Fusão de fogos de artifício

C ++

Comprimento total: 9059, Área total: 27469, Falhas: 13.

Nota: A pontuação inclui penalidades por falha.

Saída de amostra:

a 6 b 8 c 11 d 11 e 11 f 11 g 12 h 15 i 18 j 18 k 21 l 23 m 26 n 28 o 28 p 30 q 32 r 33 s 33 t 34 
------ae  
     | |  
     |---c
     b||-g
      |d| 
      f | 
    i---| 
  k---| h 
   |  j   
   |---m  
   l  | t 
     o-n| 
      |s-r
      |-| 
      p q 
Length: 39, Area: 150.

a 6 b 6 c 6 d 6 e 6 f 6 g 6 h 8 i 9 j 9 k 9 l 12 m 12 n 13 o 14 p 15 q 15 r 15 s 17 t 17 u 17 v 17 w 17 x 20 y 23 z 26 
------a  n|--w 
|d-||---k|-o|  
| g|b  |--m --x
|-|c    ||--r| 
||f     l|-q | 
||--j u--|--s|-
e|-i    |p|  y|
 h      v t  z-
Length: 56, Area: 120.

Saída completa: http://pastebin.com/raw.php?i=spBUidBV

Você não adora soluções de força bruta? Isso é um pouco mais do que um simples algoritmo de retorno: nosso trabalhador incansável se move pelo mapa, colocando fusíveis e fogos de artifício conforme necessário, enquanto testa todos os movimentos possíveis a qualquer momento. Bem, quase --- restringimos o conjunto de movimentos e abandonamos cedo os estados não ideais, para que não demore insuportavelmente longo (e, em particular, para que termine.) É necessário um cuidado especial para não criar ciclos ou intencionalmente caminhos e não voltar da mesma maneira que viemos, por isso é garantido que não visitemos o mesmo estado duas vezes. Mesmo assim, encontrar uma solução ideal pode demorar um pouco, por isso, desistimos de otimizar uma solução se demorar muito.

Este algoritmo ainda tem algum espaço livre. Por um lado, é possível encontrar melhores soluções aumentando os FRUSTRATIONparâmetros. Não existe caixa eletrônico concorrente, mas esses números podem ser aumentados se e quando ...

Compilar com: g++ fireworks.cpp -ofireworks -std=c++11 -pthread -O3.

Corra com: ./fireworks.

Lê a entrada de STDIN e grava a saída em STDOUT (possivelmente fora de ordem.)

/* Magic numbers */
#define THREAD_COUNT 2
/* When FRUSTRATION_MOVES moves have passed since the last solution was found,
 * the last (1-FRUSTRATION_STATES_BACKOFF)*100% of the backtracking states are
 * discarded and FRUSTRATION_MOVES is multiplied by FRUSTRATION_MOVES_BACKOFF.
 * The lower these values are, the faster the algorithm is going to give up on
 * searching for better solutions. */
#define FRUSTRATION_MOVES 1000000
#define FRUSTRATION_MOVES_BACKOFF 0.8
#define FRUSTRATION_STATES_BACKOFF 0.5

#include <iostream>
#include <vector>
#include <algorithm>
#include <utility>
#include <thread>
#include <mutex>
#include <string>
#include <sstream>
#include <cassert>

using namespace std;

/* A tile on the board. Either a fuse, a firework, an empty tile or an
 * out-of-boudns tile. */
struct tile {
    /* The tile's value, encoded the "obvious" way (i.e. '-', '|', 'a', etc.)
     * Empty tiles are encoded as '\0' and OOB tiles as '*'. */
    char value;
    /* For fuse tiles, the time at which the fuse is lit. */
    int time;

    operator char&() { return value; }
    operator const char&() const { return value; }

    bool is_fuse() const { return value == '-' || value == '|'; }
    /* A tile is vacant if it's empty or OOB. */
    bool is_vacant() const { return !value || value == '*'; }

    /* Prints the tile. */
    template <typename C, typename T>
    friend basic_ostream<C, T>& operator<<(basic_ostream<C, T>& os,
                                            const tile& t) {
        return os << (t.value ? t.value : ' ');
    }
};
/* Fireworks have the same encoding as tiles. */
typedef tile firework;
typedef vector<firework> fireworks;

