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Commit fd9dbb2

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feat: add solutions to lc problem: No.1714
No.1714.Sum Of Special Evenly-Spaced Elements In Array
1 parent 651e031 commit fd9dbb2

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8 files changed

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-4
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8 files changed

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‎solution/1700-1799/1714.Sum Of Special Evenly-Spaced Elements In Array/README.md‎

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@@ -47,22 +47,180 @@
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<!-- 这里可写通用的实现逻辑 -->
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**方法一:分块**
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这道题是一道比较典型的分块题目,对于步长较大的查询,我们可以直接暴力求解;对于步长较小的查询,我们可以预处理出每个位置的后缀和,然后直接查询。
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本题中,我们将步长较大的查询的步长限制为 $\sqrt{n},ドル这样就可以保证每个查询的时间复杂度为 $O(\sqrt{n})$。
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我们定义一个二维数组 $suf,ドル其中 $suf[i][j]$ be 表示从位置 $j$ 开始,步长为 $i$ 的后缀和。那么对于每个查询 $[x, y],ドル我们可以分为两种情况:
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- 如果 $y \le \sqrt{n},ドル那么我们可以直接查询 $suf[y][x]$;
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- 如果 $y \gt \sqrt{n},ドル那么我们可以直接暴力求解。
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时间复杂度 $O((n + m) \times \sqrt{n}),ドル空间复杂度 $O(n \times \sqrt{n})$。其中 $n$ 是数组的长度,而 $m$ 是查询的个数。
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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 solve(self, nums: List[int], queries: List[List[int]]) -> List[int]:
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mod = 10**9 + 7
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n = len(nums)
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m = int(sqrt(n))
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suf = [[0] * (n + 1) for _ in range(m + 1)]
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for i in range(1, m + 1):
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for j in range(n - 1, -1, -1):
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suf[i][j] = suf[i][min(n, j + i)] + nums[j]
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ans = []
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for x, y in queries:
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if y <= m:
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ans.append(suf[y][x] % mod)
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else:
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ans.append(sum(nums[x::y]) % mod)
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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 int[] solve(int[] nums, int[][] queries) {
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int n = nums.length;
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int m = (int) Math.sqrt(n);
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final int mod = (int) 1e9 + 7;
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int[][] suf = new int[m + 1][n + 1];
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for (int i = 1; i <= m; ++i) {
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for (int j = n - 1; j >= 0; --j) {
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suf[i][j] = (suf[i][Math.min(n, j + i)] + nums[j]) % mod;
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}
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}
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int k = queries.length;
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int[] ans = new int[k];
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for (int i = 0; i < k; ++i) {
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int x = queries[i][0];
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int y = queries[i][1];
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if (y <= m) {
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ans[i] = suf[y][x];
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} else {
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int s = 0;
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for (int j = x; j < n; j += y) {
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s = (s + nums[j]) % mod;
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}
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ans[i] = s;
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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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### **C++**
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```cpp
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class Solution {
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public:
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vector<int> solve(vector<int>& nums, vector<vector<int>>& queries) {
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int n = nums.size();
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int m = (int) sqrt(n);
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const int mod = 1e9 + 7;
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int suf[m + 1][n + 1];
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memset(suf, 0, sizeof(suf));
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for (int i = 1; i <= m; ++i) {
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for (int j = n - 1; ~j; --j) {
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suf[i][j] = (suf[i][min(n, j + i)] + nums[j]) % mod;
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}
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}
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vector<int> ans;
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for (auto& q : queries) {
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int x = q[0], y = q[1];
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if (y <= m) {
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ans.push_back(suf[y][x]);
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} else {
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int s = 0;
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for (int i = x; i < n; i += y) {
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s = (s + nums[i]) % mod;
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}
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ans.push_back(s);
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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 solve(nums []int, queries [][]int) (ans []int) {
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n := len(nums)
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m := int(math.Sqrt(float64(n)))
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const mod int = 1e9 + 7
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suf := make([][]int, m+1)
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for i := range suf {
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suf[i] = make([]int, n+1)
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for j := n - 1; j >= 0; j-- {
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suf[i][j] = (suf[i][min(n, j+i)] + nums[j]) % mod
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}
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}
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for _, q := range queries {
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x, y := q[0], q[1]
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if y <= m {
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ans = append(ans, suf[y][x])
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} else {
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s := 0
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for i := x; i < n; i += y {
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s = (s + nums[i]) % mod
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}
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ans = append(ans, s)
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}
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}
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return
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}
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func min(a, b int) int {
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if a < b {
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return a
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}
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return b
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}
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```
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### **TypeScript**
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```ts
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function solve(nums: number[], queries: number[][]): number[] {
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const n = nums.length;
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const m = Math.floor(Math.sqrt(n));
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const mod = 10 ** 9 + 7;
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const suf: number[][] = Array(m + 1)
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.fill(0)
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.map(() => Array(n + 1).fill(0));
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for (let i = 1; i <= m; ++i) {
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for (let j = n - 1; j >= 0; --j) {
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suf[i][j] = (suf[i][Math.min(n, j + i)] + nums[j]) % mod;
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}
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}
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const ans: number[] = [];
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for (const [x, y] of queries) {
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if (y <= m) {
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ans.push(suf[y][x]);
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} else {
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let s = 0;
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for (let i = x; i < n; i += y) {
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s = (s + nums[i]) % mod;
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}
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ans.push(s);
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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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### **...**

‎solution/1700-1799/1714.Sum Of Special Evenly-Spaced Elements In Array/README_EN.md‎

