nt/factorize.hpp

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Last update: 2024-11-09 00:49:07+00:00
Include: #include "nt/factorize.hpp"

Depends on

Code

#pragma once
#include "prelude.hpp"
#include "bit/ctz.hpp"

template <class T>
vector<pair<T, int>> factorize(T n) {
  assert(n >= 1);
  vector<pair<T, int>> ans;
  int t = ctz(n);
  if (t) ans.emplace_back(2, t), n >>= t;
  for (T d = 3; d * d <= n; d += 2) if (n % d == 0) {
    int k = 0;
    while (n % d == 0) n /= d, k++;
    ans.emplace_back(d, k);
  }
  if (n != 1) ans.emplace_back(n, 1);
  return ans;
}

#line 2 "prelude.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using vll = vector<ll>;
using vvll = vector<vector<ll>>;
using vc = vector<char>;
#define rep2(i, m, n) for (auto i = (m); i < (n); i++)
#define rep(i, n) rep2(i, 0, n)
#define repr2(i, m, n) for (auto i = (n); i-- > (m);)
#define repr(i, n) repr2(i, 0, n)
#define all(x) begin(x), end(x)
auto ndvec(int n, auto e) { return vector(n, e); }
auto ndvec(int n, auto ...e) { return vector(n, ndvec(e...)); }
auto comp_key(auto&& f) { return [&](auto&& a, auto&& b) { return f(a) < f(b); }; }
auto& max(const auto& a, const auto& b) { return a < b ? b : a; }
auto& min(const auto& a, const auto& b) { return b < a ? b : a; }
#if __cpp_lib_ranges
namespace R = std::ranges;
namespace V = std::views;
#endif
#line 3 "bit/ctz.hpp"

#pragma GCC target("bmi")

template <class T>
int ctz(T x) {
  if (!x) return sizeof(T) * 8;
  if constexpr (sizeof(T) <= sizeof(unsigned)) {
    return __builtin_ctz((unsigned)x);
  } else if constexpr (sizeof(T) <= sizeof(unsigned long long)) {
    return __builtin_ctzll((unsigned long long)x);
  } else if constexpr (sizeof(T) <= sizeof(unsigned long long) * 2) {
    unsigned long long y = x;
    return y ? ctz(y)
             : sizeof(y) * 8 + ctz((unsigned long long)(x >> sizeof(y) * 8));
  }
}
#line 4 "nt/factorize.hpp"

template <class T>
vector<pair<T, int>> factorize(T n) {
  assert(n >= 1);
  vector<pair<T, int>> ans;
  int t = ctz(n);
  if (t) ans.emplace_back(2, t), n >>= t;
  for (T d = 3; d * d <= n; d += 2) if (n % d == 0) {
    int k = 0;
    while (n % d == 0) n /= d, k++;
    ans.emplace_back(d, k);
  }
  if (n != 1) ans.emplace_back(n, 1);
  return ans;
}