quotients (#320)

Author: hitonanode

utilities/quotients.hpp

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+#pragma once
+#include <algorithm>
+#include <vector>
+
+// Generate all quotients of n
+// return: n/1, n/2, ..., n
+// Complexity: O(sqrt(n))
+template <class T = long long> std::vector<T> get_quotients(T n) {
+    std::vector<T> res;
+    for (T x = 1;; ++x) {
+        if (x * x >= n) {
+            const int sz = res.size();
+            if (x * x == n) res.push_back(x);
+            res.reserve(res.size() + sz);
+            for (int i = sz - 1; i >= 0; --i) {
+                T tmp = n / res.at(i);
+                if (tmp < x) continue;
+                if (tmp == x and tmp * tmp == n) continue;
+                res.push_back(tmp);
+            }
+            return res;
+        } else {
+            res.push_back(x);
+        }
+    }
+}

utilities/quotients.md

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+---
+title: Quotients of integer （商列挙）
+documentation_of: ./quotients.hpp
+---
+
+正の整数 $n$ に対して $\lfloor n / k \rfloor$ （ $k$ は整数）の形で表される整数を昇順に列挙する．計算量は $O(\sqrt{n})$.
+
+## 使用方法
+
+```cpp
+long long n = 10;
+vector<long long> v = get_quotients(n);  // 1, 2, 3, 5, 10
+```
+
+## 問題例
+
+- [Library Checker: Enumerate Quotients](https://judge.yosupo.jp/problem/enumerate_quotients)

utilities/test/quotients.test.cpp

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+#define PROBLEM "https://judge.yosupo.jp/problem/enumerate_quotients"
+#include "../quotients.hpp"
+
+#include <iostream>
+using namespace std;
+
+int main() {
+    cin.tie(nullptr);
+    ios::sync_with_stdio(false);
+
+    long long N;
+    cin >> N;
+
+    auto ret = get_quotients(N);
+    cout << ret.size() << '\n';
+    for (auto x : ret) cout << x << ' ';
+    cout << '\n';
+}