test/yosupo_sum_of_totient.test.cpp

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• Last update: 2021-06-21 15:24:20+09:00
• Problem: https://judge.yosupo.jp/problem/sum_of_totient_function

Depends on

• modint(固定MOD) (util/modint.cpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/sum_of_totient_function"
#include <iostream>
#include <algorithm>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <numeric>
#include <bitset>
#include <cmath>

static const int MOD = 998244353;
using ll = long long;
using uint = unsigned;
using ull = unsigned long long;
using namespace std;

template<class T> constexpr T INF = ::numeric_limits<T>::max() / 32 * 15 + 208;

#include "../util/modint.cpp"

int main() {
    ll n;
    cin >> n;
    const ll k = 20000000; // 20000000
    vector<int> dp(k+1);
    iota(dp.begin(),dp.end(), 0);
    for (int i = 2; i <= k; ++i) {
        if(dp[i] != i) continue;
        for (int j = i; j <= k; j += i) {
            dp[j] = dp[j]/i*(i-1);
        }
    }
    vector<mint> a(k+1);
    for (int i = 0; i < k; ++i) {
        a[i+1] = a[i] + dp[i+1];
    }
    vector<mint> memo(n/k+1);
    vector<bool> calced(n/k+1);
    mint pp = mint(2).inv();
    auto rec = [&](ll x, auto &&f) -> mint {
        if(x <= k) return a[x];
        if(calced[n/x]) return memo[n/x];
        auto res = mint(x)*mint(x+1)*pp;
        for (ll i = 2; i <= x; ++i) {
            ll j = x/i, newi = (i > j ? x/j : i);
            res -= mint(newi-i+1)*f(x/i, f);
            i = newi;
        }
        return calced[n/x] = 1, memo[n/x] = res;
    };
    cout << rec(n, rec).val << "\n";
    return 0;
}

#line 1 "test/yosupo_sum_of_totient.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/sum_of_totient_function"
#include <iostream>
#include <algorithm>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <numeric>
#include <bitset>
#include <cmath>

static const int MOD = 998244353;
using ll = long long;
using uint = unsigned;
using ull = unsigned long long;
using namespace std;

template<class T> constexpr T INF = ::numeric_limits<T>::max() / 32 * 15 + 208;

#line 1 "util/modint.cpp"
template <uint M>
struct modint {
    uint val;
public:
    static modint raw(int v) { modint x; x.val = v; return x; }
    modint() : val(0) {}
    template <class T>
    modint(T v) { ll x = (ll)(v%(ll)(M)); if (x < 0) x += M; val = uint(x); }
    modint(bool v) { val = ((unsigned int)(v) % M); }
    modint& operator++() { val++; if (val == M) val = 0; return *this; }
    modint& operator--() { if (val == 0) val = M; val--; return *this; }
    modint operator++(int) { modint result = *this; ++*this; return result; }
    modint operator--(int) { modint result = *this; --*this; return result; }
    modint& operator+=(const modint& b) { val += b.val; if (val >= M) val -= M; return *this; }
    modint& operator-=(const modint& b) { val -= b.val; if (val >= M) val += M; return *this; }
    modint& operator*=(const modint& b) { ull z = val; z *= b.val; val = (uint)(z % M); return *this; }
    modint& operator/=(const modint& b) { return *this = *this * b.inv(); }
    modint operator+() const { return *this; }
    modint operator-() const { return modint() - *this; }
    modint pow(long long n) const { modint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; }
    modint inv() const { return pow(M-2); }
    friend modint operator+(const modint& a, const modint& b) { return modint(a) += b; }
    friend modint operator-(const modint& a, const modint& b) { return modint(a) -= b; }
    friend modint operator*(const modint& a, const modint& b) { return modint(a) *= b; }
    friend modint operator/(const modint& a, const modint& b) { return modint(a) /= b; }
    friend bool operator==(const modint& a, const modint& b) { return a.val == b.val; }
    friend bool operator!=(const modint& a, const modint& b) { return a.val != b.val; }
};
using mint = modint<MOD>;

/**
 * @brief modint(固定MOD)
 * @docs _md/modint.md
 */
#line 21 "test/yosupo_sum_of_totient.test.cpp"

int main() {
    ll n;
    cin >> n;
    const ll k = 20000000; // 20000000
    vector<int> dp(k+1);
    iota(dp.begin(),dp.end(), 0);
    for (int i = 2; i <= k; ++i) {
        if(dp[i] != i) continue;
        for (int j = i; j <= k; j += i) {
            dp[j] = dp[j]/i*(i-1);
        }
    }
    vector<mint> a(k+1);
    for (int i = 0; i < k; ++i) {
        a[i+1] = a[i] + dp[i+1];
    }
    vector<mint> memo(n/k+1);
    vector<bool> calced(n/k+1);
    mint pp = mint(2).inv();
    auto rec = [&](ll x, auto &&f) -> mint {
        if(x <= k) return a[x];
        if(calced[n/x]) return memo[n/x];
        auto res = mint(x)*mint(x+1)*pp;
        for (ll i = 2; i <= x; ++i) {
            ll j = x/i, newi = (i > j ? x/j : i);
            res -= mint(newi-i+1)*f(x/i, f);
            i = newi;
        }
        return calced[n/x] = 1, memo[n/x] = res;
    };
    cout << rec(n, rec).val << "\n";
    return 0;
}

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