結果
| 問題 |
No.2069 み世界数式
|
| ユーザー |
 KowerKoint2010
|
| 提出日時 | 2022-09-10 08:09:40 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 24 ms / 2,000 ms |
| コード長 | 19,837 bytes |
| コンパイル時間 | 3,016 ms |
| コンパイル使用メモリ | 218,008 KB |
| 最終ジャッジ日時 | 2025-02-07 03:49:52 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 41 |
ソースコード
#line 2 "library/KowerKoint/base.hpp"
#ifdef DEBUG
#define _GLIBCXX_DEBUG
#endif
#include <bits/stdc++.h>
using namespace std;
#define REP(i, n) for(int i = 0; i < (int)(n); i++)
#define FOR(i, a, b) for(ll i = a; i < (ll)(b); i++)
#define ALL(a) (a).begin(),(a).end()
#define END(...) { print(__VA_ARGS__); return; }
using VI = vector<int>;
using VVI = vector<VI>;
using VVVI = vector<VVI>;
using ll = long long;
using VL = vector<ll>;
using VVL = vector<VL>;
using VVVL = vector<VVL>;
using ull = unsigned long long;
using VUL = vector<ull>;
using VVUL = vector<VUL>;
using VVVUL = vector<VVUL>;
using VD = vector<double>;
using VVD = vector<VD>;
using VVVD = vector<VVD>;
using VS = vector<string>;
using VVS = vector<VS>;
using VVVS = vector<VVS>;
using VC = vector<char>;
using VVC = vector<VC>;
using VVVC = vector<VVC>;
using P = pair<int, int>;
using VP = vector<P>;
using VVP = vector<VP>;
using VVVP = vector<VVP>;
using LP = pair<ll, ll>;
using VLP = vector<LP>;
using VVLP = vector<VLP>;
using VVVLP = vector<VVLP>;
template <typename T>
using PQ = priority_queue<T>;
template <typename T>
using GPQ = priority_queue<T, vector<T>, greater<T>>;
constexpr int INF = 1001001001;
constexpr ll LINF = 1001001001001001001ll;
constexpr int DX[] = {1, 0, -1, 0};
constexpr int DY[] = {0, 1, 0, -1};
template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 >& p) {
os << p.first << " " << p.second;
return os;
}
template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
is >> p.first >> p.second;
return is;
}
template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
for(int i = 0; i < (int) v.size(); i++) {
os << v[i] << (i + 1 != (int) v.size() ? " " : "");
}
return os;
}
template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
for(T &in : v) is >> in;
return is;
}
void print() { cout << '\n'; }
template<typename T>
void print(const T &t) { cout << t << '\n'; }
template<typename Head, typename... Tail>
void print(const Head &head, const Tail &... tail) {
cout << head << ' ';
print(tail...);
}
#ifdef DEBUG
void dbg() { cerr << '\n'; }
template<typename T>
void dbg(const T &t) { cerr << t << '\n'; }
template<typename Head, typename... Tail>
void dbg(const Head &head, const Tail &... tail) {
cerr << head << ' ';
dbg(tail...);
}
#else
template<typename... Args>
void dbg(const Args &... args) {}
#endif
template<typename T>
vector<vector<T>> split(typename vector<T>::const_iterator begin, typename vector<T>::const_iterator end, T val) {
vector<vector<T>> res;
vector<T> cur;
for(auto it = begin; it != end; it++) {
if(*it == val) {
res.push_back(cur);
cur.clear();
} else cur.push_back(*it);
}
res.push_back(cur);
return res;
}
vector<string> split(typename string::const_iterator begin, typename string::const_iterator end, char val) {
vector<string> res;
string cur = "";
for(auto it = begin; it != end; it++) {
if(*it == val) {
res.push_back(cur);
