C ++, meledak semua memori pada komputer di dekat Anda
Menghasilkan string terpendek di mana perhitungan tidak menyebabkan limpahan bilangan bulat 32-bit yang ditandatangani (sehingga semua hasil antara berada dalam kisaran [-2147483648, 2147483647]
Pada sistem saya ini menghasilkan solusi untuk semua nomor hingga dan termasuk 483432
dalam 30 detik saat menggunakan memori 1,8G. Bahkan angka yang lebih tinggi akan dengan cepat meledak penggunaan memori. Angka tertinggi yang dapat saya tangani pada sistem saya adalah 5113906
. Perhitungannya memakan waktu hampir 9 menit dan 24GB. Ketika selesai secara internal memiliki solusi untuk 398499338
nilai - nilai, sekitar 9% dari semua integer 32 bit (positif dan negatif)
Membutuhkan kompiler C ++ 11. Di kompilasi linux dengan:
g++ -Wall -O3 -march=native -std=gnu++11 -s befour.cpp -o befour
Tambahkan -DINT64
sebagai opsi untuk menggunakan rentang bilangan bulat 64-bit alih-alih 32-bit untuk hasil antara (ini akan menggunakan sekitar 50% lebih banyak waktu dan memori). Ini membutuhkan tipe 128 bit bawaan. Anda mungkin perlu mengubah jenis gcc __int128
. Tidak ada hasil setidaknya [1..483432]
perubahan rentang dengan memungkinkan hasil antara yang lebih besar.
Tambahkan -DOVERFLOW
sebagai opsi untuk tidak menggunakan tipe integer yang lebih besar untuk memeriksa overflow. Ini memiliki efek memungkinkan pelimpahan dan pembungkus nilai.
Jika sistem Anda memiliki tcmalloc ( https://github.com/gperftools/gperftools ), Anda dapat menautkannya dengan yang menghasilkan program yang umumnya sedikit lebih cepat dan menggunakan sedikit memori. Pada beberapa sistem UNIX Anda dapat menggunakan preload, misalnya
LD_PRELOAD=/usr/lib/libtcmalloc_minimal.so.4 befour 5
Penggunaan dasar: hasilkan dan cetak semua angka hingga target:
befour target
Pilihan:
-a
Juga cetak semua angka yang dihasilkan saat berolahraga target
-c
Juga cetak semua angka yang dihasilkan mulai dengan "carry" (dup)
-f
Temukan dan cetak angka pertama di luar target yang tidak dihasilkan
-s
Hentikan jika target dihasilkan meskipun tidak semua angka sebelumnya dihasilkan
-S
Suka -s
dan -f
dalam loop otomatis. Segera setelah target dihasilkan, temukan nomor pertama yang belum dihasilkan dan buat itu menjadi target baru
-E
Jangan langsung keluar saat tujuan tercapai. Pertama, selesaikan semua string dari panjang saat ini
-O
Jangan tampilkan string untuk semua angka hingga target. hanya string untuk target
-o
Instruksi yang diizinkan (default ke +-*/:
-b num
Literal terendah yang dapat didorong (default ke 0
)
-B num
Literal tertinggi yang dapat didorong (default ke 9
)
-r num
Hasil antara terendah yang diizinkan. Digunakan untuk menghindari underflow. (standarnya adalah INT32_MIN
,-2147483648
-R num
Hasil antara tertinggi yang diizinkan. Digunakan untuk menghindari overflow. (standarnya adalah INT32_MAX
,2147483647
-m memory
(hanya linux) keluar ketika kira-kira banyak memori tambahan ini telah dialokasikan
Beberapa kombinasi opsi yang menarik:
Hasilkan semua angka hingga target dan hitung angka terkecil yang membutuhkan generator lebih lama dari semua angka ini:
befour -fE target
Hasilkan hanya target (-s), cetak hanya target (-O)
befour -sO target
Temukan angka tertinggi yang dapat dihasilkan pada sistem Anda dengan batasan waktu dan / atau memori (Ini akan membuat sistem Anda kehabisan memori jika Anda membiarkannya berjalan. Kurangi 1 dari keluaran "cari" terakhir yang Anda lihat sebagai nilai aman terakhir ):
befour -S 1
Hasilkan solusi tanpa pernah menggunakan hasil antara negatif ( 30932
adalah nilai pertama yang membutuhkan hasil antara negatif untuk string terpendek):
befour -r0 target
Hasilkan solusi tanpa mendorong 0
(sepertinya ini tidak mengarah ke solusi suboptimal):
befour -b1 target
