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ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#767043 | #9225. Fibonacci Fusion | Misuki | TL | 310ms | 691076kb | C++20 | 16.4kb | 2024-11-20 19:40:04 | 2024-11-20 19:40:09 |
Judging History
answer
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <variant>
#include <bit>
#include <compare>
#include <concepts>
#include <numbers>
#include <ranges>
#include <span>
//#define int ll
#define INT128_MAX (__int128)(((unsigned __int128) 1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1)
#define INT128_MIN (-INT128_MAX - 1)
#define clock chrono::steady_clock::now().time_since_epoch().count()
using namespace std;
template<class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2> pr) {
return os << pr.first << ' ' << pr.second;
}
template<class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N> &arr) {
for(size_t i = 0; T x : arr) {
os << x;
if (++i != N) os << ' ';
}
return os;
}
template<class T>
ostream& operator<<(ostream& os, const vector<T> &vec) {
for(size_t i = 0; T x : vec) {
os << x;
if (++i != size(vec)) os << ' ';
}
return os;
}
template<class T>
ostream& operator<<(ostream& os, const set<T> &s) {
for(size_t i = 0; T x : s) {
os << x;
if (++i != size(s)) os << ' ';
}
return os;
}
template<class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2> &m) {
for(size_t i = 0; pair<T1, T2> x : m) {
os << x;
if (++i != size(m)) os << ' ';
}
return os;
}
#ifdef DEBUG
#define dbg(...) cerr << '(', _do(#__VA_ARGS__), cerr << ") = ", _do2(__VA_ARGS__)
template<typename T> void _do(T &&x) { cerr << x; }
template<typename T, typename ...S> void _do(T &&x, S&&...y) { cerr << x << ", "; _do(y...); }
template<typename T> void _do2(T &&x) { cerr << x << endl; }
template<typename T, typename ...S> void _do2(T &&x, S&&...y) { cerr << x << ", "; _do2(y...); }
#else
#define dbg(...)
#endif
using ll = long long;
using ull = unsigned long long;
using ldb = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
//#define double ldb
template<typename T> using min_heap = priority_queue<T, vector<T>, greater<T>>;
template<typename T> using max_heap = priority_queue<T>;
template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, class OP = plus<T>>
void pSum(rng &&v) {
if (!v.empty())
for(T p = v[0]; T &x : v | views::drop(1))
x = p = OP()(p, x);
}
template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, class OP>
void pSum(rng &&v, OP op) {
if (!v.empty())
for(T p = v[0]; T &x : v | views::drop(1))
x = p = op(p, x);
}
template<ranges::forward_range rng>
void Unique(rng &v) {
ranges::sort(v);
v.resize(unique(v.begin(), v.end()) - v.begin());
}
template<ranges::random_access_range rng>
rng invPerm(rng p) {
rng ret = p;
for(int i = 0; i < ssize(p); i++)
ret[p[i]] = i;
return ret;
}
template<ranges::random_access_range rng, ranges::random_access_range rng2>
rng Permute(rng v, rng2 p) {
rng ret = v;
for(int i = 0; i < ssize(p); i++)
ret[p[i]] = v[i];
return ret;
}
template<bool directed>
vector<vector<int>> readGraph(int n, int m, int base) {
vector<vector<int>> g(n);
for(int i = 0; i < m; i++) {
int u, v; cin >> u >> v;
u -= base, v -= base;
g[u].emplace_back(v);
if constexpr (!directed)
g[v].emplace_back(u);
}
return g;
}
template<class T>
void setBit(T &msk, int bit, bool x) {
msk = (msk & ~(T(1) << bit)) | (T(x) << bit);
}
template<class T> void flipBit(T &msk, int bit) { msk ^= T(1) << bit; }
template<class T> bool getBit(T msk, int bit) { return msk >> bit & T(1); }
template<class T>
T floorDiv(T a, T b) {
if (b < 0) a *= -1, b *= -1;
return a >= 0 ? a / b : (a - b + 1) / b;
}
template<class T>
T ceilDiv(T a, T b) {
if (b < 0) a *= -1, b *= -1;
return a >= 0 ? (a + b - 1) / b : a / b;
}
template<class T> bool chmin(T &a, T b) { return a > b ? a = b, 1 : 0; }
template<class T> bool chmax(T &a, T b) { return a < b ? a = b, 1 : 0; }
#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
typedef vector<int> vi;
//reference: https://github.com/NyaanNyaan/library/blob/master/modint/montgomery-modint.hpp#L10
//note: mod should be a prime less than 2^30.