cur.clear();
} else cur.push_back(*it);
}
res.push_back(cur);
return res;
}
template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }
template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }
template <typename T>
pair<VI, vector<T>> compress(const vector<T> &a) {
int n = a.size();
vector<T> x;
REP(i, n) x.push_back(a[i]);
sort(ALL(x)); x.erase(unique(ALL(x)), x.end());
VI res(n);
REP(i, n) res[i] = lower_bound(ALL(x), a[i]) - x.begin();
return make_pair(res, x);
}
template <typename It>
auto rle(It begin, It end) {
vector<pair<typename It::value_type, int>> res;
if(begin == end) return res;
auto pre = *begin;
int num = 1;
for(auto it = begin + 1; it != end; it++) {
if(pre != *it) {
res.emplace_back(pre, num);
pre = *it;
num = 1;
} else num++;
}
res.emplace_back(pre, num);
return res;
}
template <typename It>
vector<pair<typename It::value_type, int>> rle_sort(It begin, It end) {
vector<typename It::value_type> cloned(begin, end);
sort(ALL(cloned));
auto e = rle(ALL(cloned));
sort(ALL(e), [](const auto& l, const auto& r) { return l.second < r.second; });
return e;
}
template <typename T>
pair<vector<T>, vector<T>> factorial(int n) {
vector<T> res(n+1), rev(n+1);
res[0] = 1;
REP(i, n) res[i+1] = res[i] * (i+1);
rev[n] = 1 / res[n];
for(int i = n; i > 0; i--) {
rev[i-1] = rev[i] * i;
}
return make_pair(res, rev);
}
#line 3 "library/KowerKoint/operator.hpp"
template <typename T>
T add_op(T a, T b) { return a + b; }
template <typename T>
T sub_op(T a, T b) { return a - b; }
template <typename T>
T zero_e() { return T(0); }
template <typename T>
T div_op(T a, T b) { return a / b; }
template <typename T>
T mult_op(T a, T b) { return a * b; }
template <typename T>
T one_e() { return T(1); }
template <typename T>
T xor_op(T a, T b) { return a ^ b; }
template <typename T>
T and_op(T a, T b) { return a & b; }
template <typename T>
T or_op(T a, T b) { return a | b; }
ll mod3() { return 998244353LL; }
ll mod7() { return 1000000007LL; }
ll mod9() { return 1000000009LL; }
template <typename T>
T max_op(T a, T b) { return max(a, b); }
template <typename T>
T min_op(T a, T b) { return min(a, b); }
template <typename T>
T max_e() { return numeric_limits<T>::max(); }
template <typename T>
T min_e() { return numeric_limits<T>::min(); }
#line 2 "library/KowerKoint/integer/extgcd.hpp"
ll extgcd(ll a, ll b, ll& x, ll& y) {
x = 1, y = 0;
ll nx = 0, ny = 1;
while(b) {
ll q = a / b;
tie(a, b) = LP(b, a % b);
tie(x, nx) = LP(nx, x - nx*q);
tie(y, ny) = LP(ny, y - ny*q);
}
return a;
}
#line 2 "library/KowerKoint/integer/pow-mod.hpp"
ll inv_mod(ll n, ll m) {
ll x, y;
assert(extgcd(n, m, x, y) == 1);
x %= m;
if(x < 0) x += m;
return x;
}
ll pow_mod(ll a, ll n, ll m) {
if(n == 0) return 1LL;
if(n < 0) return inv_mod(pow_mod(a, -n, m), m);
ll res = 1;
while(n) {
if(n & 1) {
res *= a;
res %= m;
}
n >>= 1;
a *= a;
a %= m;
}
return res;
}
#line 4 "library/KowerKoint/integer/modint.hpp"
template <ll (*mod)()>
struct Modint {
ll val;
Modint(): val(0) {}
Modint(ll x): val(x) {
val %= mod();
if(val < 0) val += mod();
}
Modint& operator+=(const Modint& r) {
val += r.val;
if(val >= mod()) val -= mod();
return *this;
}
friend Modint operator+(const Modint& l, const Modint& r) {
return Modint(l) += r;
