(n); + vector ans(n); + for (const auto& e : conversions) { + g[e[0]].push_back({e[1], e[2]}); + } + auto dfs = [&](this auto&& dfs, int s, long long mul) -> void { + ans[s] = mul; + for (auto [t, w] : g[s]) { + dfs(t, mul * w % mod); + } + }; + dfs(0, 1); + return ans; + } +}; \ No newline at end of file diff --git a/solution/3500-3599/3528.Unit Conversion I/Solution.go b/solution/3500-3599/3528.Unit Conversion I/Solution.go new file mode 100644 index 0000000000000..5b69c70470577 --- /dev/null +++ b/solution/3500-3599/3528.Unit Conversion I/Solution.go @@ -0,0 +1,23 @@ +func baseUnitConversions(conversions [][]int) []int { + const mod = int(1e9 + 7) + n := len(conversions) + 1 + + g := make([][]struct{ t, w int }, n) + for _, e := range conversions { + s, t, w := e[0], e[1], e[2] + g[s] = append(g[s], struct{ t, w int }{t, w}) + } + + ans := make([]int, n) + + var dfs func(s int, mul int) + dfs = func(s int, mul int) { + ans[s] = mul + for _, e := range g[s] { + dfs(e.t, mul*e.w%mod) + } + } + + dfs(0, 1) + return ans +} diff --git a/solution/3500-3599/3528.Unit Conversion I/Solution.java b/solution/3500-3599/3528.Unit Conversion I/Solution.java new file mode 100644 index 0000000000000..7d44b96aefc6f --- /dev/null +++ b/solution/3500-3599/3528.Unit Conversion I/Solution.java @@ -0,0 +1,25 @@ +class Solution { + private final int mod = (int) 1e9 + 7; + private List[] g; + private int[] ans; + private int n; + + public int[] baseUnitConversions(int[][] conversions) { + n = conversions.length + 1; + g = new List[n]; + Arrays.setAll(g, k -> new ArrayList<>()); + ans = new int[n]; + for (var e : conversions) { + g[e[0]].add(new int[] {e[1], e[2]}); + } + dfs(0, 1); + return ans; + } + + private void dfs(int s, long mul) { + ans[s] = (int) mul; + for (var e : g[s]) { + dfs(e[0], mul * e[1] % mod); + } + } +} \ No newline at end of file diff --git a/solution/3500-3599/3528.Unit Conversion I/Solution.py b/solution/3500-3599/3528.Unit Conversion I/Solution.py new file mode 100644 index 0000000000000..2b5a94c132eb9 --- /dev/null +++ b/solution/3500-3599/3528.Unit Conversion I/Solution.py @@ -0,0 +1,15 @@ +class Solution: + def baseUnitConversions(self, conversions: List[List[int]]) -> List[int]: + def dfs(s: int, mul: int) -> None: + ans[s] = mul + for t, w in g[s]: + dfs(t, mul * w % mod) + + mod = 10**9 + 7 + n = len(conversions) + 1 + g = [[] for _ in range(n)] + for s, t, w in conversions: + g[s].append((t, w)) + ans = [0] * n + dfs(0, 1) + return ans diff --git a/solution/3500-3599/3528.Unit Conversion I/Solution.ts b/solution/3500-3599/3528.Unit Conversion I/Solution.ts new file mode 100644 index 0000000000000..c87af0f665d60 --- /dev/null +++ b/solution/3500-3599/3528.Unit Conversion I/Solution.ts @@ -0,0 +1,17 @@ +function baseUnitConversions(conversions: number[][]): number[] { + const mod = BigInt(1e9 + 7); + const n = conversions.length + 1; + const g: { t: number; w: number }[][] = Array.from({ length: n }, () => []); + for (const [s, t, w] of conversions) { + g[s].push({ t, w }); + } + const ans: number[] = Array(n).fill(0); + const dfs = (s: number, mul: number) => { + ans[s] = mul; + for (const { t, w } of g[s]) { + dfs(t, Number((BigInt(mul) * BigInt(w)) % mod)); + } + }; + dfs(0, 1); + return ans; +}