Hasilkan solusi termasuk a..f (10..15)
:
befour -B15 target
Hasilkan solusi tanpa menggunakan dup :
(tambahkan -r0
karena nilai tengah negatif tidak pernah menarik untuk kasus ini)
befour -r0 -o "+-*/" target
Menemukan nilai pertama yang tidak dapat dihasilkan untuk panjang string yang diberikan hanya menggunakan +
, -
, *
dan /
:
befour -ES -r0 -o "+-*/" 1
Ini sebenarnya akan menghasilkan beberapa istilah pertama https://oeis.org/A181898 , tetapi akan mulai menyimpang 14771
karena kami menggunakan divisi pemotongan sehingga angka dapat dilakukan dengan panjang 13 string, bukan panjang 15 sebagai seri OEIS mengharapkan:
14771: 13: 99*9*9*4+9*4/
dari pada
14771: 15: 19+5*6*7*9+7*8+
Karena tanpa pembagian pemotongan tampaknya tidak ada gunanya, seri OEIS dapat dibuat dengan menggunakan
befour -ES -r0 -o"+-*" 1
Dengan asumsi pembagian tetap tidak berguna, ini memberi saya 3 syarat tambahan sebelum saya keluar dari ingatan:
10, 19, 92, 417, 851, 4237, 14771, 73237, 298609, 1346341, 6176426, 25622578
Versi lain dari program ini menyimpan bagian dari data dalam file eksternal menambahkan 135153107 dan 675854293 setelah semua bilangan bulat 32-bit telah dihasilkan.
befour.cpp
/*
Compile using something like:
g++ -Wall -O3 -march=native -std=gnu++11 -s befour.cpp -o befour
*/
#include <iostream>
#include <fstream>
#include <sstream>
#include <stdexcept>
#include <string>
#include <vector>
#include <limits>
#include <climits>
#include <cstdint>
#include <cstdlib>
#include <chrono>
#include <unordered_map>
using namespace std;
#ifdef __GNUC__
# define HOT __attribute__((__hot__))
# define COLD __attribute__((__cold__))
# define NOINLINE __attribute__((__noinline__))
# define LIKELY(x) __builtin_expect(!!(x),1)
# define UNLIKELY(x) __builtin_expect(!!(x),0)
#else // __GNUC__
# define HOT
# define COLD
# define NOINLINE
# define LIKELY(x) (x)
# define UNLIKELY(x) (x)
#endif // __GNUC__
#ifdef INT64
using Int = int64_t; // Supported value type
# ifndef OVERFLOW
using Int2 = __int128; // Do calculations in this type. Check overflow
# endif // OVERFLOW
#else // INT64
using Int = int32_t; // Supported value type
# ifndef OVERFLOW
using Int2 = int64_t; // Do calculations in this type. Check overflow
# endif // OVERFLOW
#endif // INT64
#ifdef OVERFLOW
using Int2 = Int;
#endif // OVERFLOW
// Supported value range
Int2 MIN = numeric_limits<Int>::lowest();
Int2 MAX = numeric_limits<Int>::max();
Int HALF_MIN, HALF_MAX;
// The initial values we can push
Int ATOM_MIN = 0;
Int ATOM_MAX = 9;
bool all = false; // Output all reached values
bool all_carry = false; // Output all values reachable using carry
bool early_exit = true; // Exit before finishing level if goal reached
bool find_hole = false; // Look for first unconstructed > target
bool output = true; // Output [1..target] instead of just target
bool single = false; // Only go for target instead of [1..target]
bool explore = false; // Don't stop, increase N until out of memory
bool do_dup = false; // Use operator :
bool do_multiply= false; // Use operator *
bool do_add = false; // Use operator +
bool do_subtract= false; // Use operator -
bool do_divide = false; // Use operator /
char const* operators = "+-*/:"; // Use these operators
size_t max_mem = SIZE_MAX; // Stop if target memory reached
size_t const MEM_CHECK = 1000000;
chrono::steady_clock::time_point start;
NOINLINE size_t get_memory(bool set_base_mem = false) {
static size_t base_mem = 0;
size_t const PAGE_SIZE = 4096;
// Linux specific. Won't hurt on other systems, just gets no result
size_t mem = 0;
std::ifstream statm;
statm.open("/proc/self/statm");
statm >> mem;
mem *= PAGE_SIZE;
if (set_base_mem) base_mem = mem;
else mem -= base_mem;
return mem;
}
// Handle commandline options.