/* The fuse map. It has physical dimensions (its bounding-box) but is
 * conceptually infinite (filled with empty tiles.) */
class board {
    /* The tiles, ordered left-to-right top-to-bottom. */
    vector<tile> p_data;
    /* The board dimensions. */
    int p_width, p_height;
    /* The total fuse length. */
    int p_length;

public:
    board(): p_width(0), p_height(0), p_length(0) {}

    /* Physical dimensions. */
    int width() const { return p_width; }
    int height() const { return p_height; }
    int area() const { return width() * height(); }
    /* Total fuse length. */
    int length() const { return p_length; }

    /* Returns the tile at (x, y). If x or y are negative, returns an OOB
     * tile. */
    tile get(int x, int y) const {
        if (x < 0 || y < 0)
            return {'*'};
        else if (x >= width() || y >= height())
            return {'\0'};
        else
            return p_data[y * width() + x];
    }
    /* Sets the tile at (x, y). x and y must be nonnegative and the tile at
     * (x, y) must be empty. */
    board& set(int x, int y, const tile& t) & {
        assert(x >= 0 && y >= 0);
        assert(!get(x, y));
        if (x >= width() || y >= height()) {
            int new_width = x >= width() ? x + 1 : width();
            int new_height = y >= height() ? y + 1 : height();
            vector<tile> temp(new_width * new_height, {'\0'});
            for (int l = 0; l < height(); ++l)
                copy(
                    p_data.begin() + l * width(),
                    p_data.begin() + (l + 1) * width(),
                    temp.begin() + l * new_width
                );
            p_data.swap(temp);
            p_width = new_width;
            p_height = new_height;
        }
        p_data[y * width() + x] = t;
        if (t.is_fuse())
            ++p_length;
        return *this;
    }
    board&& set(int x, int y, const tile& t) && { return move(set(x, y, t)); }

    /* Prints the board. */
    template <typename C, typename T>
    friend basic_ostream<C, T>& operator<<(basic_ostream<C, T>& os,
                                            const board& b) {
        for (int y = 0; y < b.height(); ++y) {
            for (int x = 0; x < b.width(); ++x)
                os << b.get(x, y);
            os << endl;
        }
        return os;
    }
};

/* A state of the tiling algorithm. */
struct state {
    /* The current board. */
    board b;
    /* The next firework to tile. */
    fireworks::const_iterator fw;
    /* The current location. */
    int x, y;
    /* The current movement direction. 'N'orth 'S'outh 'E'ast, 'W'est or
     * 'A'ny. */
    char dir;
};

