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feat: add solutions to lc problem: No.2941 (doocs#2005)
No.2941.Maximum GCD-Sum of a Subarray
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# [2941. Maximum GCD-Sum of a Subarray](https://leetcode.cn/problems/maximum-gcd-sum-of-a-subarray)
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[English Version](/solution/2900-2999/2941.Maximum%20GCD-Sum%20of%20a%20Subarray/README_EN.md)
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## 题目描述
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<!-- 这里写题目描述 -->
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<p>You are given an array of integers <code>nums</code> and an integer <code>k</code>.</p>
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<p>The <strong>gcd-sum</strong> of an array <code>a</code> is calculated as follows:</p>
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<ul>
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<li>Let <code>s</code> be the sum of all the elements of <code>a</code>.</li>
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<li>Let <code>g</code> be the <strong>greatest common divisor</strong> of all the elements of <code>a</code>.</li>
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<li>The gcd-sum of <code>a</code> is equal to <code>s * g</code>.</li>
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</ul>
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<p>Return <em>the <strong>maximum gcd-sum</strong> of a subarray of</em> <code>nums</code> <em>with at least</em> <code>k</code> <em>elements.</em></p>
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<p>&nbsp;</p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [2,1,4,4,4,2], k = 2
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<strong>Output:</strong> 48
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<strong>Explanation:</strong> We take the subarray [4,4,4], the gcd-sum of this array is 4 * (4 + 4 + 4) = 48.
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It can be shown that we can not select any other subarray with a gcd-sum greater than 48.</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [7,3,9,4], k = 1
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<strong>Output:</strong> 81
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<strong>Explanation:</strong> We take the subarray [9], the gcd-sum of this array is 9 * 9 = 81.
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It can be shown that we can not select any other subarray with a gcd-sum greater than 81.</pre>
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<p>&nbsp;</p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>n == nums.length</code></li>
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<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
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<li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>
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<li><code>1 &lt;= k &lt;= n</code></li>
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</ul>
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## 解法
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<!-- 这里可写通用的实现逻辑 -->
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<!-- tabs:start -->
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### **Python3**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```python
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class Solution:
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def maxGcdSum(self, nums: List[int], k: int) -> int:
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s = list(accumulate(nums, initial=0))
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f = []
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ans = 0
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for i, v in enumerate(nums):
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g = []
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for j, x in f:
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y = gcd(x, v)
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if not g or g[-1][1] != y:
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g.append((j, y))
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f = g
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f.append((i, v))
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for j, x in f:
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if i - j + 1 >= k:
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ans = max(ans, (s[i + 1] - s[j]) * x)
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return ans
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```
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### **Java**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```java
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class Solution {
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public long maxGcdSum(int[] nums, int k) {
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int n = nums.length;
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long[] s = new long[n + 1];
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for (int i = 1; i <= n; ++i) {
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s[i] = s[i - 1] + nums[i - 1];
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}
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List<int[]> f = new ArrayList<>();
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long ans = 0;
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for (int i = 0; i < n; ++i) {
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List<int[]> g = new ArrayList<>();
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for (var e : f) {
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int j = e[0], x = e[1];
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int y = gcd(x, nums[i]);
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if (g.isEmpty() || g.get(g.size() - 1)[1] != y) {
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g.add(new int[] {j, y});
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}
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}
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f = g;
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f.add(new int[] {i, nums[i]});
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for (var e : f) {
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int j = e[0], x = e[1];
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if (i - j + 1 >= k) {
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ans = Math.max(ans, (s[i + 1] - s[j]) * x);
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}
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}
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}
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return ans;
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}
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private int gcd(int a, int b) {
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return b == 0 ? a : gcd(b, a % b);
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}
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}
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```
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### **C++**
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```cpp
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class Solution {
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public:
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long long maxGcdSum(vector<int>& nums, int k) {
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int n = nums.size();
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long long s[n + 1];
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s[0] = 0;
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for (int i = 1; i <= n; ++i) {
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s[i] = s[i - 1] + nums[i - 1];
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}
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vector<pair<int, int>> f;
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long long ans = 0;
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for (int i = 0; i < n; ++i) {
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vector<pair<int, int>> g;
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for (auto [j, x] : f) {
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int y = gcd(x, nums[i]);
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if (g.empt() || g.back().second != y) {
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g.emplace_back(j, y);
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}
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}
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f = move(g);
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f.emplace_back(i, nums[i]);
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for (auto [j, x] : f) {
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if (i - j + 1 >= k) {
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ans = max(ans, (s[i + 1] - s[j]) * x);
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}
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}
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}
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return ans;
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}
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};
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```
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### **Go**
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```go
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func maxGcdSum(nums []int, k int) int64 {
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n := len(nums)
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s := make([]int64, n+1)
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s[0] = 0
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for i, x := range nums {
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s[i+1] = s[i] + int64(x)
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}
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type pair [2]int
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var f []pair
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var ans int64
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for i := 0; i < n; i++ {
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var g []pair
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for _, p := range f {
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j, x := p[0], p[1]
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y := int(gcd(int(x), nums[i]))
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if len(g) == 0 || g[len(g)-1][1] != y {
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g = append(g, pair{j, y})
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}
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}
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f = g
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f = append(f, pair{i, nums[i]})
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for _, p := range f {
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j, x := p[0], p[1]
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if i-j+1 >= k {
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ans = max(ans, (s[i+1]-s[j])*int64(x))
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}
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}
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}
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return ans
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}
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func gcd(a, b int) int {
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if b == 0 {
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return a
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}
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return gcd(b, a%b)
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}
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```
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### **TypeScript**
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```ts
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function maxGcdSum(nums: number[], k: number): number {
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const n: number = nums.length;
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const s: number[] = Array(n + 1).fill(0);
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for (let i = 1; i <= n; i++) {
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s[i] = s[i - 1] + nums[i - 1];
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}
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let f: [number, number][] = [];
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let ans: number = 0;
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for (let i = 0; i < n; ++i) {
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const g: [number, number][] = [];
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for (const [j, x] of f) {
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const y: number = gcd(x, nums[i]);
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if (g.length === 0 || g.at(-1)[1] !== y) {
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g.push([j, y]);
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}
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}
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f = g;
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f.push([i, nums[i]]);
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for (const [j, x] of f) {
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if (i - j + 1 >= k) {
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ans = Math.max(ans, (s[i + 1] - s[j]) * x);
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}
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}
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}
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return ans;
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}
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function gcd(a: number, b: number): number {
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return b === 0 ? a : gcd(b, a % b);
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}
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```
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### **TypeScript**
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```ts
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function maxGcdSum(nums: number[], k: number): number {
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const n: number = nums.length;
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const s: number[] = Array(n + 1).fill(0);
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for (let i = 1; i <= n; i++) {
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s[i] = s[i - 1] + nums[i - 1];
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}
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let f: [number, number][] = [];
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let ans: number = 0;
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for (let i = 0; i < n; ++i) {
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const g: [number, number][] = [];
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for (const [j, x] of f) {
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const y: number = gcd(x, nums[i]);
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if (g.length === 0 || g.at(-1)[1] !== y) {
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g.push([j, y]);
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}
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}
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f = g;
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f.push([i, nums[i]]);
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for (const [j, x] of f) {
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if (i - j + 1 >= k) {
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ans = Math.max(ans, (s[i + 1] - s[j]) * x);
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}
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}
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}
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return ans;
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}
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function gcd(a: number, b: number): number {
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return b === 0 ? a : gcd(b, a % b);
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}
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```
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### **...**
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```
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```
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<!-- tabs:end -->

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