diff --git a/solution/3600-3699/3618.Split Array by Prime Indices/README.md b/solution/3600-3699/3618.Split Array by Prime Indices/README.md index 0ef7d7b1daf79..2f8a57f998a13 100644 --- a/solution/3600-3699/3618.Split Array by Prime Indices/README.md +++ b/solution/3600-3699/3618.Split Array by Prime Indices/README.md @@ -80,32 +80,153 @@ edit_url: https://github.com/doocs/leetcode/edit/main/solution/3600-3699/3618.Sp -### 方法一 +### 方法一：埃氏筛 + 模拟 + +我们可以用埃氏筛法预处理出 $[0, 10^5]$ 范围内的所有质数。然后遍历数组 $ +\textit{nums}$，对于 $\textit{nums}[i]$，如果 $i$ 是质数，则将 $\textit{nums}[i]$ 加到答案中，否则将 $-\textit{nums}[i]$ 加到答案中。最后返回答案的绝对值。 + +忽略预处理的时间和空间，时间复杂度 $O(n)$，其中 $n$ 是数组 $\textit{nums}$ 的长度，空间复杂度 $O(1)$。 #### Python3 ```python - +m = 10**5 + 10 +primes = [True] * m +primes[0] = primes[1] = False +for i in range(2, m): + if primes[i]: + for j in range(i + i, m, i): + primes[j] = False + + +class Solution: + def splitArray(self, nums: List[int]) -> int: + return abs(sum(x if primes[i] else -x for i, x in enumerate(nums))) ``` #### Java ```java - +class Solution { + private static final int M = 100000 + 10; + private static boolean[] primes = new boolean[M]; + + static { + for (int i = 0; i < M; i++) { + primes[i] = true; + } + primes[0] = primes[1] = false; + + for (int i = 2; i < M; i++) { + if (primes[i]) { + for (int j = i + i; j < M; j += i) { + primes[j] = false; + } + } + } + } + + public long splitArray(int[] nums) { + long ans = 0; + for (int i = 0; i < nums.length; ++i) { + ans += primes[i] ? nums[i] : -nums[i]; + } + return Math.abs(ans); + } +} ``` #### C++ ```cpp - +const int M = 1e5 + 10; +bool primes[M]; +auto init = [] { + memset(primes, true, sizeof(primes)); + primes[0] = primes[1] = false; + for (int i = 2; i < M; ++i) { + if (primes[i]) { + for (int j = i + i; j < M; j += i) { + primes[j] = false; + } + } + } + return 0; +}(); + +class Solution { +public: + long long splitArray(vector& nums) { + long long ans = 0; + for (int i = 0; i < nums.size(); ++i) { + ans += primes[i] ? nums[i] : -nums[i]; + } + return abs(ans); + } +}; ``` #### Go ```go +const M = 100000 + 10 + +var primes [M]bool + +func init() { + for i := 0; i < M; i++ { + primes[i] = true + } + primes[0], primes[1] = false, false + + for i := 2; i < M; i++ { + if primes[i] { + for j := i + i; j < M; j += i { + primes[j] = false + } + } + } +} + +func splitArray(nums []int) (ans int64) { + for i, num := range nums { + if primes[i] { + ans += int64(num) + } else { + ans -= int64(num) + } + } + return max(ans, -ans) +} +``` +#### TypeScript + +```ts +const M = 100000 + 10; +const primes: boolean[] = Array(M).fill(true); + +const init = (() => { + primes[0] = primes[1] = false; + + for (let i = 2; i < M; i++) { + if (primes[i]) { + for (let j = i + i; j < M; j += i) { + primes[j] = false; + } + } + } +})(); + +function splitArray(nums: number[]): number { + let ans = 0; + for (let i = 0; i < nums.length; i++) { + ans += primes[i] ? nums[i] : -nums[i]; + } + return Math.abs(ans); +} ``` diff --git a/solution/3600-3699/3618.Split Array by Prime Indices/README_EN.md b/solution/3600-3699/3618.Split Array by Prime Indices/README_EN.md index fb6bdd1ef7c47..ed7c083b3b062 100644 --- a/solution/3600-3699/3618.Split Array by Prime Indices/README_EN.md +++ b/solution/3600-3699/3618.Split Array by Prime Indices/README_EN.md @@ -78,32 +78,152 @@ edit_url: https://github.com/doocs/leetcode/edit/main/solution/3600-3699/3618.Sp -### Solution 1 +### Solution 1: Sieve of Eratosthenes + Simulation + +We can use the Sieve of Eratosthenes to preprocess all prime numbers in the range $[0, 10^5]$. Then we iterate through the array $\textit{nums}$. For $\textit{nums}[i]$, if $i$ is a prime number, we add $\textit{nums}[i]$ to the answer; otherwise, we add $-\textit{nums}[i]$ to the answer. Finally, we return the absolute value of the answer. + +Ignoring the preprocessing time and space, the time complexity is $O(n)$, where $n$ is the length of the array $\textit{nums}$, and the space complexity is $O(1)$. #### Python3 ```python - +m = 10**5 + 10 +primes = [True] * m +primes[0] = primes[1] = False +for i in range(2, m): + if primes[i]: + for j in range(i + i, m, i): + primes[j] = False + + +class Solution: + def splitArray(self, nums: List[int]) -> int: + return abs(sum(x if primes[i] else -x for i, x in enumerate(nums))) ``` #### Java ```java - +class Solution { + private static final int M = 100000 + 10; + private static boolean[] primes = new boolean[M]; + + static { + for (int i = 0; i < M; i++) { + primes[i] = true; + } + primes[0] = primes[1] = false; + + for (int i = 2; i < M; i++) { + if (primes[i]) { + for (int j = i + i; j < M; j += i) { + primes[j] = false; + } + } + } + } + + public long splitArray(int[] nums) { + long ans = 0; + for (int i = 0; i < nums.length; ++i) { + ans += primes[i] ? nums[i] : -nums[i]; + } + return Math.abs(ans); + } +} ``` #### C++ ```cpp - +const int M = 1e5 + 10; +bool primes[M]; +auto init = [] { + memset(primes, true, sizeof(primes)); + primes[0] = primes[1] = false; + for (int i = 2; i < M; ++i) { + if (primes[i]) { + for (int j = i + i; j < M; j += i) { + primes[j] = false; + } + } + } + return 0; +}(); + +class Solution { +public: + long long splitArray(vector& nums) { + long long ans = 0; + for (int i = 0; i < nums.size(); ++i) { + ans += primes[i] ? nums[i] : -nums[i]; + } + return abs(ans); + } +}; ``` #### Go ```go +const M = 100000 + 10 + +var primes [M]bool + +func init() { + for i := 0; i < M; i++ { + primes[i] = true + } + primes[0], primes[1] = false, false + + for i := 2; i < M; i++ { + if primes[i] { + for j := i + i; j < M; j += i { + primes[j] = false + } + } + } +} + +func splitArray(nums []int) (ans int64) { + for i, num := range nums { + if primes[i] { + ans += int64(num) + } else { + ans -= int64(num) + } + } + return max(ans, -ans) +} +``` +#### TypeScript + +```ts +const M = 100000 + 10; +const primes: boolean[] = Array(M).fill(true); + +const init = (() => { + primes[0] = primes[1] = false; + + for (let i = 2; i < M; i++) { + if (primes[i]) { + for (let j = i + i; j < M; j += i) { + primes[j] = false; + } + } + } +})(); + +function splitArray(nums: number[]): number { + let ans = 0; + for (let i = 0; i < nums.length; i++) { + ans += primes[i] ? nums[i] : -nums[i]; + } + return Math.abs(ans); +} ``` diff --git a/solution/3600-3699/3618.Split Array by Prime Indices/Solution.cpp b/solution/3600-3699/3618.Split Array by Prime Indices/Solution.cpp new file mode 100644 index 0000000000000..896e6027a692d --- /dev/null +++ b/solution/3600-3699/3618.Split Array by Prime Indices/Solution.cpp @@ -0,0 +1,25 @@ +const int M = 1e5 + 10; +bool primes[M]; +auto init = [] { + memset(primes, true, sizeof(primes)); + primes[0] = primes[1] = false; + for (int i = 2; i < M; ++i) { + if (primes[i]) { + for (int j = i + i; j < M; j += i) { + primes[j] = false; + } + } + } + return 0; +}(); + +class Solution { +public: + long long splitArray(vector& nums) { + long long ans = 0; + for (int i = 0; i < nums.size(); ++i) { + ans += primes[i] ? nums[i] : -nums[i]; + } + return abs(ans); + } +}; \ No newline at end of file diff --git a/solution/3600-3699/3618.Split Array by Prime Indices/Solution.go b/solution/3600-3699/3618.Split Array by Prime Indices/Solution.go new file mode 100644 index 0000000000000..21930686a3115 --- /dev/null +++ b/solution/3600-3699/3618.Split Array by Prime Indices/Solution.go @@ -0,0 +1,29 @@ +const M = 100000 + 10 + +var primes [M]bool + +func init() { + for i := 0; i < M; i++ { + primes[i] = true + } + primes[0], primes[1] = false, false + + for i := 2; i < M; i++ { + if primes[i] { + for j := i + i; j < M; j += i { + primes[j] = false + } + } + } +} + +func splitArray(nums []int) (ans int64) { + for i, num := range nums { + if primes[i] { + ans += int64(num) + } else { + ans -= int64(num) + } + } + return max(ans, -ans) +} diff --git a/solution/3600-3699/3618.Split Array by Prime Indices/Solution.java b/solution/3600-3699/3618.Split Array by Prime Indices/Solution.java new file mode 100644 index 0000000000000..2226459f0a7e9 --- /dev/null +++ b/solution/3600-3699/3618.Split Array by Prime Indices/Solution.java @@ -0,0 +1,27 @@ +class Solution { + private static final int M = 100000 + 10; + private static boolean[] primes = new boolean[M]; + + static { + for (int i = 0; i < M; i++) { + primes[i] = true; + } + primes[0] = primes[1] = false; + + for (int i = 2; i < M; i++) { + if (primes[i]) { + for (int j = i + i; j < M; j += i) { + primes[j] = false; + } + } + } + } + + public long splitArray(int[] nums) { + long ans = 0; + for (int i = 0; i < nums.length; ++i) { + ans += primes[i] ? nums[i] : -nums[i]; + } + return Math.abs(ans); + } +} diff --git a/solution/3600-3699/3618.Split Array by Prime Indices/Solution.py b/solution/3600-3699/3618.Split Array by Prime Indices/Solution.py new file mode 100644 index 0000000000000..963f5741ecced --- /dev/null +++ b/solution/3600-3699/3618.Split Array by Prime Indices/Solution.py @@ -0,0 +1,12 @@ +m = 10**5 + 10 +primes = [True] * m +primes[0] = primes[1] = False +for i in range(2, m): + if primes[i]: + for j in range(i + i, m, i): + primes[j] = False + + +class Solution: + def splitArray(self, nums: List[int]) -> int: + return abs(sum(x if primes[i] else -x for i, x in enumerate(nums))) diff --git a/solution/3600-3699/3618.Split Array by Prime Indices/Solution.ts b/solution/3600-3699/3618.Split Array by Prime Indices/Solution.ts new file mode 100644 index 0000000000000..0c8838482c956 --- /dev/null +++ b/solution/3600-3699/3618.Split Array by Prime Indices/Solution.ts @@ -0,0 +1,22 @@ +const M = 100000 + 10; +const primes: boolean[] = Array(M).fill(true); + +const init = (() => { + primes[0] = primes[1] = false; + + for (let i = 2; i < M; i++) { + if (primes[i]) { + for (let j = i + i; j < M; j += i) { + primes[j] = false; + } + } + } +})(); + +function splitArray(nums: number[]): number { + let ans = 0; + for (let i = 0; i < nums.length; i++) { + ans += primes[i] ? nums[i] : -nums[i]; + } + return Math.abs(ans); +}