結果
| 問題 |
No.1334 Multiply or Add
|
| コンテスト | |
| ユーザー |
 mtsd
|
| 提出日時 | 2021-01-08 23:02:11 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 24,437 bytes |
| コンパイル時間 | 2,808 ms |
| コンパイル使用メモリ | 148,120 KB |
| 実行使用メモリ | 10,736 KB |
| 最終ジャッジ日時 | 2024-11-16 15:09:57 |
| 合計ジャッジ時間 | 5,202 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 68 WA * 3 |
ソースコード
#include <algorithm>
#include <bitset>
#include <cassert>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <cstring>
#include <deque>
#include <functional>
#include <iostream>
#include <iomanip>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <unordered_map>
#include <unordered_set>
#include <vector>
#include <cstdint>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef pair<int,int> pii;
#define MP make_pair
#define PB push_back
#define inf 1000000007
#define rep(i,n) for(int i = 0; i < (int)(n); ++i)
#define all(x) (x).begin(),(x).end()
template<typename A, size_t N, typename T>
void Fill(A (&array)[N], const T &val){
std::fill( (T*)array, (T*)(array+N), val );
}
template<class T> inline bool chmax(T &a, T b){
if(a<b){
a = b;
return true;
}
return false;
}
template<class T> inline bool chmin(T &a, T b){
if(a>b){
a = b;
return true;
}
return false;
}
class MPI : public vector<int> {
private:
static constexpr int root = 3;
static constexpr int MOD_ = 998244353; // 2^23 * 119 + 1 (2^22 桁以下の数の積を計算可能)
bool sign;
static void trim_sign(MPI& num){
if(num.isZero()) num.sign = false;
}
static void trim_digit(MPI& num){
while(num.back() == 0 && (int)num.size() >= 2) num.pop_back();
}
static bool abs_less(const MPI& a, const MPI& b){
if(a.size() != b.size()) return a.size() < b.size();
for(int index = (int)a.size() - 1; index >= 0; index--){
if(a[index] != b[index]) return a[index] < b[index];
}
return false;
}
static void num_sbst(MPI& a, const MPI& b){
int n = (int)b.size();
a.resize(n);
for(int i = 0; i < n; i++) a[i] = b[i];
}
static void add(const MPI& a, const MPI& b, MPI& res){
num_sbst(res, a);
int mx = (int)max(a.size(), b.size());
res.resize(mx, 0);
int carry = 0;
for(int i = 0; i < mx; i++){
int val = res[i] + ((i < (int)b.size()) ? b[i] : 0) + carry;
carry = val/10;
res[i] = val%10;
}
if(carry) res.push_back(1);
}
static void sub(const MPI& a, const MPI& b, MPI& res){
num_sbst(res, a);
int carry = 0;
for(int i = 0; i < (int)res.size(); i++){
int val = res[i] - carry - ((i < (int)b.size()) ? b[i] : 0);
if(val < 0){
carry = 1, val += 10;
}else{
carry = 0;
}
res[i] = val;
}
trim_digit(res), trim_sign(res);
}
static int add_(const int x, const int y) { return (x + y < MOD_) ? x + y : x + y - MOD_; }
static int mul_(const int x, const int y) { return (long long)x * y % MOD_; }
static int power(int x, int n){
int res = 1;
while(n > 0){
if(n & 1) res = mul_(res, x);
x = mul_(x, x);
n >>= 1;
}
return res;
}
static int inverse(const int x) { return power(x, MOD_ - 2); }
static void ntt(vector<int>& a, const bool rev = false){
int i,j,k,s,t,v,w,wn;
const int size = (int)a.size();
const int height = (int)log2(2 * size - 1);
for(i = 0; i < size; i++){
j = 0;
for(k = 0; k < height; k++) j |= (i >> k & 1) << (height - 1 - k);
if(i < j) std::swap(a[i], a[j]);
}
for(i = 1; i < size; i *= 2) {
w = power(root, (MOD_ - 1) / (i * 2));
if(rev) w = inverse(w);
for(j = 0; j < size; j += i * 2){
wn = 1;
for(k = 0; k < i; k++){
s = a[j + k], t = mul_(a[j + k + i], wn);
a[j + k] = add_(s, t);
a[j + k + i] = add_(s, MOD_ - t);
wn = mul_(wn, w);
}
}
}
if(rev){
v = inverse(size);
for (i = 0; i < size; i++) a[i] = mul_(a[i], v);
}
}