// Simplified getopt for systems that don't have it in their library (Windows..)
class GetOpt {
private:
string const options;
char const* const* argv;
int nextchar = 0;
int optind = 1;
char ch = '?';
char const* optarg = nullptr;
public:
int ind() const { return optind; }
char const* arg() const { return optarg; }
char option() const { return ch; }
GetOpt(string const options_, char const* const* argv_) :
options(options_), argv(argv_) {}
char next() {
while (1) {
if (nextchar == 0) {
if (!argv[optind] ||
argv[optind][0] != '-' ||
argv[optind][1] == 0) return ch = 0;
if (argv[optind][1] == '-' && argv[optind][2] == 0) {
++optind;
return ch = 0;
}
nextchar = 1;
}
ch = argv[optind][nextchar++];
if (ch == 0) {
++optind;
nextchar = 0;
continue;
}
auto pos = options.find(ch);
if (pos == string::npos) ch = '?';
else if (options[pos+1] == ':') {
if (argv[optind][nextchar]) {
optarg = &argv[optind][nextchar];
} else {
optarg = argv[++optind];
if (!optarg) return ch = options[0] == ':' ? ':' : '?';
}
++optind;
nextchar = 0;
}
return ch;
}
}
};
using ms = chrono::milliseconds;
Int missing, N;
size_t cached, cached_next;
uint8_t const CARRY_MASK = '\x80';
uint8_t const LITERAL = 0;
struct How {
// Describes how to construct a number
Int left;
Int right;
uint8_t ops, op;
How(uint8_t ops_, uint8_t op_, Int carry_=0, Int left_=0, Int right_=0) :
left(left_),
right(right_),
ops(ops_),
op(carry_ ? CARRY_MASK | op_ : op_)
{}
How() = default;
How(How&&) = default;
How& operator=(How&&) = default;
static How const* predict(Int carry, Int value, int& ops);
static void print_predicted(ostream& out, Int carry, Int value, How const* Value = nullptr);
void print(ostream& out, Int carry = 0, bool length = false) const;
};
ostream& operator<<(ostream& out, How const& how) {
how.print(out, 0, true);
return out;
}
using NumSet = vector<Int>;
using NumSets = vector<NumSet>;
struct Known: public unordered_map<Int, How>
{
void store(NumSet& L, Int accu, uint8_t ops, uint8_t op,
Int left=0, Int carry_right=0, Int right=0) {
++cached;
emplace(accu, How(ops, op, carry_right, left, right));
// operator[](accu) = How(ops, op, carry_right, left, right);
L.emplace_back(accu);
}
void maybe_store(Known const& known0, NumSet& L,
Int accu, uint8_t ops, uint8_t op,
Int carry_left, Int left, Int carry_right, Int right) {
if (count(accu)) return;
if (carry_left) {
auto found = known0.find(accu);
// If we can do as good or better without carry use that
if (found != known0.end() && found->second.ops <= ops) return;
}
store(L, accu, ops, op, left, carry_right, right);
if (carry_left) return;
if (single) {
if (UNLIKELY(accu == N)) known0.maybe_explore();
} else if (1 <= accu && accu <= N) --missing;
}
NOINLINE void maybe_explore() const COLD {
--missing;
if (explore && early_exit) do_explore();
}
NOINLINE void do_explore() const COLD {
auto i = N;
while (i < MAX && count(++i));
auto end = chrono::steady_clock::now();
auto elapsed = chrono::duration_cast<ms>(end-start).count();
cerr << "Found " << N << " at " << elapsed / 1000. << " s";
auto mem = get_memory();
if (mem) cerr << " (" << mem / 1000 / 1000. << " MB)";
if (i < MAX || !count(i)) {
