#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstring>
#include <fstream>
#include <iostream>
#include <unordered_map>
#include <vector>
#ifdef PROFILING
#include <chrono>
#endif
constexpr char INPUT_FILE_NAME[] = "cautbin.in";
constexpr char OUTPUT_FILE_NAME[] = "cautbin.out";
class IO_Base
{
protected:
IO_Base() = default;
virtual ~IO_Base() = default;
// https://cplusplus.com/reference/system_error/errc/
const std::unordered_map<int, std::string> FILE_OPEN_ERROR = {
{ENOENT, "File does not exist."},
{EACCES, "Permission denied."},
{EEXIST, "File already exists."},
{EISDIR, "File is a directory."},
{ENOSPC, "No space left on device."},
{EROFS, "Read-only file system."},
{ETXTBSY, "Text file busy."},
{-1, "Unlisted error type."},
{0, "No error."}
};
virtual void Close_IN() = 0;
virtual void Close_OUT() = 0;
virtual void PrintError(const char* const _file_name,
const int _error_num,
const std::string& _error_source) = 0;
};
class IO final : IO_Base
{
// C++ I/O functions: https://en.cppreference.com/w/cpp/io
protected:
// The Singleton has a private constructor to prevent direct instantiation.
IO(const char input_file_name[], const char output_file_name[])
{
GetInputStream(input_file_name);
GetOutputStream(output_file_name);
}
// The Singleton has a private destructor to prevent deletion.
~IO() override
{
is_instance_destroyed() = true;
Close_IN();
Close_OUT();
}
public:
// Don't make these nullptr. They are not pointers.
std::ifstream IN;
std::ofstream OUT;
// Delete copy constructor. Singletons should not be cloneable.
IO(const IO&) = delete;
// Delete move constructor. Singletons should not be movable.
IO(const IO&&) = delete;
// Delete assignment operator. Singletons should not be assignable.
IO& operator=(const IO&) = delete;
/* Singleton pattern. Only one instance of the class can exist.
* Thread safe: Initialization is guaranteed to happen only once.
* A static member object instance is declared. This object is only created
* the first time the function is called. Static local variables are
* guaranteed to be initialized only once, even in multithreaded environments.
* Subsequent calls to GetInstance() simply return the existing instance object.
* Returning reference instead of pointer further discourages attempts to delete.
*/
static IO& GetInstance(const char input_file_name[], const char output_file_name[])
{
static IO io_Instance(input_file_name, output_file_name);
if (is_instance_destroyed())
{
// We check for The Dead Reference Problem.
// Our singleton is designed to only be destroyed at program termination.
std::cerr << "ERROR: Attempt to access destroyed singleton instance." << std::endl;
assert(false);
}
return io_Instance;
}
private:
static bool& is_instance_destroyed()
{
/* This variable is used to check for The Dead Reference Problem
* by enabling the class to check if its singleton has been destroyed.
*/
static bool is_instance_destroyed = false;
return is_instance_destroyed;
}
void GetInputStream(const char _input_file_name[])
{
IN.open(_input_file_name);
if (!IN.is_open()) // Check if the open operation failed
{
if (IN.fail())
{
PrintError(_input_file_name, errno, "Failed to open input");
assert(IN);
}
if (IN.bad())
{
PrintError(_input_file_name, errno, "Fatal I/O error: bad-bit is set in input");
assert(IN);
}
}
}
void GetOutputStream(const char _output_file_name[])
{
OUT.open(_output_file_name);
if (!OUT.is_open()) // Check if the open operation failed
{
if (OUT.fail())
{
PrintError(_output_file_name, errno, "Failed to open output");
assert(OUT);
}
if (OUT.bad())
{
PrintError(_output_file_name, errno, "Fatal I/O error: bad-bit is set in output");
assert(OUT);
}
}
}
void Close_IN() override final
{
IN.close();
}
void Close_OUT() override final
{
OUT.close();
}
void PrintError(const char* const _file_name,
const int _error_num,
const std::string& _error_source) final override
{
int error_code = -1;
if (FILE_OPEN_ERROR.find(_error_num) != FILE_OPEN_ERROR.end())