/* Adds a state to the state-stack if its total fuse length and bounding-box
 * area are not worse than the current best ones. */
void add_state(vector<state>& states, int max_length, int max_area,
                state&& new_s) {
    if (new_s.b.length() < max_length ||
        (new_s.b.length() == max_length && new_s.b.area() <= max_area)
    )
        states.push_back(move(new_s));
}
/* Adds the state after moving in a given direction, if it's a valid move. */
void add_movement(vector<state>& states, int max_length, int max_area,
                    const state& s, char dir) {
    int x = s.x, y = s.y;
    char parallel_fuse;
    switch (dir) {
    case 'E': if (s.dir == 'W') return; ++x; parallel_fuse = '|'; break;
    case 'W': if (s.dir == 'E') return; --x; parallel_fuse = '|'; break;
    case 'S': if (s.dir == 'N') return; ++y; parallel_fuse = '-'; break;
    case 'N': if (s.dir == 'S') return; --y; parallel_fuse = '-'; break;
    }
    const tile t = s.b.get(s.x, s.y), nt = s.b.get(x, y);
    assert(t.is_fuse());
    if (nt.is_fuse() && !(t == parallel_fuse && nt == parallel_fuse))
        add_state(states, max_length, max_area, {s.b, s.fw, x, y, dir});
}
/* Adds the state after moving in a given direction and tiling a fuse, if it's a
 * valid move. */
void add_fuse(vector<state>& states, int max_length, int max_area,
                const state& s, char dir, char fuse) {
    int x = s.x, y = s.y;
    int sgn;
    bool horz;
    switch (dir) {
    case 'E': ++x; sgn = 1; horz = true; break;
    case 'W': --x; sgn = -1; horz = true; break;
    case 'S': ++y; sgn = 1; horz = false; break;
    case 'N': --y; sgn = -1; horz = false; break;
    }
    if (s.b.get(x, y))
        /* Tile is not empty. */
        return;
    /* Make sure we don't create cycles or reconnect a firework. */
    const tile t = s.b.get(s.x, s.y);
    assert(t.is_fuse());
    if (t == '-') {
        if (horz) {
            if (fuse == '-') {
                if (!s.b.get(x + sgn, y).is_vacant() ||
                    s.b.get(x, y - 1) == '|' ||
                    s.b.get(x, y + 1) == '|')
                    return;
            } else {
                if (s.b.get(x + sgn, y) == '-' ||
                    !s.b.get(x, y - 1).is_vacant() ||
                    !s.b.get(x, y + 1).is_vacant())
                    return;
            }
        } else {
            if (!s.b.get(x, y + sgn).is_vacant() ||
                s.b.get(x - 1, y) == '-' ||
                s.b.get(x + 1, y) == '-')
                return;
        }
    } else {
        if (!horz) {
            if (fuse == '|') {
                if (!s.b.get(x, y + sgn).is_vacant() ||
                    s.b.get(x - 1, y) == '-' ||
                    s.b.get(x + 1, y) == '-')
                    return;
            } else {
                if (s.b.get(x, y + sgn) == '|' ||
                    !s.b.get(x - 1, y).is_vacant() ||
                    !s.b.get(x + 1, y).is_vacant())
                    return;
            }
        } else {
            if (!s.b.get(x + sgn, y).is_vacant() ||
                s.b.get(x, y - 1) == '|' ||
                s.b.get(x, y + 1) == '|')
                return;
        }
    }
    /* Ok. */
    add_state(
        states,
        max_length,
        max_area,
        {board(s.b).set(x, y, {fuse, t.time + 1}), s.fw, x, y, dir}
    );
}
/* Adds the state after adding a firework at the given direction, if it's a
 * valid move. */
void add_firework(vector<state>& states, int max_length, int max_area,
                    const state& s, char dir) {
    int x = s.x, y = s.y;
    int sgn;
    bool horz;
    switch (dir) {
    case 'E': ++x; sgn = 1; horz = true; break;
    case 'W': --x; sgn = -1; horz = true; break;
    case 'S': ++y; sgn = 1; horz = false; break;
    case 'N': --y; sgn = -1; horz = false; break;
    }
    if (s.b.get(x, y))
        /* Tile is not empty. */
        return;
    /* Make sure we don't run into an undeliberate fuse. */
    if (horz) {
        if (s.b.get(x + sgn, y) == '-' || s.b.get(x, y - 1) == '|' ||
            s.b.get(x, y + 1) == '|')
            return;
    } else {
        if (s.b.get(x, y + sgn) == '|' || s.b.get(x - 1, y) == '-' ||
            s.b.get(x + 1, y) == '-')
            return;
    }
    /* Ok. */
    add_state(
        states,
        max_length,
        max_area,
        /* After adding a firework, we can move in any direction. */
        {board(s.b).set(x, y, {*s.fw}), s.fw + 1, s.x, s.y, 'A'}
    );
}
void add_possible_moves(vector<state>& states, int max_length, int max_area,
                        const state& s) {
    /* We add the new states in reverse-desirability order. The most
     * (aesthetically) desirable states are added last. */

    const tile t = s.b.get(s.x, s.y);
    assert(t.is_fuse());

    /* Move in all (possible) directions. */
    for (char dir : "WENS")
        if (dir) add_movement(states, max_length, max_area, s, dir);