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### **Python3**
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```python
51-
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class Solution:
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def solve(self, nums: List[int], queries: List[List[int]]) -> List[int]:
53+
mod = 10**9 + 7
54+
n = len(nums)
55+
m = int(sqrt(n))
56+
suf = [[0] * (n + 1) for _ in range(m + 1)]
57+
for i in range(1, m + 1):
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for j in range(n - 1, -1, -1):
59+
suf[i][j] = suf[i][min(n, j + i)] + nums[j]
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ans = []
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for x, y in queries:
62+
if y <= m:
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ans.append(suf[y][x] % mod)
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else:
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ans.append(sum(nums[x::y]) % mod)
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return ans
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```
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### **Java**
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```java
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class Solution {
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public int[] solve(int[] nums, int[][] queries) {
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int n = nums.length;
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int m = (int) Math.sqrt(n);
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final int mod = (int) 1e9 + 7;
77+
int[][] suf = new int[m + 1][n + 1];
78+
for (int i = 1; i <= m; ++i) {
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for (int j = n - 1; j >= 0; --j) {
80+
suf[i][j] = (suf[i][Math.min(n, j + i)] + nums[j]) % mod;
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}
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}
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int k = queries.length;
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int[] ans = new int[k];
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for (int i = 0; i < k; ++i) {
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int x = queries[i][0];
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int y = queries[i][1];
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if (y <= m) {
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ans[i] = suf[y][x];
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} else {
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int s = 0;
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for (int j = x; j < n; j += y) {
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s = (s + nums[j]) % mod;
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}
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ans[i] = s;
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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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### **C++**
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```cpp
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class Solution {
107+
public:
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vector<int> solve(vector<int>& nums, vector<vector<int>>& queries) {
109+
int n = nums.size();
110+
int m = (int) sqrt(n);
111+
const int mod = 1e9 + 7;
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int suf[m + 1][n + 1];
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memset(suf, 0, sizeof(suf));
114+
for (int i = 1; i <= m; ++i) {
115+
for (int j = n - 1; ~j; --j) {
116+
suf[i][j] = (suf[i][min(n, j + i)] + nums[j]) % mod;
117+
}
118+
}
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vector<int> ans;
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for (auto& q : queries) {
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int x = q[0], y = q[1];
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if (y <= m) {
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ans.push_back(suf[y][x]);
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} else {
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int s = 0;
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for (int i = x; i < n; i += y) {
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s = (s + nums[i]) % mod;
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}
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ans.push_back(s);
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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 solve(nums []int, queries [][]int) (ans []int) {
141+
n := len(nums)
142+
m := int(math.Sqrt(float64(n)))
143+
const mod int = 1e9 + 7
144+
suf := make([][]int, m+1)
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for i := range suf {
146+
suf[i] = make([]int, n+1)
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for j := n - 1; j >= 0; j-- {
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suf[i][j] = (suf[i][min(n, j+i)] + nums[j]) % mod
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}
150+
}
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for _, q := range queries {
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x, y := q[0], q[1]
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if y <= m {
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ans = append(ans, suf[y][x])
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} else {
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s := 0
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for i := x; i < n; i += y {
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s = (s + nums[i]) % mod
159+
}
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ans = append(ans, s)
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}
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}
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return
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}
165+
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func min(a, b int) int {
167+
if a < b {
168+
return a
169+
}
170+
return b
171+
}
172+
```
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### **TypeScript**
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```ts
177+
function solve(nums: number[], queries: number[][]): number[] {
178+
const n = nums.length;
179+
const m = Math.floor(Math.sqrt(n));
180+
const mod = 10 ** 9 + 7;
181+
const suf: number[][] = Array(m + 1)
182+
.fill(0)
183+
.map(() => Array(n + 1).fill(0));
184+
for (let i = 1; i <= m; ++i) {
185+
for (let j = n - 1; j >= 0; --j) {
186+
suf[i][j] = (suf[i][Math.min(n, j + i)] + nums[j]) % mod;
187+
}
188+
}
189+
const ans: number[] = [];
190+
for (const [x, y] of queries) {
191+
if (y <= m) {
192+
ans.push(suf[y][x]);
193+
} else {
194+
let s = 0;
195+
for (let i = x; i < n; i += y) {
196+
s = (s + nums[i]) % mod;
197+
}
198+
ans.push(s);
199+
}
200+
}
201+
return ans;
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}
58203
```
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### **...**
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@@ -0,0 +1,29 @@
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class Solution {
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public:
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vector<int> solve(vector<int>& nums, vector<vector<int>>& queries) {
4+
int n = nums.size();
5+
int m = (int) sqrt(n);
6+
const int mod = 1e9 + 7;
7+
int suf[m + 1][n + 1];
8+
memset(suf, 0, sizeof(suf));
9+
for (int i = 1; i <= m; ++i) {
10+
for (int j = n - 1; ~j; --j) {
11+
suf[i][j] = (suf[i][min(n, j + i)] + nums[j]) % mod;
12+
}
13+
}
14+
vector<int> ans;
15+
for (auto& q : queries) {
16+
int x = q[0], y = q[1];
17+
if (y <= m) {
18+
ans.push_back(suf[y][x]);
19+
} else {
20+
int s = 0;
21+
for (int i = x; i < n; i += y) {
22+
s = (s + nums[i]) % mod;
23+
}
24+
ans.push_back(s);
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}
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}
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return ans;
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}
29+
};

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