}
Modint& operator-=(const Modint& r) {
val -= r.val;
if(val < 0) val += mod();
return *this;
}
friend Modint operator-(const Modint& l, const Modint& r) {
return Modint(l) -= r;
}
Modint& operator*=(const Modint& r) {
val *= r.val;
val %= mod();
return *this;
}
Modint operator*(const Modint& r) {
return (Modint(*this) *= r);
}
friend Modint operator*(const Modint& l, const Modint& r) {
return Modint(l) *= r;
}
Modint pow(ll n) const {
return Modint(pow_mod(val, n, mod()));
}
Modint inv() const {
return Modint(inv_mod(val, mod()));
}
Modint& operator/=(const Modint& r) {
return (*this *= r.inv());
}
friend Modint operator/(const Modint& l, const Modint& r) {
return Modint(l) /= r;
}
Modint& operator^=(const ll n) {
val = pow_mod(val, n, mod());
return *this;
}
Modint operator^(const ll n) {
return this->pow(n);
}
Modint operator+() const { return *this; }
Modint operator-() const { return Modint() - *this; }
Modint& operator++() {
val++;
if(val == mod()) val = 0LL;
return *this;
}
Modint& operator++(int) {
Modint res(*this);
++*this;
return res;
}
Modint& operator--() {
if(val == 0LL) val = mod();
val--;
return *this;
}
Modint& operator--(int) {
Modint res(*this);
--*this;
return res;
}
friend bool operator==(const Modint& l, const Modint& r) {
return l.val == r.val;
}
friend bool operator!=(const Modint& l, const Modint& r) {
return l.val != r.val;
}
static pair<vector<Modint>, vector<Modint>> factorial(int n) {
vector<Modint> fact(n+1), rfact(n+1);
fact[0] = 1;
REP(i, n) fact[i+1] = fact[i] * (i+1);
rfact[n] = 1 / fact[n];
for(int i = n-1; i >= 0; i--) rfact[i] = rfact[i+1] * (i+1);
return {fact, rfact};
}
friend istream& operator>>(istream& is, Modint& mi) {
is >> mi.val;
return is;
}
friend ostream& operator<<(ostream& os, const Modint& mi) {
os << mi.val;
return os;
}
};
using MI3 = Modint<mod3>;
using V3 = vector<MI3>;
using VV3 = vector<V3>;
using VVV3 = vector<VV3>;
using MI7 = Modint<mod7>;
using V7 = vector<MI7>;
using VV7 = vector<V7>;
using VVV7 = vector<VV7>;
using MI9 = Modint<mod9>;
using V9 = vector<MI9>;
using VV9 = vector<V9>;
using VVV9 = vector<VV9>;
#line 3 "library/KowerKoint/counting/counting.hpp"
template <typename T>
struct Counting {
vector<T> fact, ifact;
Counting() {}
Counting(ll n) {
expand(n);
}
void expand(ll n) {
ll sz = (ll)fact.size();
if(sz > n) return;
fact.resize(n+1);
ifact.resize(n+1);
fact[0] = 1;
FOR(i, max(1LL, sz), n+1) fact[i] = fact[i-1] * i;
ifact[n] = 1 / fact[n];
for(ll i = n-1; i >= sz; i--) ifact[i] = ifact[i+1] * (i+1);
}
T p(ll n, ll r) {
assert(n >= r);
assert(r >= 0);
expand(n);
return fact[n] * ifact[n-r];
}
T c(ll n, ll r) {
assert(n >= r);
assert(r >= 0);
expand(n);
return fact[n] * ifact[r] * ifact[n-r];
}
T h(ll n, ll r) {
assert(n >= 0);
assert(r >= 0);
return c(n+r-1, r);
}
T stirling(ll n, ll k) {
assert(n >= k);
assert(k >= 0);
if(n == 0) return 1;
T res = 0;
int sign = k%2? -1 : 1;
expand(k);
REP(i, k+1) {
res += sign * ifact[i] * ifact[k-i] * T(i).pow(n);
sign *= -1;
}
return res;
}
vector<vector<T>> stirling_table(ll n, ll k) {
assert(n >= 0 && k >= 0);
vector<vector<T>> res(n+1, vector<T>(k+1));
res[0][0] = 1;
FOR(i, 1, n+1) FOR(j, 1, k+1) {
res[i][j] = res[i-1][j-1] + j * res[i-1][j];
