diff --git a/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/README.md b/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/README.md index 8cb4ba6c20f50..557522f03bf7e 100644 --- a/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/README.md +++ b/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/README.md @@ -129,32 +129,123 @@ tags: -### 方法一 +### 方法一：递推 + +我们定义 $f[i]$ 表示巫师 $i$ 完成上一瓶药水的时间。 + +对于当前的药水 $x$，我们需要计算每个巫师完成该药水的时间。定义 $\textit{tot}$ 表示当前药水完成的时间，初始时 $\textit{tot} = 0$。 + +对于每个巫师 $i$，他开始处理当前药水的时间为 $\max(\textit{tot}, f[i])$，处理该药水需要的时间为 $skill[i] \times mana[x]$，因此他完成该药水的时间为 $\max(\textit{tot}, f[i]) + skill[i] \times mana[x]$。我们更新 $\textit{tot}$ 为该值。 + +由于酿造过程要求药水在当前巫师完成工作后必须立即传递给下一个巫师并开始处理，因此我们需要更新每个巫师完成上一瓶药水的时间 $f[i]$。对于最后一个巫师 $n-1$，我们直接将 $f[n-1]$ 更新为 $\textit{tot}$。对于其他巫师 $i$，我们可以通过倒序遍历来更新 $f[i]$，具体地，$f[i] = f[i+1] - skill[i+1] \times mana[x]$。 + +最终 $f[n-1]$ 即为所有药水酿造完成的最短总时间。 + +时间复杂度 $O(n \times m)$，空间复杂度 $O(n)$。其中 $n$ 和 $m$ 分别为巫师和药水的数量。 #### Python3 ```python - +class Solution: + def minTime(self, skill: List[int], mana: List[int]) -> int: + max = lambda a, b: a if a > b else b + n = len(skill) + f = [0] * n + for x in mana: + tot = 0 + for i in range(n): + tot = max(tot, f[i]) + skill[i] * x + f[-1] = tot + for i in range(n - 2, -1, -1): + f[i] = f[i + 1] - skill[i + 1] * x + return f[-1] ``` #### Java ```java - +class Solution { + public long minTime(int[] skill, int[] mana) { + int n = skill.length; + long[] f = new long[n]; + for (int x : mana) { + long tot = 0; + for (int i = 0; i < n; ++i) { + tot = Math.max(tot, f[i]) + skill[i] * x; + } + f[n - 1] = tot; + for (int i = n - 2; i >= 0; --i) { + f[i] = f[i + 1] - skill[i + 1] * x; + } + } + return f[n - 1]; + } +} ``` #### C++ ```cpp - +class Solution { +public: + long long minTime(vector& skill, vector& mana) { + int n = skill.size(); + vector f(n); + for (int x : mana) { + long long tot = 0; + for (int i = 0; i < n; ++i) { + tot = max(tot, f[i]) + 1LL * skill[i] * x; + } + f[n - 1] = tot; + for (int i = n - 2; i >= 0; --i) { + f[i] = f[i + 1] - 1LL * skill[i + 1] * x; + } + } + return f[n - 1]; + } +}; ``` #### Go ```go +func minTime(skill []int, mana []int) int64 { + n := len(skill) + f := make([]int64, n) + for _, x := range mana { + var tot int64 + for i := 0; i < n; i++ { + tot = max(tot, f[i]) + int64(skill[i])*int64(x) + } + f[n-1] = tot + for i := n - 2; i >= 0; i-- { + f[i] = f[i+1] - int64(skill[i+1])*int64(x) + } + } + return f[n-1] +} +``` +#### TypeScript + +```ts +function minTime(skill: number[], mana: number[]): number { + const n = skill.length; + const f: number[] = Array(n).fill(0); + for (const x of mana) { + let tot = 0; + for (let i = 0; i < n; ++i) { + tot = Math.max(tot, f[i]) + skill[i] * x; + } + f[n - 1] = tot; + for (let i = n - 2; i >= 0; --i) { + f[i] = f[i + 1] - skill[i + 1] * x; + } + } + return f[n - 1]; +} ``` diff --git a/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/README_EN.md b/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/README_EN.md index a1b737797afdf..9ca512c915c8a 100644 --- a/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/README_EN.md +++ b/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/README_EN.md @@ -126,32 +126,123 @@ tags: -### Solution 1 +### Solution 1: Dynamic Programming + +We define $f[i]$ as the time when wizard $i$ completes the previous potion. + +For the current potion $x$, we need to calculate the completion time for each wizard. Let $\textit{tot}$ represent the completion time of the current potion, initially $\textit{tot} = 0$. + +For each wizard $i$, the time he starts processing the current potion is $\max(\textit{tot}, f[i])$, and the time required to process this potion is $skill[i] \times mana[x]$. Therefore, the time he completes this potion is $\max(\textit{tot}, f[i]) + skill[i] \times mana[x]$. We update $\textit{tot}$ to this value. + +Since the brewing process requires that the potion must be immediately passed to the next wizard and processing must start immediately after the current wizard completes their work, we need to update the completion time $f[i]$ for each wizard's previous potion. For the last wizard $n-1$, we directly update $f[n-1]$ to $\textit{tot}$. For other wizards $i$, we can update $f[i]$ by traversing in reverse order, specifically, $f[i] = f[i+1] - skill[i+1] \times mana[x]$. + +Finally, $f[n-1]$ is the minimum total time required to complete brewing all potions. + +The time complexity is $O(n \times m)$ and the space complexity is $O(n)$, where $n$ and $m$ are the number of wizards and potions respectively. #### Python3 ```python - +class Solution: + def minTime(self, skill: List[int], mana: List[int]) -> int: + max = lambda a, b: a if a > b else b + n = len(skill) + f = [0] * n + for x in mana: + tot = 0 + for i in range(n): + tot = max(tot, f[i]) + skill[i] * x + f[-1] = tot + for i in range(n - 2, -1, -1): + f[i] = f[i + 1] - skill[i + 1] * x + return f[-1] ``` #### Java ```java - +class Solution { + public long minTime(int[] skill, int[] mana) { + int n = skill.length; + long[] f = new long[n]; + for (int x : mana) { + long tot = 0; + for (int i = 0; i < n; ++i) { + tot = Math.max(tot, f[i]) + skill[i] * x; + } + f[n - 1] = tot; + for (int i = n - 2; i >= 0; --i) { + f[i] = f[i + 1] - skill[i + 1] * x; + } + } + return f[n - 1]; + } +} ``` #### C++ ```cpp - +class Solution { +public: + long long minTime(vector& skill, vector& mana) { + int n = skill.size(); + vector f(n); + for (int x : mana) { + long long tot = 0; + for (int i = 0; i < n; ++i) { + tot = max(tot, f[i]) + 1LL * skill[i] * x; + } + f[n - 1] = tot; + for (int i = n - 2; i >= 0; --i) { + f[i] = f[i + 1] - 1LL * skill[i + 1] * x; + } + } + return f[n - 1]; + } +}; ``` #### Go ```go +func minTime(skill []int, mana []int) int64 { + n := len(skill) + f := make([]int64, n) + for _, x := range mana { + var tot int64 + for i := 0; i < n; i++ { + tot = max(tot, f[i]) + int64(skill[i])*int64(x) + } + f[n-1] = tot + for i := n - 2; i >= 0; i-- { + f[i] = f[i+1] - int64(skill[i+1])*int64(x) + } + } + return f[n-1] +} +``` +#### TypeScript + +```ts +function minTime(skill: number[], mana: number[]): number { + const n = skill.length; + const f: number[] = Array(n).fill(0); + for (const x of mana) { + let tot = 0; + for (let i = 0; i < n; ++i) { + tot = Math.max(tot, f[i]) + skill[i] * x; + } + f[n - 1] = tot; + for (let i = n - 2; i >= 0; --i) { + f[i] = f[i + 1] - skill[i + 1] * x; + } + } + return f[n - 1]; +} ``` diff --git a/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/Solution.cpp b/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/Solution.cpp new file mode 100644 index 0000000000000..ebce489d1dd1a --- /dev/null +++ b/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/Solution.cpp @@ -0,0 +1,18 @@ +class Solution { +public: + long long minTime(vector& skill, vector& mana) { + int n = skill.size(); + vector f(n); + for (int x : mana) { + long long tot = 0; + for (int i = 0; i < n; ++i) { + tot = max(tot, f[i]) + 1LL * skill[i] * x; + } + f[n - 1] = tot; + for (int i = n - 2; i >= 0; --i) { + f[i] = f[i + 1] - 1LL * skill[i + 1] * x; + } + } + return f[n - 1]; + } +}; diff --git a/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/Solution.go b/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/Solution.go new file mode 100644 index 0000000000000..c5b258517f8f5 --- /dev/null +++ b/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/Solution.go @@ -0,0 +1,15 @@ +func minTime(skill []int, mana []int) int64 { + n := len(skill) + f := make([]int64, n) + for _, x := range mana { + var tot int64 + for i := 0; i < n; i++ { + tot = max(tot, f[i]) + int64(skill[i])*int64(x) + } + f[n-1] = tot + for i := n - 2; i >= 0; i-- { + f[i] = f[i+1] - int64(skill[i+1])*int64(x) + } + } + return f[n-1] +} diff --git a/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/Solution.java b/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/Solution.java new file mode 100644 index 0000000000000..80282f67dad6e --- /dev/null +++ b/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/Solution.java @@ -0,0 +1,17 @@ +class Solution { + public long minTime(int[] skill, int[] mana) { + int n = skill.length; + long[] f = new long[n]; + for (int x : mana) { + long tot = 0; + for (int i = 0; i < n; ++i) { + tot = Math.max(tot, f[i]) + skill[i] * x; + } + f[n - 1] = tot; + for (int i = n - 2; i >= 0; --i) { + f[i] = f[i + 1] - skill[i + 1] * x; + } + } + return f[n - 1]; + } +} diff --git a/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/Solution.py b/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/Solution.py new file mode 100644 index 0000000000000..bec342c48fe0d --- /dev/null +++ b/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/Solution.py @@ -0,0 +1,13 @@ +class Solution: + def minTime(self, skill: List[int], mana: List[int]) -> int: + max = lambda a, b: a if a > b else b + n = len(skill) + f = [0] * n + for x in mana: + tot = 0 + for i in range(n): + tot = max(tot, f[i]) + skill[i] * x + f[-1] = tot + for i in range(n - 2, -1, -1): + f[i] = f[i + 1] - skill[i + 1] * x + return f[-1] diff --git a/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/Solution.ts b/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/Solution.ts new file mode 100644 index 0000000000000..32d47a7e26eca --- /dev/null +++ b/solution/3400-3499/3494.Find the Minimum Amount of Time to Brew Potions/Solution.ts @@ -0,0 +1,15 @@ +function minTime(skill: number[], mana: number[]): number { + const n = skill.length; + const f: number[] = Array(n).fill(0); + for (const x of mana) { + let tot = 0; + for (let i = 0; i < n; ++i) { + tot = Math.max(tot, f[i]) + skill[i] * x; + } + f[n - 1] = tot; + for (let i = n - 2; i >= 0; --i) { + f[i] = f[i + 1] - skill[i + 1] * x; + } + } + return f[n - 1]; +}