cerr << ", now looking for " << i << endl;
N = i;
++missing;
} else
cerr << ", every value has now been generated" << endl;
}
};
struct KnowHow {
// Describes all numbers we know how to construct
NumSets num_sets;
Known known;
KnowHow() = default;
~KnowHow() = default;
KnowHow(KnowHow const&) = delete;
KnowHow& operator=(KnowHow const&) = delete;
};
// Describes all numbers we know how to construct for a given carry
// Key 0 is special: the numbers we can construct without carry (the solutions)
unordered_map<Int, KnowHow> known_how;
// Try to predict if a subtree is a delayed How and avoid descending
// into it (since it may not exist yet)
How const* How::predict(Int carry, Int value, int& ops) {
How* Value;
if (carry) {
if (value == carry) {
Value = nullptr;
ops = 0;
} else {
Value = &known_how.at(carry).known.at(value);
ops = Value->ops;
}
} else {
if (ATOM_MIN <= value && value <= ATOM_MAX) {
Value = nullptr;
ops = 0;
} else {
Value = &known_how.at(0).known.at(value);
ops = Value->ops;
}
}
return Value;
}
void How::print_predicted(ostream& out, Int carry, Int value, How const* Value) {
if (Value) Value->print(out, carry);
else if (carry) out << ":";
else if (value > 9) out << static_cast<char>(value-10+'a');
else out << value;
}
void How::print(ostream& out, Int carry_left, bool length) const {
if (length) out << 2*ops+1 << ": ";
Int carry_right = 0;
auto op_ = op;
switch(op_) {
case LITERAL:
How::print_predicted(out, 0, left);
break;
case '*' | CARRY_MASK:
case '/' | CARRY_MASK:
case '+' | CARRY_MASK:
case '-' | CARRY_MASK:
carry_right = left;
op_ &= ~CARRY_MASK;
// Intentional drop through
case '*':
case '/':
case '+':
case '-':
{
int left_ops, right_ops;
auto Left = How::predict(carry_left, left, left_ops);
// Int right = 0;
auto Right = How::predict(carry_right, right, right_ops);
// Sanity check: tree = left_tree + root + right_tree
if (ops != left_ops + right_ops +1) {
char buffer[80];
snprintf(buffer, sizeof(buffer),
"Broken number %d %c %d, length %d != %d + %d + 1",
static_cast<int>(left), op_, static_cast<int>(right),
ops, left_ops, right_ops);
throw(logic_error(buffer));
}
How::print_predicted(out, carry_left, left, Left);
How::print_predicted(out, carry_right, right, Right);
}
// Intentional drop through
case ':':
out << op_;
break;
default:
throw(logic_error("Unknown op " + string{static_cast<char>(op_)}));
break;
}
}
// carryX indicates Xv was reached using carry. If not we also know [L, known] is known_how[0]
// carryY indicates Y was reached using carry (carryY == Xv if so)
void combine(NumSet& L, Known& known, Known const& known0, int ops, Int carryX, Int2 Xv, Int carryY, NumSet const&Y) HOT;
void combine(NumSet& L, Known& known, Known const& known0, int ops, Int carryX, Int2 Xv, Int carryY, NumSet const&Y) {
for (Int Yv: Y) {
// Yv == 0 can never lead to an optimal calculation
if (Yv == 0) continue;
Int2 accu;
if (do_multiply) {
accu = Xv * Yv;
if (accu <= MAX && accu >= MIN)
known.maybe_store(known0, L, accu, ops, '*', carryX, Xv, carryY, Yv);
}
if (do_add) {
accu = Xv + Yv;
if (accu <= MAX && accu >= MIN)
known.maybe_store(known0, L, accu, ops, '+', carryX, Xv, carryY, Yv);
}