}
return res;
}
T bell(ll n, ll k) {
assert(n >= 0 && k >= 0);
expand(k);
vector<T> tmp(k+1);
int sign = 1;
tmp[0] = 1;
FOR(i, 1, k+1) {
sign *= -1;
tmp[i] = tmp[i-1] + sign * ifact[i];
}
T res = 0;
REP(i, k+1) {
res += T(i).pow(n) * ifact[i] * tmp[k-i];
}
return res;
}
vector<vector<T>> partition_table(ll n, ll k) {
assert(n >= 0);
vector<vector<T>> res(n+1, vector<T>(k+1));
REP(i, k+1) res[0][i] = 1;
FOR(i, 1, n+1) FOR(j, 1, k+1) {
res[i][j] = res[i][j-1] + (i<j? 0 : res[i-j][j]);
}
return res;
}
};
#line 2 "library/KowerKoint/bit/bitset.hpp"
struct Bitset {
private:
void correct() {
for(int i = n - (bnum-1)*64; i < 64; i++) {
v[bnum-1] &= ~(1 << i);
}
}
public:
vector<ull> v;
int n, bnum;
Bitset(int n_ = 0) : n(n_) {
bnum = (n+63) / 64;
v.resize(bnum);
}
int operator[](int i) {
return (v[i/64] >> (i%64)) & 1;
}
int count() {
int c = 0;
for (int i = 0; i < v.size(); i++) {
c += __builtin_popcountll(v[i]);
}
return c;
}
int count_range(int l, int r) {
int c = 0;
int l2 = (l+63) / 64;
int r2 = r / 64;
for(int i = l2; i < r2; i++) {
c += __builtin_popcountll(v[i]);
}
if(l < l2 * 64) {
for(int i = l % 64; i < 64; i++) c += (v[l2-1] >> i) & 1;
}
if(r2 * 64 < r) {
for(int i = 0; i < r % 64; i++) c += (v[r2] >> i) & 1;
}
return c;
}
bool all() {
return count() == n;
}
bool any() {
return count() > 0;
}
bool none() {
return count() == 0;
}
void set(int i) {
v[i / 64] |= 1ull << (i % 64);
}
void reset(int i) {
v[i / 64] &= ~(1ull << (i % 64));
}
void flip(int i) {
v[i / 64] ^= 1ull << (i % 64);
}
void resize(int n_) {
n = n_;
v.resize((n+63) / 64);
correct();
}
void all_set() {
fill(v.begin(), v.end(), ~0ULL);
correct();
}
void all_reset() {
fill(v.begin(), v.end(), 0);
}
void all_flip() {
for (int i = 0; i < v.size(); i++) {
v[i] = ~v[i];
}
correct();
}
Bitset& operator&=(const Bitset& b) {
for(int i = 0; i < min(bnum, b.bnum); i++) {
v[i] &= b.v[i];
}
return *this;
}
Bitset operator&(const Bitset& b) const {
return Bitset(*this) &= b;
}
Bitset& operator|=(const Bitset& b) {
for(int i = 0; i < min(bnum, b.bnum); i++) {
v[i] |= b.v[i];
}
correct();
return *this;
}
Bitset operator|(const Bitset& b) const {
return Bitset(*this) |= b;
}
Bitset& operator^=(const Bitset& b) {
for(int i = 0; i < min(bnum, b.bnum); i++) {
v[i] ^= b.v[i];
}
correct();
return *this;
}
Bitset operator^(const Bitset& b) const {
return Bitset(*this) ^= b;
}
Bitset operator~() const {
Bitset b(*this);
b.all_flip();
return b;
}
bool operator==(const Bitset& b) const {
return v == b.v;
}
bool operator!=(const Bitset& b) const {
return v != b.v;
}
Bitset& operator<<=(int sz) {
for(int i = bnum-1; i >= 0; i--) {
if(i-sz/64 >= 0) v[i] = v[i-sz/64] << (sz%64);
if(i-sz/64-1 >= 0) v[i] |= v[i-sz/64-1] >> (64-sz%64);
}
correct();
return *this;
}
Bitset operator<<(int sz) const {
return Bitset(*this) <<= sz;
}
Bitset& operator>>=(int sz) {
for(int i = 0; i < bnum; i++) {
if(i+sz/64 < bnum) v[i] = v[i+sz/64] >> (sz%64);
if(i+sz/64+1 < bnum) v[i] |= v[i+sz/64+1] << (64-sz%64);
}
return *this;
}
Bitset operator>>(int sz) const {
return Bitset(*this) >>= sz;
}
};
#line 3 "Contests/main.cpp"
/* #include <atcoder/all> */
/* using namespace atcoder; */
/* #include "KowerKoint/expansion/ac-library/all.hpp" */