template<uint32_t mod>
struct MontgomeryModInt {
using mint = MontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 res = 1, base = mod;
for(i32 i = 0; i < 31; i++)
res *= base, base *= base;
return -res;
}
static constexpr u32 get_mod() {
return mod;
}
static constexpr u32 n2 = -u64(mod) % mod; //2^64 % mod
static constexpr u32 r = get_r(); //-P^{-1} % 2^32
u32 a;
static u32 reduce(const u64 &b) {
return (b + u64(u32(b) * r) * mod) >> 32;
}
static u32 transform(const u64 &b) {
return reduce(u64(b) * n2);
}
MontgomeryModInt() : a(0) {}
MontgomeryModInt(const int64_t &b)
: a(transform(b % mod + mod)) {}
mint pow(u64 k) const {
mint res(1), base(*this);
while(k) {
if (k & 1)
res *= base;
base *= base, k >>= 1;
}
return res;
}
mint inverse() const { return (*this).pow(mod - 2); }
u32 get() const {
u32 res = reduce(a);
return res >= mod ? res - mod : res;
}
mint& operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
mint& operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
mint& operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
mint& operator/=(const mint &b) {
a = reduce(u64(a) * b.inverse().a);
return *this;
}
mint operator-() { return mint() - mint(*this); }
bool operator==(mint b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
bool operator!=(mint b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
friend mint operator+(mint c, mint d) { return c += d; }
friend mint operator-(mint c, mint d) { return c -= d; }
friend mint operator*(mint c, mint d) { return c *= d; }
friend mint operator/(mint c, mint d) { return c /= d; }
friend ostream& operator<<(ostream& os, const mint& b) {
return os << b.get();
}
friend istream& operator>>(istream& is, mint& b) {
int64_t val;
is >> val;
b = mint(val);
return is;
}
};
using mint = MontgomeryModInt<998244353>;
//reference: https://judge.yosupo.jp/submission/69896
//remark: MOD = 2^K * C + 1, R is a primitive root modulo MOD
//remark: a.size() <= 2^K must be satisfied
//some common modulo: 998244353 = 2^23 * 119 + 1, R = 3
// 469762049 = 2^26 * 7 + 1, R = 3
// 1224736769 = 2^24 * 73 + 1, R = 3
template<int32_t k = 23, int32_t c = 119, int32_t r = 3, class Mint = MontgomeryModInt<998244353>>
struct NTT {
using u32 = uint32_t;
static constexpr u32 mod = (1 << k) * c + 1;
static constexpr u32 get_mod() { return mod; }
static void ntt(vector<Mint> &a, bool inverse) {
static array<Mint, 30> w, w_inv;
if (w[0] == 0) {
Mint root = 2;
while(root.pow((mod - 1) / 2) == 1) root += 1;
for(int i = 0; i < 30; i++)
w[i] = -(root.pow((mod - 1) >> (i + 2))), w_inv[i] = 1 / w[i];
}
int n = ssize(a);
if (not inverse) {
for(int m = n; m >>= 1; ) {
Mint ww = 1;
for(int s = 0, l = 0; s < n; s += 2 * m) {
for(int i = s, j = s + m; i < s + m; i++, j++) {
Mint x = a[i], y = a[j] * ww;
a[i] = x + y, a[j] = x - y;
}
ww *= w[__builtin_ctz(++l)];
}
}
} else {
for(int m = 1; m < n; m *= 2) {
Mint ww = 1;
for(int s = 0, l = 0; s < n; s += 2 * m) {
for(int i = s, j = s + m; i < s + m; i++, j++) {
Mint x = a[i], y = a[j];
a[i] = x + y, a[j] = (x - y) * ww;
}
ww *= w_inv[__builtin_ctz(++l)];
}
}
Mint inv = 1 / Mint(n);
for(Mint &x : a) x *= inv;
}
}
static vector<Mint> conv(vector<Mint> a, vector<Mint> b) {
int sz = ssize(a) + ssize(b) - 1;
int n = bit_ceil((u32)sz);
a.resize(n, 0);
ntt(a, false);
b.resize(n, 0);
ntt(b, false);
for(int i = 0; i < n; i++)
a[i] *= b[i];
ntt(a, true);