static void mul(const MPI& a, const MPI& b, MPI& res){
const int size = (int)a.size() + (int)b.size() - 1;
int t = 1;
while (t < size) t <<= 1;
vector<int> A(t, 0), B(t, 0);
for(int i = 0; i < (int)a.size(); i++) A[i] = a[i];
for(int i = 0; i < (int)b.size(); i++) B[i] = b[i];
ntt(A), ntt(B);
for(int i = 0; i < t; i++) A[i] = mul_(A[i], B[i]);
ntt(A, true);
res.resize(size);
int carry = 0;
for(int i = 0; i < size; i++){
int val = A[i] + carry;
carry = val / 10;
res[i] = val % 10;
}
if(carry) res.push_back(carry);
trim_digit(res), trim_sign(res);
}
bool isZero() const {
return (int)size() == 1 && (*this)[0] == 0;
}
static bool div_geq(const MPI& mod, const MPI& num){
if((int)mod.size() != (int)num.size()) return (int)mod.size() > (int)num.size();
int n = (int)mod.size();
for(int i = 0; i < n; i++){
if(mod[i] != num[n-1-i]){
return mod[i] > num[n-1-i];
}
}
return true;
}
static void div_(const MPI& a, const MPI& b, MPI& quo, MPI& mod){
vector<MPI> mult(9);
mult[0] = b;
for(int i = 0; i < 8; i++) mult[i+1] = mult[i] + b;
for(int i = (int)a.size() - 1; i >= 0; i--){
if(mod.isZero()){
mod.back() = a[i];
}else{
mod.push_back(a[i]);
}
if(div_geq(mod, b)){
int l = 0, r = 9;
reverse(mod.begin(), mod.end());
while(r-l>1){
int mid = (l+r)/2;
if(mult[mid] > mod){
r = mid;
}else{
l = mid;
}
}
mod -= mult[l];
reverse(mod.begin(), mod.end());
quo.push_back(l+1);
}else{
quo.push_back(0);
}
}
reverse(quo.begin(), quo.end());
trim_digit(quo);
reverse(mod.begin(), mod.end());
}
public:
MPI() : sign(false){ this->push_back(0); }
MPI(long long val) : sign(false){
if(val == 0){
this->push_back(0);
}else{
if(val < 0) sign = true, val = -val;
while(val){
this->push_back(val%10);
val /= 10;
}
}
}
MPI(const string& s) : sign(false){
if(s.empty()){
this->push_back(0);
return;
}
if(s[0] == '-') sign = true;
for(int i = (int)s.size() - 1; i >= sign; i--) this->push_back(s[i]-'0');
}
long long to_ll() const {
long long res = 0, dig = 1;
for(int i = 0; i < (int)size(); i++){
res += dig * (*this)[i], dig *= 10;
}
if(sign) res = -res;
return res;
}
string to_string() const {
int n = (int)size() + sign;
string s(n, ' ');
if(sign) s[0] = '-';
for(int i = sign; i < n; i++) s[i] = (char)('0'+(*this)[n-1-i]);
return s;
}
friend istream& operator>>(istream& is, MPI& num) {
string s;
is >> s;
num = MPI(s);
return is;
}
friend ostream& operator<<(ostream& os, const MPI& num) {
if(num.sign) os << '-';
for(int i = (int)num.size()-1; i >= 0; i--) os << (char)('0'+num[i]);
return os;
}
MPI& operator=(long long val) {
*this = MPI(val);
return *this;
}
bool operator<(const MPI& another) const {
if(sign ^ another.sign) return sign;
if(size() != another.size()) return (size() < another.size()) ^ sign;
for(int index = (int)size() - 1; index >= 0; index--){
if((*this)[index] != another[index]) return ((*this)[index] < another[index]) ^ sign;
}
return false;
}
bool operator<(const long long num) const {
return *this < MPI(num);
}
friend bool operator<(const long long num, const MPI& another){
return MPI(num) < another;
}
bool operator>(const MPI& another) const {
return another < *this;
}
bool operator>(const long long num) const {
return *this > MPI(num);
}
friend bool operator>(const long long num, const MPI& another){
return MPI(num) > another;
}
bool operator<=(const MPI& another) const {
return !(*this > another);
}
bool operator<=(const long long num) const {
return *this <= MPI(num);
}
friend bool operator<=(const long long num, const MPI& another){
return MPI(num) <= another;
}
bool operator>=(const MPI& another) const {