if (do_subtract) {
accu = Xv - Yv;
if (accu <= MAX && accu >= MIN)
known.maybe_store(known0, L, accu, ops, '-', carryX, Xv, carryY, Yv);
}
if (do_divide) {
accu = Xv / Yv;
if (accu <= MAX && accu >= MIN)
known.maybe_store(known0, L, accu, ops, '/', carryX, Xv, carryY, Yv);
}
}
}
// value was constructed using a carry if and only if value != 0
NumSet const& level(KnowHow& known_how0, Int value, int ops) HOT;
NumSet const& level(KnowHow& known_how0, Int value, int ops) {
auto& from_value = known_how[value];
if (from_value.num_sets.size() <= static_cast<size_t>(ops)) {
auto& known = from_value.known;
if (from_value.num_sets.size() != static_cast<size_t>(ops)) {
if (value == 0 || ops != 1)
throw(logic_error("Unexpected level skip"));
// This was because of delayed carry creation.
// The delay is over. Create the base case
from_value.num_sets.resize(ops+1);
known.store(from_value.num_sets[0], value, 0, ':', value);
} else
from_value.num_sets.resize(ops+1);
auto& L = from_value.num_sets[ops];
if (ops == 0) {
if (value) {
known.store(L, value, ops, ':', value);
} else {
for (auto i = ATOM_MIN; i <= ATOM_MAX; ++i) {
if (single) {
if (i == N) --missing;
} else {
if (0 < i && i <= N) --missing;
}
known.store(L, i, 0, LITERAL, i);
}
}
} else {
auto& known0 = known_how0.known;
// for (auto k=ops-1; k>=0; --k) {
for (auto k=0; k<ops; ++k) {
auto const& X = from_value.num_sets[ops-1-k];
auto const& Y = known_how0.num_sets[k];
for (Int Xv: X) {
// Plain combine must come before carry combine so a plain
// solution will prune a same length carry solution
combine(L, known, known0, ops, value, Xv, 0, Y);
if (!missing && early_exit) goto DONE;
if (do_dup && (Xv > ATOM_MAX || Xv < ATOM_MIN)) {
// Dup Xv, construct something using k operators, combine
if (k == 0 && Xv != 0) {
// Delay creation of carry known_how[Xv] for 1 level
// This is purely a memory and speed optimization
// Subtraction gives 0 which is never optimal
// Division gives 1 which is never optimal
// Multiplication gives Xv ** 2
// Could be == Xv if Xv== 0 or Xv == 1, but will be
// pruned by atom - atom or atom / atom
Int2 accu = Xv;
accu *= accu;
if (accu <= MAX && accu >= MIN) {
known.maybe_store(known0, L, accu, ops, '*',
value, Xv, Xv, Xv);
}
// Addition gives Xv * 2 (!= Xv)
if (HALF_MIN <= Xv && Xv <= HALF_MAX)
known.maybe_store(known0, L, 2*Xv, ops, '+',
value, Xv, Xv, Xv);
} else {
auto& Z = level(known_how0, Xv, k);
combine(L, known, known0, ops, value, Xv, Xv, Z);
}
if (!missing && early_exit) goto DONE;
}
if (max_mem != SIZE_MAX && cached > cached_next) {
cached_next = cached + MEM_CHECK;
if (get_memory() >= max_mem) goto DONE;
}
}
}
}
// L.shrink_to_fit();
}
DONE:
return from_value.num_sets[ops];
}
void my_main(int argc, char const* const* argv) {
GetOpt options("acfm:sSEOo:b:B:r:R:", argv);
while (options.next())
switch (options.option()) {
case 'a': all = true; break;
case 'b': {
auto tmp = atoll(options.arg());
ATOM_MIN = static_cast<Int>(tmp);
if (static_cast<long long int>(ATOM_MIN) != tmp)
throw(range_error("ATOM_MIN is out of range"));
break;
}
case 'B': {
auto tmp = atoll(options.arg());
ATOM_MAX = static_cast<Int>(tmp);
