結果
| 問題 | No.732 3PrimeCounting |
| ユーザー |
 st1vdy
|
| 提出日時 | 2021-08-11 11:22:10 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 101 ms / 3,000 ms |
| コード長 | 8,288 bytes |
| コンパイル時間 | 2,711 ms |
| コンパイル使用メモリ | 213,776 KB |
| 最終ジャッジ日時 | 2025-01-23 17:30:24 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 89 |
ソースコード
#define _SILENCE_CXX17_C_HEADER_DEPRECATION_WARNING#define _CRT_SECURE_NO_WARNINGS#include <bits/stdc++.h>using namespace std;namespace FFT {typedef double dbl;struct num {dbl x, y;num() { x = y = 0; }num(dbl x, dbl y) : x(x), y(y) { }};inline num operator+(num a, num b) { return num(a.x + b.x, a.y + b.y); }inline num operator-(num a, num b) { return num(a.x - b.x, a.y - b.y); }inline num operator*(num a, num b) { return num(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x); }inline num conj(num a) { return num(a.x, -a.y); }int base = 1;vector<num> roots = { {0, 0}, {1, 0} };vector<int> rev = { 0, 1 };const dbl PI = acosl(-1.0);void ensure_base(int nbase) {if (nbase <= base) {return;}rev.resize(1 << nbase);for (int i = 0; i < (1 << nbase); i++) {rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));}roots.resize(1 << nbase);while (base < nbase) {dbl angle = 2 * PI / (1 << (base + 1));for (int i = 1 << (base - 1); i < (1 << base); i++) {roots[i << 1] = roots[i];dbl angle_i = angle * (2 * i + 1 - (1 << base));roots[(i << 1) + 1] = num(cos(angle_i), sin(angle_i));}base++;}}void fft(vector<num>& a, int n = -1) {if (n == -1) {n = a.size();}assert((n & (n - 1)) == 0);int zeros = __builtin_ctz(n);ensure_base(zeros);int shift = base - zeros;for (int i = 0; i < n; i++) {if (i < (rev[i] >> shift)) {swap(a[i], a[rev[i] >> shift]);}}for (int k = 1; k < n; k <<= 1) {for (int i = 0; i < n; i += 2 * k) {for (int j = 0; j < k; j++) {num z = a[i + j + k] * roots[j + k];a[i + j + k] = a[i + j] - z;a[i + j] = a[i + j] + z;}}}}vector<num> fa, fb;vector<int> multiply(vector<int>& a, vector<int>& b) {int need = a.size() + b.size() - 1;int nbase = 1;while ((1 << nbase) < need) nbase++;ensure_base(nbase);int sz = 1 << nbase;if (sz > (int)fa.size()) {fa.resize(sz);}for (int i = 0; i < sz; i++) {int x = (i < (int)a.size() ? a[i] : 0);int y = (i < (int)b.size() ? b[i] : 0);fa[i] = num(x, y);}fft(fa, sz);num r(0, -0.25 / (sz >> 1));for (int i = 0; i <= (sz >> 1); i++) {int j = (sz - i) & (sz - 1);num z = (fa[j] * fa[j] - conj(fa[i] * fa[i])) * r;if (i != j) {fa[j] = (fa[i] * fa[i] - conj(fa[j] * fa[j])) * r;}fa[i] = z;}for (int i = 0; i < (sz >> 1); i++) {num A0 = (fa[i] + fa[i + (sz >> 1)]) * num(0.5, 0);num A1 = (fa[i] - fa[i + (sz >> 1)]) * num(0.5, 0) * roots[(sz >> 1) + i];fa[i] = A0 + A1 * num(0, 1);}fft(fa, sz >> 1);vector<int> res(need);for (int i = 0; i < need; i++) {if (i % 2 == 0) {res[i] = fa[i >> 1].x + 0.5;} else {res[i] = fa[i >> 1].y + 0.5;}}return res;}vector<long long> square(const vector<int>& a) {int need = a.size() + a.size() - 1;int nbase = 1;while ((1 << nbase) < need) nbase++;ensure_base(nbase);int sz = 1 << nbase;if ((sz >> 1) > (int)fa.size()) {fa.resize(sz >> 1);}for (int i = 0; i < (sz >> 1); i++) {int x = (2 * i < (int)a.size() ? a[2 * i] : 0);int y = (2 * i + 1 < (int)a.size() ? a[2 * i + 1] : 0);fa[i] = num(x, y);}fft(fa, sz >> 1);num r(1.0 / (sz >> 1), 0.0);for (int i = 0; i <= (sz >> 2); i++) {int j = ((sz >> 1) - i) & ((sz >> 1) - 1);num fe = (fa[i] + conj(fa[j])) * num(0.5, 0);num fo = (fa[i] - conj(fa[j])) * num(0, -0.5);num aux = fe * fe + fo * fo * roots[(sz >> 1) + i] * roots[(sz >> 1) + i];num tmp = fe * fo;fa[i] = r * (conj(aux) + num(0, 2) * conj(tmp));fa[j] = r * (aux + num(0, 2) * tmp);}fft(fa, sz >> 1);vector<long long> res(need);for (int i = 0; i < need; i++) {if (i % 2 == 0) {res[i] = fa[i >> 1].x + 0.5;} else {res[i] = fa[i >> 1].y + 0.5;}}return res;}vector<int> multiply_mod(vector<int>& a, vector<int>& b, int m, int eq = 0) {int need = a.size() + b.size() - 1;int nbase = 0;while ((1 << nbase) < need) nbase++;ensure_base(nbase);int sz = 1 << nbase;if (sz > (int)fa.size()) {fa.resize(sz);}for (int i = 0; i < (int)a.size(); i++) {int x = (a[i] % m + m) % m;fa[i] = num(x & ((1 << 15) - 1), x >> 15);}fill(fa.begin() + a.size(), fa.begin() + sz, num{ 0, 0 });fft(fa, sz);if (sz > (int) fb.size()) {fb.resize(sz);}if (eq) {copy(fa.begin(), fa.begin() + sz, fb.begin());} else {for (int i = 0; i < (int)b.size(); i++) {int x = (b[i] % m + m) % m;fb[i] = num(x & ((1 << 15) - 1), x >> 15);}fill(fb.begin() + b.size(), fb.begin() + sz, num{ 0, 0 });fft(fb, sz);}dbl ratio = 0.25 / sz;num r2(0, -1);num r3(ratio, 0);num r4(0, -ratio);num r5(0, 1);for (int i = 0; i <= (sz >> 1); i++) {int j = (sz - i) & (sz - 1);num a1 = (fa[i] + conj(fa[j]));num a2 = (fa[i] - conj(fa[j])) * r2;num b1 = (fb[i] + conj(fb[j])) * r3;num b2 = (fb[i] - conj(fb[j])) * r4;if (i != j) {num c1 = (fa[j] + conj(fa[i]));num c2 = (fa[j] - conj(fa[i])) * r2;num d1 = (fb[j] + conj(fb[i])) * r3;num d2 = (fb[j] - conj(fb[i])) * r4;fa[i] = c1 * d1 + c2 * d2 * r5;fb[i] = c1 * d2 + c2 * d1;}fa[j] = a1 * b1 + a2 * b2 * r5;fb[j] = a1 * b2 + a2 * b1;}fft(fa, sz);fft(fb, sz);vector<int> res(need);for (int i = 0; i < need; i++) {long long aa = fa[i].x + 0.5;long long bb = fb[i].x + 0.5;long long cc = fa[i].y + 0.5;res[i] = (aa + ((bb % m) << 15) + ((cc % m) << 30)) % m;}return res;}vector<int> square_mod(vector<int>& a, int m) {return multiply_mod(a, a, m, 1);}};vector<bool> isPrime; // true 表示非素数 false 表示是素数vector<int> prime; // 保存素数int sieve(int n) {isPrime.resize(n + 1, false);isPrime[0] = isPrime[1] = true;for (int i = 2; i <= n; i++) {if (!isPrime[i]) prime.emplace_back(i);for (int j = 0; j < (int)prime.size() && prime[j] * i <= n; ++j) {isPrime[prime[j] * i] = true;if (!(i % prime[j])) break;}}return (int)prime.size();}int main() {ios::sync_with_stdio(false);cin.tie(nullptr);cout.tie(nullptr);int n;cin >> n;sieve(3 * n + 1);vector<int> a(n + 1, 0), b(n + 1, 0), c(2 * n + 1, 0);for (int i = 2; i <= n; i++) {if (!isPrime[i]) {a[i] = b[i] = 1;c[i * 2] = 1;}}a = FFT::multiply(a, b);a = FFT::multiply(a, b);c = FFT::multiply(c, b);long long res = 0;for (int i = 2; i <= 3 * n; i++) {if (!isPrime[i]) {res += (a[i] - c[i] * 3) / 6;//cout << (a[i] - c[i] * 3) / 6 << " " << i << "\n";}}cout << res;return 0;}