return !(*this < another);
}
bool operator>=(const long long num) const {
return *this >= MPI(num);
}
friend bool operator>=(const long long num, const MPI& another){
return MPI(num) >= another;
}
bool operator==(const MPI& another) const {
if(sign ^ another.sign) return false;
if(size() != another.size()) return false;
for(int index = (int)size() - 1; index >= 0; index--){
if((*this)[index] != another[index]) return false;
}
return true;
}
bool operator==(const long long num) const {
return *this == MPI(num);
}
friend bool operator==(const long long num, const MPI& another){
return MPI(num) == another;
}
bool operator!=(const MPI& another) const {
return !(*this == another);
}
bool operator!=(const long long num) const {
return *this != MPI(num);
}
friend bool operator!=(const long long num, const MPI& another){
return MPI(num) != another;
}
explicit operator bool() const noexcept { return !isZero(); }
bool operator!() const noexcept { return !static_cast<bool>(*this); }
explicit operator int() const noexcept { return (int)this->to_ll(); }
explicit operator long long() const noexcept { return this->to_ll(); }
MPI operator+() const {
return *this;
}
MPI operator-() const {
MPI res = *this;
res.sign = !sign;
return res;
}
friend MPI abs(const MPI& num){
MPI res = num;
res.sign = false;
return res;
}
MPI operator+(const MPI& num) const {
MPI res; res.sign = sign;
if(sign != num.sign){
if(abs_less(*this, num)){
res.sign = num.sign;
sub(num, *this, res);
return res;
}else{
sub(*this, num, res);
return res;
}
}
add(*this, num, res);
return res;
}
MPI operator+(long long num) const {
return *this + MPI(num);
}
friend MPI operator+(long long a, const MPI& b){
return b + a;
}
MPI& operator+=(const MPI& num){
*this = *this + num;
return *this;
}
MPI& operator+=(long long num){
*this = *this + num;
return *this;
}
MPI& operator++(){
return *this += 1;
}
MPI operator++(int){
MPI res = *this;
*this += 1;
return res;
}
MPI operator-(const MPI& num) const {
if(sign != num.sign){
MPI res; res.sign = sign;
add(*this, num, res);
return res;
}
MPI res; res.sign = (abs_less(*this, num) ^ sign);
if(res.sign){
sub(num, *this, res);
}else{
sub(*this, num, res);
}
return res;
}
MPI operator-(long long num) const {
return *this - MPI(num);
}
friend MPI operator-(long long a, const MPI& b){
return b - a;
}
MPI& operator-=(const MPI& num){
*this = *this - num;
return *this;
}
MPI& operator-=(long long num){
*this = *this - num;
return *this;
}
MPI& operator--(){
return *this -= 1;
}
MPI operator--(int){
MPI res = *this;
*this -= 1;
return res;
}
MPI operator*(const MPI& num) const {
MPI res; res.sign = (sign^num.sign);
mul(*this, num, res);
return res;
}
MPI operator*(long long num) const {
return *this * MPI(num);
}
friend MPI operator*(long long a, const MPI& b){
return b * a;
}
MPI& operator*=(const MPI& num){
*this = *this * num;
return *this;
}
MPI& operator*=(long long num){
*this = *this * num;
return *this;
}
MPI operator/(const MPI& num) const {
MPI num_ = abs(num);
MPI a, b;
div_(*this, num_, a, b);
a.sign = (sign^num.sign);
trim_sign(a);
return a;
}
MPI operator/(long long num) const {
return *this / MPI(num);
}
friend MPI operator/(long long a, const MPI& b){
return b / a;
}
MPI& operator/=(const MPI& num){
*this = *this / num;
return *this;
}
MPI& operator/=(long long num){
*this = *this / num;
return *this;
}
MPI operator%(const MPI& num) const {
MPI num_ = abs(num);
MPI a, b;
div_(*this, num_, a, b);
b.sign = sign;
trim_sign(b);
return b;
}
MPI operator%(long long num) const {
return *this % MPI(num);