struct Component {
int op_pos;
Bitset cand;
};
int m, ans;
string expr;
map<P, Component> number, factor, term, expression;
void pre_number(int l, int r) {
Bitset b(m+1);
int res = 0;
FOR(i, l, r) {
res *= 10;
res += expr[i] - '0';
}
b.set(res);
number[P(l, r)] = {r, b};
}
void pre_expression(int, int);
void pre_factor(int l, int r) {
if(expr[l] == '(') {
pre_expression(l+1, r-1);
factor[P(l, r)] = {l, expression[P(l+1,r-1)].cand};
} else {
pre_number(l, r);
factor[P(l, r)] = number[P(l, r)];
}
}
void pre_term(int l, int r) {
int p = r-1;
int blace = 0;
while(p >= l && expr[p] != '&' || blace != 0) {
if(expr[p] == ')') blace++;
if(expr[p] == '(') blace--;
p--;
}
if(p == l-1) {
pre_factor(l, r);
term[P(l, r)] = {p, factor[P(l, r)].cand};
} else {
Bitset b(m+1);
pre_term(l, p);
pre_factor(p+1, r);
auto& bi = term[P(l, p)].cand;
auto& bj = factor[P(p+1, r)].cand;
REP(i, m+1) {
if(!bi[i]) continue;
REP(j, m+1) {
if(!bj[j]) continue;
if(i*j <= m) b.set(i*j);
if(j!=0) b.set(i/j);
}
}
term[P(l, r)] = {p, b};
}
}
void pre_expression(int l, int r) {
int p = r-1;
int blace = 0;
while(p >= l && expr[p] != '$' || blace != 0) {
if(expr[p] == ')') blace++;
if(expr[p] == '(') blace--;
p--;
}
if(p == l-1) {
pre_term(l, r);
expression[P(l, r)] = {p, term[P(l, r)].cand};
} else {
Bitset b(m+1);
pre_expression(l, p);
pre_term(p+1, r);
auto& bi = expression[P(l, p)].cand;
auto& bj = term[P(p+1, r)].cand;
REP(i, m+1) {
if(!bi[i]) continue;
REP(j, m+1) {
if(!bj[j]) continue;
if(i+j <= m) b.set(i+j);
if(i-j>=0) b.set(i-j);
}
}
expression[P(l, r)] = {p, b};
}
}
void post_expression(int, int, int);
void post_factor(int l, int r, int target) {
if(factor[P(l, r)].op_pos == l) post_expression(l+1, r-1, target);
}
void post_term(int l, int r, int target) {
int p = term[P(l, r)].op_pos;
if(p == l-1) post_factor(l, r, target);
else {
auto& bi = term[P(l, p)].cand;
auto& bj = factor[P(p+1, r)].cand;
REP(i, m+1) {
if(!bi[i]) continue;
REP(j, m+1) {
if(!bj[j]) continue;
if(i*j == target) {
expr[p] = '*';
post_term(l, p, i);
post_factor(p+1, r, j);
return;
}
if(j!=0&&i/j==target) {
expr[p] = '/';
post_term(l, p, i);
post_factor(p+1, r, j);
return;
}
}
}
}
}
void post_expression(int l, int r, int target) {
int p = expression[P(l, r)].op_pos;
if(p == l-1) post_term(l, r, target);
else {
auto& bi = expression[P(l, p)].cand;
auto& bj = term[P(p+1, r)].cand;
REP(i, m+1) {
if(!bi[i]) continue;
REP(j, m+1) {
if(!bj[j]) continue;
if(i+j == target) {
expr[p] = '+';
post_expression(l, p, i);
post_term(p+1, r, j);
return;
}
if(i-j == target) {
expr[p] = '-';
post_expression(l, p, i);
post_term(p+1, r, j);
return;
}
}
}
}
}
void solve(){
cin >> m >> ans >> expr;
pre_expression(0, expr.size());
if(!expression[P(0, expr.size())].cand[ans]) print(-1);
else {
post_expression(0, expr.size(), ans);
print(expr);
}
}
// generated by oj-template v4.7.2 (https://github.com/online-judge-tools/template-generator)
int main() {
// Fasterize input/output script
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(100);
// scanf/printf user should delete this fasterize input/output script
int t = 1;
//cin >> t; // comment out if solving multi testcase
for(int testCase = 1;testCase <= t;++testCase){
solve();
}
return 0;
}