if (static_cast<long long int>(ATOM_MAX) != tmp)
throw(range_error("ATOM_MAX is out of range"));
break;
}
case 'c': all_carry = true; break;
case 'f': find_hole = true; break;
case 'm': max_mem = atoll(options.arg()); break;
case 'S': explore = true; // intended drop through to single
case 's': single = true; break;
case 'o': operators = options.arg(); break;
case 'E': early_exit = false; break;
case 'r': {
auto tmp = atoll(options.arg());
MIN = static_cast<Int>(tmp);
if (static_cast<long long int>(MIN) != tmp)
throw(range_error("MIN is out of range"));
break;
}
case 'R': {
auto tmp = atoll(options.arg());
MAX = static_cast<Int>(tmp);
if (static_cast<long long int>(MAX) != tmp)
throw(range_error("MAX is out of range"));
break;
}
case 'O': output = false; break;
default:
cerr << "usage: " << argv[0] << " [-a] [-c] [-f] [-D] [-E] [-O] [-s] [-b atom_min] [-B atom_max] [r range_min] [-R range_max] [-m max_mem] [max]" << endl;
exit(EXIT_FAILURE);
}
// Avoid silly option combinations
if (MIN > MAX) throw(logic_error("MIN above MAX"));
if (ATOM_MIN > ATOM_MAX) throw(logic_error("ATOM_MIN above ATOM_MAX"));
if (ATOM_MIN < 0) throw(range_error("Cannot represent negative atoms"));
if (ATOM_MAX > 35) throw(range_error("Cannot represent atoms > 35"));
if (ATOM_MIN < MIN) throw(range_error("ATOM_MIN is out of range"));
if (ATOM_MAX > MAX) throw(range_error("ATOM_MAX is out of range"));
HALF_MIN = MIN / 2;
HALF_MAX = MAX / 2;
for (auto ops=operators; *ops; ++ops)
switch(*ops) {
case '*': do_multiply = true; break;
case '/': do_divide = true; break;
case '+': do_add = true; break;
case '-': do_subtract = true; break;
case ':': do_dup = true; break;
default:
throw(logic_error("Unknown operator"));
}
long long int const NN =
options.ind() < argc ? atoll(argv[options.ind()]) : 1;
if (NN < MIN || NN > MAX)
throw(range_error("Target number is out of range"));
N = NN;
if (N < 1) {
single = true;
output = false;
}
cerr << "N=" << N << ", using " << sizeof(Int) * CHAR_BIT << " bits without overflow" << endl;
missing = single ? 1 : N;
cached = cached_next = 0;
auto& known_how0 = known_how[0];
auto& known = known_how0.known;
auto mem = get_memory(true);
if (!mem && max_mem != SIZE_MAX)
throw(runtime_error("Cannot get memory usage on this system"));
// Start calculation
start = chrono::steady_clock::now();
// Fill in initial values [0..9]
level(known_how0, 0, 0);
// Grow number of allowed operations until all requested numbers are reached
// for (auto ops=1; ops <=5; ++ops) {
for (auto ops=1;;++ops) {
if (missing == 0) {
if (!explore) break;
known_how0.known.do_explore();
if (missing == 0) break;
}
if (max_mem != SIZE_MAX && get_memory() >= max_mem) break;
auto end = chrono::steady_clock::now();
auto elapsed = chrono::duration_cast<ms>(end-start).count();
cerr << "Reaching for " << 2*ops+1 << " instructions at " << elapsed/1000. << " s";
if (mem) cerr << " (" << get_memory() / 1000 / 1000. << " MB)";
cerr << endl;
auto old_cached = cached;
level(known_how0, 0, ops);
if (cached == old_cached) {
cerr << "Oops, all possible numbers have been generated and we still weren't finished" << endl;
break;
}
}
// We are done generating all numbers.