    /* If the fuse is too short for the next firework, keep adding fuse. */
    if (t.time < s.fw->time) {
        if (t == '-') {
            add_fuse(states, max_length, max_area, s, 'N', '|');
            add_fuse(states, max_length, max_area, s, 'S', '|');
            add_fuse(states, max_length, max_area, s, 'W', '|');
            add_fuse(states, max_length, max_area, s, 'W', '-');
            add_fuse(states, max_length, max_area, s, 'E', '|');
            add_fuse(states, max_length, max_area, s, 'E', '-');
        } else {
            add_fuse(states, max_length, max_area, s, 'W', '-');
            add_fuse(states, max_length, max_area, s, 'E', '-');
            add_fuse(states, max_length, max_area, s, 'N', '-');
            add_fuse(states, max_length, max_area, s, 'N', '|');
            add_fuse(states, max_length, max_area, s, 'S', '-');
            add_fuse(states, max_length, max_area, s, 'S', '|');
        }
    } else if (t.time == s.fw->time) {
        /* If we have enough fuse for the next firework, place the firework (if
         * possible) and don't add more fuse, or else we'll never finish... */
        if (t == '-') {
            add_firework(states, max_length, max_area, s, 'W');
            add_firework(states, max_length, max_area, s, 'E');
        } else {
            add_firework(states, max_length, max_area, s, 'N');
            add_firework(states, max_length, max_area, s, 'S');
        }
    }
}

void thread_proc(mutex& lock, int& total_length, int& total_area,
                    int& failures) {
    fireworks fw;
    vector<state> states;

    while (true) {
        /* Read input. */
        string input;
        {
            lock_guard<mutex> lg(lock);

            while (!cin.eof() && input.empty())
                getline(cin, input);
            if (input.empty())
                break;
        }
        fw.clear();
        int length = 0, area;
        {
            stringstream is;
            is << input;
            while (!is.eof()) {
                char c;
                int t;
                if (is >> c >> t) {
                    /* Fireworks must be sorted by launch time. */
                    assert(fw.empty() || t >= fw.back().time);
                    fw.push_back({c, t});
                    length += t;
                }
            }
            assert(!fw.empty());
            area = fw.back().time * fw.back().time;
        }

        /* Add initial state. */
        states.push_back({board().set(0, 0, {'-', 1}), fw.begin(), 0, 0, 'A'});

        board solution;
        int moves = 0;
        int frustration_moves = FRUSTRATION_MOVES;

        while (!states.empty()) {
            /* Check for solutions (all fireworks consumed.) */
            while (!states.empty() && states.back().fw == fw.end()) {
                state& s = states.back();
                /* Did we find a better solution? */
                if (solution.area() == 0 || s.b.length() < length ||
                    (s.b.length() == length && s.b.area() < area)
                ) {
                    solution = move(s.b);
                    moves = 0;
                    length = solution.length();
                    area = solution.area();
                }
                states.pop_back();
            }

            /* Expand the top state. */
            if (!states.empty()) {
                state s = move(states.back());
                states.pop_back();
                add_possible_moves(states, length, area, s);
            }

            /* Getting frustrated? */
            ++moves;
            if (moves > frustration_moves) {
                /* Get rid of some data. */
                states.erase(
                    states.begin() + states.size() * FRUSTRATION_STATES_BACKOFF,
                    states.end()
                );
                frustration_moves *= FRUSTRATION_MOVES_BACKOFF;
                moves = 0;
            }
        }

        /* Print solution. */
        {
            lock_guard<mutex> lg(lock);

            cout << input << endl;

            if (solution.area())
                cout << solution;
            else {
                cout << "FAILED!" << endl;
                ++failures;
            }

            cout << "Length: " << length <<
                    ", Area: " << area <<
                    "." << endl << endl;
            total_length += length;
            total_area += area;
        }
    }
}

int main(int argc, const char* argv[]) {
    thread threads[THREAD_COUNT];
    mutex lock;
    int total_length = 0, total_area = 0, failures = 0;

    for (int i = 0; i < THREAD_COUNT; ++i)
        threads[i] = thread(thread_proc, ref(lock), ref(total_length),
                            ref(total_area), ref(failures));
    for (int i = 0; i < THREAD_COUNT; ++i)
        threads[i].join();

    cout << "Total Length: " << total_length <<
            ", Total Area: " << total_area <<
            ", Failures: " << failures <<
            "." << endl;
}

Pitão

Comprimento total: 17387, Área total: 62285, Falhas: 44.