{
error_code = _error_num;
}
std::cerr << _error_source << " file: " << _file_name << "\n"
<< "ERROR: " << strerror(errno) << "\n"
<< " " << FILE_OPEN_ERROR.at(error_code) << std::endl;
}
};
#ifdef PROFILING
class Profiling
{
private:
std::chrono::time_point<std::chrono::system_clock> time_begin, time_end;
std::chrono::duration<double, std::nano> duration_nano = std::chrono::nanoseconds(0);
const char* functionName;
const char* comment;
public:
explicit Profiling(const char* _functionName, const char* _comment = "")
: functionName(_functionName), comment(_comment)
{
Begin_Profiling();
}
void Begin_Profiling()
{
time_begin = std::chrono::high_resolution_clock::now();
}
void End_Profiling()
{
time_end = std::chrono::high_resolution_clock::now();
/* Getting number of nanoseconds as a double. */
duration_nano = std::chrono::duration_cast<std::chrono::nanoseconds>(time_end - time_begin);
Show_Profiling_Results();
}
void Show_Profiling_Results() const
{
std::cout << functionName << " : "
<< duration_nano.count() / 1'000'000'000 << "s | "
<< duration_nano.count() / 1'000'000 << "ms | "
<< duration_nano.count() / 1'000 << "\xE6s | "
<< duration_nano.count() << "ns\n"
<< " " << comment << "\n";
}
};
#endif
unsigned int log2_32(uint32_t value)
{
constexpr int tab32[32] = {
0,
9,
1,
10,
13,
21,
2,
29,
11,
14,
16,
18,
22,
25,
3,
30,
8,
12,
20,
28,
15,
17,
24,
7,
19,
27,
23,
6,
26,
5,
4,
31
};
value |= value >> 1;
value |= value >> 2;
value |= value >> 4;
value |= value >> 8;
value |= value >> 16;
return tab32[value * 0x07C4ACDD >> 27];
}
unsigned int binary_search(const std::vector<int>& numbers,
const int _value,
const unsigned int lower_bound,
const unsigned int upper_bound,
unsigned int step)
{
unsigned int index = lower_bound;
while (step)
{
if (index + step <= upper_bound && numbers[index + step] <= _value)
{
index += step;
}
step >>= 1;
}
return index;
}
unsigned int reverse_binary_search(const std::vector<int>& numbers,
const int _value,
const unsigned int lower_bound,
const unsigned int upper_bound,
unsigned int step)
{
unsigned int index = upper_bound;
while (step)
{
if (index >= lower_bound + step && numbers[index - step] >= _value)
{
index -= step;
}
step >>= 1;
}
return index;
}
int main()
{
#ifdef PROFILING
Profiling profiling = Profiling(__PRETTY_FUNCTION__);
#endif
IO& io = IO::GetInstance(INPUT_FILE_NAME, OUTPUT_FILE_NAME);
unsigned int array_size;
io.IN >> array_size; // 1 ≤ array_size ≤ 100 000
std::vector<int> numbers(array_size + 1); // INT_MIN ≤ numbers[i] ≤ INT_MAX; numbers[i] <= numbers[i+1]
for (unsigned int i = 1; i <= array_size; i++)
{
io.IN >> numbers[i];
}
const unsigned int log2_array_size = log2_32(array_size);
const unsigned int max_step = 1 << log2_array_size;
unsigned int queries_count; // 1 ≤ queries_count ≤ 100 000
io.IN >> queries_count;
while (queries_count--)
{
short query_type; // 0 ≤ query_type ≤ 2
int query_value; // INT_MIN ≤ query_value ≤ INT_MAX
io.IN >> query_type >> query_value;
switch (query_type)
{
case 0:
{
// Find the first occurrence of query_value in the array.
// If it exists, return the position of the last occurrence.
// If it doesn't exist, return -1.
const unsigned int position = binary_search(numbers, query_value, 1, array_size, max_step);
if (numbers[position] != query_value)
{
io.OUT << "-1\n";
}
else
{
io.OUT << position << '\n';
}
break;
}
case 1:
{
// Find the last number smaller or equal than query_value.
const unsigned int position = binary_search(numbers, query_value, 1, array_size, max_step);
io.OUT << position << '\n';
break;
}
case 2:
{
// Find the first number greater or equal than query_value.
const unsigned int position = reverse_binary_search(numbers,
query_value,
1,
array_size,
max_step);
io.OUT << position << '\n';
break;
}
default:
{
std::cerr << "ERROR: Invalid query type.\n";
io.OUT << "ERROR: Invalid query type.\n";
assert(false);
}
}
}
#ifdef PROFILING
profiling.End_Profiling();
#endif
return 0;
}