auto end = chrono::steady_clock::now();
// Report the result
// length = 2*ops + 1
Int limit = known_how0.num_sets.size()*2-1;
cerr << "Some numbers needed " << limit << " instructions" << endl;
auto elapsed = chrono::duration_cast<ms>(end-start).count();
start = end;
stringstream out;
out << "Calculation: " << elapsed/1000. << " s\n";
for (auto i = output ? 1 : N; i <= N; ++i) {
if (single || missing) {
auto got = known.find(i);
if (got != known.end())
cout << i << ": " << got->second << "\n";
else
cout << i << " not generated\n";
} else
cout << i << ": " << known.at(i) << "\n";
}
if (output) {
end = chrono::steady_clock::now();
elapsed = chrono::duration_cast<ms>(end-start).count();
start = end;
out << "Printing: " << elapsed/1000. << " s\n";
}
if (find_hole) {
Int hole;
for (auto i = single ? 1 : N+1; 1; ++i) {
if (!known_how0.known.count(i) || i == 0) {
hole = i;
break;
}
}
out << "First missing value " << hole << "\n";
end = chrono::steady_clock::now();
elapsed = chrono::duration_cast<ms>(end-start).count();
start = end;
out << "Missing: " << elapsed/1000. << " s\n";
}
if (all) {
for (auto const& entry: known_how0.known) {
cout << entry.first << ": " << entry.second << "\n";
}
end = chrono::steady_clock::now();
elapsed = chrono::duration_cast<ms>(end-start).count();
start = end;
out << "All: " << elapsed/1000. << " s\n";
}
if (all_carry) {
for (auto const& carry: known_how) {
auto carry_left = carry.first;
if (carry_left == 0) continue;
cout << "Carry " << carry_left << "\n";
for (auto const& how: carry.second.known) {
cout << " " << how.first << ": ";
how.second.print(cout, carry_left, true);
cout << "\n";
}
}
end = chrono::steady_clock::now();
elapsed = chrono::duration_cast<ms>(end-start).count();
start = end;
out << "All carry: " << elapsed/1000. << " s\n";
}
mem = get_memory();
if (mem) cerr << "used about " << mem / 1000 / 1000. << " MB\n";
cerr << out.str();
cerr << "Cached " << cached << " results = " << known.size() << " plain + " << cached - known.size() << " carry" << endl;
}
int main(int argc, char const* const* argv) {
try {
my_main(argc, argv);
} catch(exception& e) {
cerr << "Error: " << e.what() << endl;
quick_exit(EXIT_FAILURE);
}
// Cleaning up the datastructures can take ages
quick_exit(EXIT_SUCCESS);
}
Beberapa test case:
1: 1: 1
11: 3: 29+
26: 5: 29*8+
27: 3: 39*
100: 5: 19+:*
2431: 9: 56*9*9*1+
3727: 9: 69*7+:*6+
86387: 11: 67*:*1-7*7*
265729: 11: 39*:*:*2/9+
265620: 13: 99*::*6/*7+3*
1921600: 9: 77*:*:*3/
21523360: 9: 99*:*:*2/
57168721: 11: 99*6+:*8-:*
30932: 11: 159*-:4*:*+
56
langsung ke stack, bagaimana kita bisa mendorong78
ke stack?