math/linear_sieve.hpp

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• Last update: 2026-07-22 17:15:56+00:00
• Include: #include "math/linear_sieve.hpp"

Verified with

• test/math/aizu0009.test.cpp
• test/math/aizu2870.test.cpp
• test/math/yuki106.test.cpp

Code

#ifndef LINEAR_SIEVE_HPP
#define LINEAR_SIEVE_HPP

#include <cassert>
#include <map>
#include <vector>

struct linear_sieve {
    explicit linear_sieve(int n) : lpf(n + 1) {
        for (auto i = 2; i <= n; ++i) {
            if (lpf[i] == 0) {
                lpf[i] = i;
                primes.push_back(i);
            }
            for (auto p : primes) {
                if (lpf[i] < p || n < 1LL * i * p) {
                    break;
                }
                lpf[i * p] = p;
            }
        }
    }
    std::map<int, int> factorize(int x) const { // O(log x)
        assert(1 <= x && x < int(lpf.size()));
        std::map<int, int> f;
        while (1 < x) {
            ++f[lpf[x]];
            x /= lpf[x];
        }
        return f;
    }
    bool is_prime(int x) const { // O(1)
        assert(1 <= x && x < int(lpf.size()));
        return lpf[x] == x;
    }
    std::vector<int> lpf;
    std::vector<int> primes;
};

#endif // LINEAR_SIEVE_HPP

#line 1 "math/linear_sieve.hpp"



#include <cassert>
#include <map>
#include <vector>

struct linear_sieve {
    explicit linear_sieve(int n) : lpf(n + 1) {
        for (auto i = 2; i <= n; ++i) {
            if (lpf[i] == 0) {
                lpf[i] = i;
                primes.push_back(i);
            }
            for (auto p : primes) {
                if (lpf[i] < p || n < 1LL * i * p) {
                    break;
                }
                lpf[i * p] = p;
            }
        }
    }
    std::map<int, int> factorize(int x) const { // O(log x)
        assert(1 <= x && x < int(lpf.size()));
        std::map<int, int> f;
        while (1 < x) {
            ++f[lpf[x]];
            x /= lpf[x];
        }
        return f;
    }
    bool is_prime(int x) const { // O(1)
        assert(1 <= x && x < int(lpf.size()));
        return lpf[x] == x;
    }
    std::vector<int> lpf;
    std::vector<int> primes;
};

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