}
friend MPI operator%(long long a, const MPI& b){
return b % a;
}
MPI& operator%=(const MPI& num){
*this = *this % num;
return *this;
}
MPI& operator%=(long long num){
*this = *this % num;
return *this;
}
MPI div2() const {
MPI res; res.sign = sign;
int n = (int)this->size(), carry = 0;
for(int i = n-1; i >= 0; i--){
int val = (*this)[i]+carry*10;
carry = val%2;
if(i != n-1 || val >= 2) res.push_back(val/2);
}
reverse(res.begin(), res.end());
trim_digit(res);
return res;
}
friend MPI sqrt(const MPI& x){
if(x <= MPI(0)) return MPI(0);
MPI s = 1, t = x;
while(s < t){
s = s + s, t = t.div2();
}
do{ t = s, s = (x / s + s).div2();
}while(s < t);
return t;
}
friend MPI log10(const MPI& x){
assert(x > MPI(0));
return MPI((int)x.size());
}
friend MPI pow(MPI a, MPI b){
assert(b >= 0);
MPI res(1);
while(b){
if(b[0] % 2){
res *= a;
}
a *= a;
b = b.div2();
}
return res;
}
};
template <unsigned int mod>
class ModInt {
private:
unsigned int v;
static unsigned int norm(const unsigned int& x){ return x < mod ? x : x - mod; }
static ModInt make(const unsigned int& x){ ModInt m; return m.v = x, m; }
static ModInt inv(const ModInt& x){ return make(inverse(x.v, mod)); }
static unsigned int inverse(int a, int m){
int u[] = {a, 1, 0}, v[] = {m, 0, 1}, t;
while(*v){
t = *u / *v;
swap(u[0] -= t * v[0], v[0]), swap(u[1] -= t * v[1], v[1]), swap(u[2] -= t * v[2], v[2]);
}
return (u[1] % m + m) % m;
}
public:
ModInt() : v{0}{}
ModInt(const long long val) : v{norm(val % mod + mod)} {}
ModInt(const ModInt<mod>& n) : v{n()} {}
explicit operator bool() const noexcept { return v != 0; }
bool operator!() const noexcept { return !static_cast<bool>(*this); }
ModInt& operator=(const ModInt& n){ return v = n(), (*this); }
ModInt& operator=(const long long val){ return v = norm(val % mod + mod), (*this); }
ModInt operator+() const { return *this; }
ModInt operator-() const { return v == 0 ? make(0) : make(mod - v); }
ModInt operator+(const ModInt& val) const { return make(norm(v + val())); }
ModInt operator-(const ModInt& val) const { return make(norm(v + mod - val())); }
ModInt operator*(const ModInt& val) const { return make((long long)v * val() % mod); }
ModInt operator/(const ModInt& val) const { return *this * inv(val); }
ModInt& operator+=(const ModInt& val){ return *this = *this + val; }
ModInt& operator-=(const ModInt& val){ return *this = *this - val; }
ModInt& operator*=(const ModInt& val){ return *this = *this * val; }
ModInt& operator/=(const ModInt& val){ return *this = *this / val; }
ModInt operator+(const long long val) const { return ModInt{v + val}; }
ModInt operator-(const long long val) const { return ModInt{v - val}; }
ModInt operator*(const long long val) const { return ModInt{(long long)v * (val % mod)}; }
ModInt operator/(const long long val) const { return ModInt{(long long)v * inv(val)}; }
ModInt& operator+=(const long long val){ return *this = *this + val; }
ModInt& operator-=(const long long val){ return *this = *this - val; }
ModInt& operator*=(const long long val){ return *this = *this * val; }
ModInt& operator/=(const long long val){ return *this = *this / val; }
bool operator==(const ModInt& val) const { return v == val.v; }
bool operator!=(const ModInt& val) const { return !(*this == val); }
bool operator==(const long long val) const { return v == norm(val % mod + mod); }
bool operator!=(const long long val) const { return !(*this == val); }
unsigned int operator()() const { return v; }
friend ModInt operator+(const long long val, const ModInt& n) { return n + val; }
