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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#766071 | #9225. Fibonacci Fusion | Misuki# | TL | 1560ms | 134368kb | C++20 | 19.1kb | 2024-11-20 16:05:42 | 2024-11-20 16:05:43 |
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; }
//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) {
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');
}
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) const {
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) const { return b < *this; }
bool operator<=(const bigint &b) { return !(*this > b); }
bool operator>=(const bigint &b) { return !(*this < b); }
bool operator==(const bigint &b) const { 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();
}
};
const bigint<true> zero("0");
//source: KACTL(for det() and inv())
template<class Mint>
struct matrix : vector<vector<Mint>> {
matrix(int n, int m) : vector<vector<Mint>>(n, vector<Mint>(m, Mint("0"))) {}
//matrix(int n) : vector<vector<Mint>>(n, vector<Mint>(n, 0)) {}
int n() const { return ssize(*this); }
int m() const { return ssize((*this)[0]); }
static matrix I(int n) {
auto res = matrix(n, n);
for(int i = 0; i < n; i++)
res[i][i] = 1;
return res;
}
matrix& operator+=(const matrix &b) {
assert(n() == b.n());
assert(m() == b.m());
for(int i = 0; i < n(); i++)
for(int j = 0; j < m(); j++)
(*this)[i][j] += b[i][j];
return *this;
}
matrix& operator-=(const matrix &b) {
assert(n() == b.n());
assert(m() == b.m());
for(int i = 0; i < n(); i++)
for(int j = 0; j < m(); j++)
(*this)[i][j] -= b[i][j];
return *this;
}
matrix& operator*=(const matrix &b) {
assert(m() == b.n());
auto res = matrix(n(), b.m());
for(int i = 0; i < n(); i++)
for(int k = 0; k < m(); k++)
for(int j = 0; j < b.m(); j++)
if ((i != 0 or j != 1) and (*this)[i][k] != zero and b[k][j] != zero)
res[i][j] += (*this)[i][k] * b[k][j];
res[0][1] = res[1][0];
this -> swap(res);
return *this;
}
matrix pow(ll k) const {
assert(n() == m());
auto res = I(n()), base = *this;
while(k) {
if (k & 1) res *= base;
base *= base, k >>= 1;
}
return res;
}
Mint det() const {
Mint res = 1;
auto a = *this;
for(int i = 0; i < n(); i++) {
for(int j = i + 1; j < m(); j++) {
while(a[j][i] != 0) {
Mint t = a[i][i] / a[j][i];
if (t != 0)
for(int k = i; k < n(); k++)
a[i][k] -= a[j][k] * t;
swap(a[i], a[j]);
res = -res;
}
}
res *= a[i][i];
if (res == 0) return 0;
}
return res;
}
matrix inv() const {
assert(n() == m());
matrix a = *this, tmp = I(n());
vector<int> col(n());
for(int i = 0; i < n(); i++) col[i] = i;
for(int i = 0; i < n(); i++) {
int r = i, c = i;
for(int j = i; j < n(); j++) {
for(int k = i; k < n(); k++) {
if (a[j][k] != 0) {
r = j, c = k;
goto found;
}
}
}
return matrix(0);
found:
a[i].swap(a[r]), tmp[i].swap(tmp[r]);
for(int j = 0; j < n(); j++)
swap(a[j][i], a[j][c]), swap(tmp[j][i], tmp[j][c]);
swap(col[i], col[c]);
Mint v = 1 / a[i][i];
for(int j = i + 1; j < n(); j++) {
Mint f = a[j][i] * v;
a[j][i] = 0;
for(int k = i + 1; k < n(); k++)
a[j][k] -= f * a[i][k];
for(int k = 0; k < n(); k++)
tmp[j][k] -= f * tmp[i][k];
}
for(int j = i + 1; j < n(); j++)
a[i][j] *= v;
for(int j = 0; j < n(); j++)
tmp[i][j] *= v;
a[i][i] = 1;
}
for(int i = n() - 1; i > 0; i--) {
for(int j = 0; j < i; j++) {
Mint v = a[j][i];
for(int k = 0; k < n(); k++)
tmp[j][k] -= v * tmp[i][k];
}
}
for(int i = 0; i < n(); i++)
for(int j = 0; j < n(); j++)
a[col[i]][col[j]] = tmp[i][j];
return a;
}
matrix operator-() { return matrix(n(), m()) - (*this); }
friend matrix operator+(matrix a, matrix b) { return a += b; }
friend matrix operator-(matrix a, matrix b) { return a -= b; }
friend matrix operator*(matrix a, matrix b) { return a *= b; }
friend ostream& operator<<(ostream& os, const matrix& b) {
for(int i = 0; i < b.n(); i++) {
os << '\n';
for(int j = 0; j < b.m(); j++)
os << b[i][j] << ' ';
}
return os;
}
friend istream& operator>>(istream& is, matrix& b) {
for(int i = 0; i < b.n(); i++)
for(int j = 0; j < b.m(); j++)
is >> b[i][j];
return is;
}
};
using M = matrix<bigint<true>>;
vector<M> ms;
M fib(int w) {
M v = ms[0];
int len = 1;
for(auto &vv : ms) {
if (len + ssize(vv[0][0].val) < w - 30)
v *= vv;
}
return v;
}
signed main() {
ios::sync_with_stdio(false), cin.tie(NULL);
ms.emplace_back(2, 2);
ms.back()[0][0] = ms.back()[0][1] = ms.back()[1][0] = bigint<true>("1");
while(2 * ssize(ms.back()[0][0].val) <= 2'000'000) {
ms.emplace_back(ms.back() * ms.back());
dbg(ms.back()[0][0].val.size());
}
int n; cin >> n;
vector<bigint<true>> a;
for(int i = 0; i < n; i++) {
string s; cin >> s;
a.emplace_back(s);
}
sort(a.begin(), a.end(), [](auto &x, auto &y) { return x < y; });
vector<int> nxt(n, -1);
ll ans = 0;
for(int i = 0, j = 0; i < n; i = j) {
while(j < n and a[i] == a[j]) j++;
nxt[i] = j;
auto m = fib(ssize(a[i].val));
bigint<true> c = m[0][0], d = m[0][1];
dbg(a[i]);
while(ssize(c.val) <= ssize(a[i].val) + 1) {
if (c > a[i]) {
auto tar = c - a[i];
int l = lower_bound(a.begin(), a.begin() + i, tar) - a.begin();
if (l != i and a[l] == tar) {
int r = nxt[l];
ans += (ll)(r - l) * (j - i);
}
if (a[i] + a[i] == c)
ans += (ll)(j - i) * (j - i - 1) / 2;
}
dbg(c, ans);
bigint<true> e = c + d;
c = d, d = e;
}
dbg(a[i], ans);
}
cout << ans << '\n';
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 1560ms
memory: 134368kb
input:
6 50 8 8 5 72 354224848179261915070
output:
4
result:
ok 1 number(s): "4"
Test #2:
score: -100
Time Limit Exceeded
input:
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