a.resize(sz);
return a;
}
};
//#include<modint/MontgomeryModInt.cpp>
//#include<poly/NTTmint.cpp>
template<bool fast_mul = true>
struct bigint {
int sgn;
vector<int> val;
static constexpr int LOG = fast_mul ? 1 : 9;
static constexpr int W = fast_mul ? 10 : 1'000'000'000;
bigint(string s = "0") {
if (!s.empty() and s[0] == '-') {
sgn = -1;
s.erase(s.begin());
} else {
sgn = 1;
}
s.insert(0, (LOG - ssize(s) % LOG) % LOG, '0');
if (s.empty()) s = string(LOG, '0');
val.resize(size(s) / LOG);
ranges::reverse(s);
for(int i = ssize(s) - 1; i >= 0; i--)
val[i / LOG] = val[i / LOG] * 10 + (s[i] - '0');
}
int log10() {
assert(sgn == 1);
int x = LOG * (ssize(val) - 1), y = val.back();
while(y) x++, y /= 10;
return x - 1;
}
void norm() {
if (sgn == -1 and ssize(val) == 1 and val[0] == 0)
sgn = 1;
}
bool abs_less(const bigint &b) const {
if (size(val) != size(b.val))
return size(val) < size(b.val);
for(int i = ssize(val) - 1; i >= 0; i--)
if (val[i] != b.val[i])
return val[i] < b.val[i];
return false;
}
bigint& operator+=(const bigint &b) {
if (sgn != b.sgn) {
*this -= -b;
} else if (abs_less(b)) {
*this = b + *this;
} else {
for(int i = 0; i < min(ssize(val), ssize(b.val)); i++) {
val[i] += b.val[i];
if (int q = val[i] / W; q > 0) {
if (i + 1 == ssize(val)) val.emplace_back();
val[i] -= q * W, val[i + 1] += q;
}
}
int j = min(ssize(val), ssize(b.val));
while(j < ssize(val) and val[j] >= W) {
int q = val[j] / W;
if (j + 1 == ssize(val)) val.emplace_back();
val[j] -= q * W, val[j + 1] += q, j++;
}
}
norm();
return *this;
}
bigint& operator-=(const bigint &b) {
if (sgn != b.sgn) {
*this += -b;
} else if (abs_less(b)) {
*this = b - *this, sgn = -sgn;
} else {
for(int i = 0; i < min(ssize(val), ssize(b.val)); i++) {
val[i] -= b.val[i];
if (val[i] < 0)
val[i] += W, val[i + 1] -= 1;
}
int j = min(ssize(val), ssize(b.val));
while(j < ssize(val) and val[j] < 0)
val[j] += W, val[j + 1] -= 1, j++;
while(ssize(val) > 1 and val.back() == 0) val.pop_back();
}
norm();
return *this;
}
bigint& operator*=(const bigint &b) {
if constexpr (LOG == 1) {
static NTT ntt;
vector<mint> c(size(val)), d(size(b.val));
for(int i = 0; i < ssize(c); i++) c[i] = val[i];
for(int i = 0; i < ssize(d); i++) d[i] = b.val[i];
c = ntt.conv(c, d);
vector<int> tmp(ssize(c));
for(int i = 0; i < ssize(c); i++)
tmp[i] = c[i].get();
for(int i = 0; i < ssize(tmp); i++) {
if (int q = tmp[i] / W; q > 0) {
if (i + 1 == ssize(tmp)) tmp.emplace_back();
tmp[i] -= q * W, tmp[i + 1] += q;
}
}
val.swap(tmp);
} else {
vector<int> tmp(ssize(val) + ssize(b.val) + 1);
for(int i = 0; i < ssize(val); i++) {
for(int j = 0; j < ssize(b.val); j++) {
if (int q = tmp[i + j] / W; q > 0)
tmp[i + j] -= q * W, tmp[i + j + 1] += q;
ll x = (ll)val[i] * b.val[j];
tmp[i + j] += x % W, tmp[i + j + 1] += x / W;
if (int q = tmp[i + j] / W; q > 0)
tmp[i + j] -= q * W, tmp[i + j + 1] += q;
}
}
val.swap(tmp);
}
while(ssize(val) > 1 and val.back() == 0) val.pop_back();
sgn *= b.sgn;
norm();
return *this;
}
bool operator<(const bigint &b) {
if (sgn != b.sgn) return sgn == -1;
else if (sgn == 1) return abs_less(b);
else return b.abs_less(*this);
}
bool operator>(const bigint &b) { return b < *this; }
bool operator<=(const bigint &b) { return !(*this > b); }
bool operator>=(const bigint &b) { return !(*this < b); }
bool operator==(const bigint &b) { return sgn == b.sgn and val == b.val; }
friend bigint operator+(bigint a, bigint b) { return a += b; }