Saída de amostra:

a 6 b 8 c 11 d 11 e 11 f 11 g 12 h 15 i 18 j 18 k 21 l 23 m 26 n 28 o 28 p 30 q 32 r 33 s 33 t 34
------a                
     |----f            
     |---c             
     b|||---h          
      |dg  |           
      e    |-j         
           |---k       
           i  |        
              |---m    
              l  |-o   
                 |--p  
                 n |--s
                   |-r 
                   q|  
                    t  
Length: 45, Area: 345.

Saída completa: http://pastebin.com/raw.php?i=mgiqXCRK

Para referência, aqui está uma abordagem muito mais simples. Ele tenta conectar fogos de artifício a uma única linha de fusível principal, criando uma forma de "escada". Se um fogo de artifício não puder se conectar diretamente à linha principal (o que acontece quando dois ou mais fogos de artifício acendem ao mesmo tempo), ele rastreia a linha principal procurando um ponto em que possa se ramificar perpendicularmente para baixo ou para a direita (e falha se esse ponto não existe.)

Sem surpresa, ele é pior que o solucionador de força bruta, mas não por uma margem enorme . Honestamente, eu esperava que a diferença fosse um pouco maior.

Corra com: python fireworks.py.

from __future__ import print_function
import sys

total_length = total_area = failures = 0

for line in sys.stdin:
    # Read input.
    line = line.strip()
    if line == "": continue
    fws = line.split(' ')
    # The fireworks are a list of pairs of the form (<letter>, <time>).
    fws = [(fws[i], int(fws[i + 1])) for i in xrange(0, len(fws), 2)]

    # The board is a dictionary of the form <coord>: <tile>.
    # The first tile marks the "starting point" and is out-of-bounds.
    board = {(-1, 0): '*'}
    # The tip of the main "staircase" fuse.
    tip_x, tip_y = -1, 0
    tip_time = 0
    # We didn't fail. Yet...
    failed = False

    for (fw, fw_time) in fws:
        dt = fw_time - tip_time
        # Can we add the firework to the main fuse line?
        if dt > 0:
            # We can. Alternate the direction to create a "staircase" pattern.
            if board[(tip_x, tip_y)] == '-':    dx, dy = 0, 1; fuse = '|'
            else:                               dx, dy = 1, 0; fuse = '-'
            x, y = tip_x, tip_y
            tip_x += dt * dx
            tip_y += dt * dy
            tip_time += dt
        else:
            # We can't. Trace the main fuse back until we find a point where we
            # can thread, or fail if we reach the starting point.
            x, y = tip_x, tip_y
            while board[(x, y)] != '*':
                horz = board[(x, y)] == '-'
                if horz:    dx, dy = 0, 1; fuse = '|'
                else:       dx, dy = 1, 0; fuse = '-'
                if dt > 0 and (x + dx, y + dy) not in board: break
                if horz:    x -= 1
                else:       y -= 1
                dt += 1
            if board[(x, y)] == '*':
                failed = True
                break
        # Add the fuse and firework.
        for i in xrange(dt):
            x += dx; y += dy
            board[(x, y)] = fuse
        board[(x + dx, y + dy)] = fw

    # Print output.
    print(line)
    if not failed:
        max_x, max_y = (max(board, key=lambda p: p[i])[i] + 1 for i in (0, 1))
        for y in xrange(max_y):
            for x in xrange(max_x):
                print(board.get((x, y), ' '), end = "")
            print()
        length = len(board) - len(fws) - 1
        area = max_x * max_y
    else:
        print("FAILED!")
        failures += 1
        length = sum(map(lambda fw: fw[1], fws))
        area = fws[-1][1] ** 2
    print("Length: %d, Area: %d.\n" % (length, area))
    total_length += length; total_area += area

print("Total Length: %d, Total Area: %d, Failures: %d." %
        (total_length, total_area, failures))

DarwinBot
fonte

Por curiosidade, quanto tempo leva para concluir com os parâmetros atuais?

Geobits

@ Geobits: Depende da máquina, obviamente, e eu não assisti muito de perto, mas penso em vinte minutos, mais ou menos.

precisa saber é o seguinte

Fusão de fogos de artifício

Visão geral

Desafio

Casos de teste

Respostas:

C ++

Comprimento total: 9059, Área total: 27469, Falhas: 13.

Pitão

Comprimento total: 17387, Área total: 62285, Falhas: 44.