friend ModInt operator-(const long long val, const ModInt& n) { return ModInt{val - n()}; }
friend ModInt operator*(const long long val, const ModInt& n) { return n * val; }
friend ModInt operator/(const long long val, const ModInt& n) { return ModInt{val} / n; }
friend bool operator==(const long long val, const ModInt& n) { return n == val; }
friend bool operator!=(const long long val, const ModInt& n) { return !(val == n); }
friend istream& operator>>(istream& is, ModInt& n){
unsigned int v;
return is >> v, n = v, is;
}
friend ostream& operator<<(ostream& os, const ModInt& n){ return (os << n()); }
friend ModInt mod_pow(ModInt x, long long n){
ModInt ans = 1;
while(n){
if(n & 1) ans *= x;
x *= x, n >>= 1;
}
return ans;
}
};
#define MOD 1000000007
using mod = ModInt<MOD>;
#define MAX_N 200000
mod inv[MAX_N],fac[MAX_N],finv[MAX_N];
void make()
{
fac[0] = fac[1] = 1;
finv[0] = finv[1] = 1;
inv[1] = 1;
for(int i=2;i<MAX_N;i++){
inv[i] = MOD - inv[MOD % i] * (MOD / i);
fac[i] = fac[i-1] * i;
finv[i] = finv[i-1] * inv[i];
}
}
mod comb(int a, int b)
{
if(a<b) return 0;
return fac[a] * finv[b] * finv[a-b];
}
class UnionFind {
private:
int sz;
vector<int> par, size_;
public:
UnionFind(){}
UnionFind(int node_size) : sz(node_size), par(sz), size_(sz, 1){
iota(par.begin(), par.end(), 0);
}
int find(int x){
if(par[x] == x) return x;
else return par[x] = find(par[x]);
}
void unite(int x,int y){
x = find(x), y = find(y);
if(x == y) return;
if(size_[x] < size_[y]) swap(x,y);
par[y] = x;
size_[x] += size_[y];
}
int size(int x){
x = find(x);
return size_[x];
}
bool same(int x,int y){
return find(x) == find(y);
}
};
int main(){
cin.tie(0);
ios::sync_with_stdio(false);
int n;
cin >> n;
vector<ll> a(n);
rep(i,n) cin >> a[i];
vector<char> res(n);
vector<vector<pair<int,int> > > p;
vector<pair<int,int> > tmp;
int id = 0;
while(id!=n){
int k = 0;
if(a[id]==1){
while(id!=n&&a[id]==1){
id++;
k++;
}
tmp.push_back(MP(0,k));
}else{
if(a[id]==0){
p.push_back(tmp);
tmp.clear();
tmp.push_back(MP(3,0));
p.push_back(tmp);
tmp.clear();
id++;
}else{
tmp.push_back(MP(1,a[id]));
id++;
}
}
}
p.push_back(tmp);
id = 0;
for(auto& x:p){
if(x.size()==0)continue;
if(x[0].first==3){
res[id] = '+';
id++;
continue;
}
int m = x.size();
MPI sm = 0;
MPI K = 1;
bool fflag = 0;
rep(i,m){
if(x[i].first==0){
if(i!=0&&i!=m-1){
sm += x[i].second;
}
}else{
K *= x[i].second;
if(K >= 100000000000LL){
fflag = 1;
break;
}
}
}
if(fflag){
rep(i,m){
if(x[i].first==0){
if(i==0||i==m-1){
rep(j,x[i].second){
res[id] = '+';
id++;
}
}else{
rep(j,x[i].second){
res[id] = '*';
id++;
}
}
}else{
res[id] = '*';
id++;
if(i==m-2&&x[i+1].first==0){
res[id-1] = '+';
}
}
}
res[id-1] = '+';
}else{
MPI mx = 0;
int mxbit = 0;
rep(bit,1<<(m-1)){
UnionFind uf(m);
rep(i,m-1){
if((bit>>i)&1){
uf.unite(i,i+1);
}
}
MPI S = 0;
MPI tmp = 1;
bool flag = 1;
rep(i,m){
if(i==m-1||!uf.same(i,i+1)){
if(flag){
S += x[i].second;
}else{
if(x[i].first==0){
}else{
tmp *= x[i].second;
}
S += tmp;
}
flag = 1;
tmp = 1;
}else{
flag = 0;
if(x[i].first==0){
}else{
tmp *= x[i].second;
}
}
}
if(chmax(mx,S)){
mxbit = bit;
}
}
UnionFind uf(m);
rep(i,m-1){
if((mxbit>>i)&1){
uf.unite(i,i+1);
}
}
bool flag = 0;
rep(i,m){
if(i==m-1||!uf.same(i,i+1)){
if(x[i].first==0){
rep(j,x[i].second){
res[id] = '+';
id++;
}
}else{
res[id] = '+';
id++;
}
flag = 1;
}else{
if(x[i].first==0){
rep(j,x[i].second){
res[id] = '*';
id++;
}
}else{
res[id] = '*';
id++;
}
flag = 0;
}
}
}
}
mod ans = 0;
mod PP = 1;
rep(i,n){
PP *= a[i];
if(i!=n-1){
if(res[i]=='+'){
ans += PP;
PP = 1;
}
}
}
ans += PP;
cout << ans << endl;
return 0;
}