friend bigint operator-(bigint a, bigint b) { return a -= b; }
friend bigint operator*(bigint a, bigint b) { return a *= b; }
bigint operator-() const {
bigint b = *this;
b.sgn = -b.sgn;
return b;
}
string to_string() const {
string s;
for(int i = 0; i < ssize(val); i++) {
int x = val[i];
for(int j = 0; j < LOG; j++)
s += '0' + (x % 10), x /= 10;
}
while(ssize(s) > 1 and s.back() == '0') s.pop_back();
if (sgn == -1) s += '-';
ranges::reverse(s);
return s;
}
friend ostream& operator<<(ostream& os, const bigint& b) {
return os << b.to_string();
}
};
//source: KACTL(https://github.com/kth-competitive-programming/kactl)
ull modmul(ull a, ull b, ull M) {
ll ret = a * b - M * ull(1.L / M * a * b);
return ret + M * (ret < 0) - M * (ret >= (ll)M);
}
ull modpow(ull b, ull e, ull mod) {
ull ans = 1;
for (; e; b = modmul(b, b, mod), e /= 2)
if (e & 1) ans = modmul(ans, b, mod);
return ans;
}
bool isPrime(ull n) {
if (n < 2 || n % 6 % 4 != 1) return (n | 1) == 3;
ull A[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022},
s = __builtin_ctzll(n-1), d = n >> s;
for (ull a : A) { // ^ count trailing zeroes
ull p = modpow(a%n, d, n), i = s;
while (p != 1 && p != n - 1 && a % n && i--)
p = modmul(p, p, n);
if (p != n-1 && i != s) return 0;
}
return 1;
}
template<class T, size_t N>
array<T, N>& operator+=(array<T, N> &a, const array<T, N> &b) {
for(size_t i = 0; i < N; i++)
a[i] += b[i];
return a;
}
template<class T, size_t N>
array<T, N>& operator-=(array<T, N> &a, const array<T, N> &b) {
for(size_t i = 0; i < N; i++)
a[i] -= b[i];
return a;
}
template<class T, size_t N>
array<T, N> operator+(array<T, N> a, array<T, N> b) { return a += b; }
template<class T, size_t N>
array<T, N> operator-(array<T, N> a, array<T, N> b) { return a -= b; }
using B = bigint<true>;
using HA = array<int, 16>;
mt19937 rng(clock);
uniform_int_distribution<int> unif(500'000'000, 1'000'000'000);
HA m;
HA fromB(B a) {
HA r = {};
for(int i = 0; i < 16; i++)
for(ll base = 1; int x : a.val)
r[i] = (r[i] + base * x) % m[i], base = base * B::W % m[i];
return r;
}
HA fib[11'000'000];
signed main() {
ios::sync_with_stdio(false), cin.tie(NULL);
for(int &x : m) while(!isPrime(x = unif(rng))) ;
fill(fib[1].begin(), fib[1].end(), 1);
for(int i = 2; i < 11'000'000; i++)
for(int j = 0; j < 16; j++)
fib[i][j] = (fib[i - 1][j] + fib[i - 2][j]) % m[j];
int n; cin >> n;
vector<B> a(n);
for(int i = 0; i < n; i++) {
string s; cin >> s;
a[i] = B(s);
}
sort(a.begin(), a.end(), [](B &a, B &b) { return a < b; });
ll ans = 0;
map<HA, int> f;
for(int i = 0; i < n; i++) {
int k = a[i].log10() / log10l((1 + sqrtl(5)) / 2);
dbg(a[i], k);
for(int l = max(k - 10, 2); l <= k + 16; l++) {
auto tar = fib[l] - fromB(a[i]);
for(int j = 0; j < 16; j++) tar[j] = (tar[j] % m[j] + m[j]) % m[j];
if (f.contains(tar)) ans += f[tar];
}
f[fromB(a[i])]++;
}
cout << ans << '\n';
return 0;
}
详细
Test #1:
score: 100
Accepted
time: 310ms
memory: 691076kb
input:
6 50 8 8 5 72 354224848179261915070
output:
4
result:
ok 1 number(s): "4"
Test #2:
score: -100
Time Limit Exceeded
input:
28 200878223506436882933619847964496455022155117513398820563747455993172799881403389571477889821109288771413214004090719097929400406252135763028179112130390003528046316900603668569910008417315162907579003880220844686222148696041857432602133894827753998572080650383305777912447151917272483538029469449...