算法竞赛入门经典 习题6-12

UVa810

A Dicey Problem

一个迷宫里有一骰子，骰子可以上下左右移动的条件是相邻格中的数字和骰子朝上面的数字相同，或者相邻格子中为*。求一条从起点出发，最终回到起点的路径。

深搜和广搜应该都可解，试了下深搜超时了，不得已改成广搜。但是广搜也需要记录状态，否则还是会超时。

这道题另外麻烦的地方是骰子的滚动，只能通过空间想象进行硬编码。

#include <iostream>
#include <array>
#include <deque>
#include <set>
#include <string>
#include <vector>

using namespace std;

struct Dice
{
	static const array<int, 7> opposite;
	static const vector<vector<int>> LeftRotation;
	int top, facing;
	Dice(int top, int facing) : top(top), facing(facing) {}
	void up()
	{
		int opp = opposite[top];
		top = facing;
		facing = opp;
	}
	void down()
	{
		int opp = opposite[facing];
		facing = top;
		top = opp;
	}
	void left()
	{
		top = LeftRotation[facing - 1][top - 1];
	}
	void right()
	{
		top = opposite[LeftRotation[facing - 1][top - 1]];
	}
	int state() const
	{
		return top * 10 + facing;
	}
};

const array<int, 7> Dice::opposite = { 0, 6, 5, 4, 3, 2 ,1 };

const vector<vector<int>> Dice::LeftRotation = {
	{ -1, 4, 2 ,5, 3, -1 },
	{ 3, -1, 6, 1, -1, 4 },
	{ 5, 1, -1, -1, 6, 2 },
	{ 2, 6, -1, -1, 1, 5 },
	{ 4, -1, 1, 6, -1, 3 },
	{ -1, 3, 5, 2, 4, -1 }
};

struct Node
{
	Dice dice;
	size_t row, col;
	vector<pair<size_t, size_t>> path;
	Node(const Dice &dice, size_t row, size_t col) : dice(dice), row(row), col(col)
	{
		path.push_back(make_pair(row, col));
	}
	void up()
	{
		dice.up();
		row--;
		path.push_back(make_pair(row, col));
	}
	void down()
	{
		dice.down();
		row++;
		path.push_back(make_pair(row, col));
	}
	void left()
	{
		dice.left();
		col--;
		path.push_back(make_pair(row, col));
	}
	void right()
	{
		dice.right();
		col++;
		path.push_back(make_pair(row, col));
	}
};

class Solution
{
public:
	Solution(const string &name, const vector<vector<int>> &maze, size_t StartRow, size_t StartCol, int top, int facing)
		: name(name), maze(maze), EndRow(StartRow), EndCol(StartCol), dice(top, facing),
		states(maze.size(), vector<set<int>>(maze[0].size()))
	{
		deque<Node> deq;
		deq.emplace_back(dice, StartRow, StartCol);
		while (!deq.empty()) {
			Node curr = deq.front();
			deq.pop_front();
			if (curr.path.size() != 1 && curr.row == EndRow && curr.col == EndCol) {
				path = curr.path;
				break;
			}
			if (curr.row > 0 && movable(curr.row - 1, curr.col, curr.dice)) {
				Node node = curr;
				node.up();
				if(!visiting(node)) {
					deq.push_back(node);
				}
			}
			if (curr.row + 1 < maze.size() && movable(curr.row + 1, curr.col, curr.dice)) {
				Node node = curr;
				node.down();
				if (!visiting(node)) {
					deq.push_back(node);
				}
			}
			if (curr.col > 0 && movable(curr.row, curr.col - 1, curr.dice)) {
				Node node = curr;
				node.left();
				if (!visiting(node)) {
					deq.push_back(node);
				}
			}
			if (curr.col + 1 < maze[0].size() && movable(curr.row, curr.col + 1, curr.dice)) {
				Node node = curr;
				node.right();
				if (!visiting(node)) {
					deq.push_back(node);
				}
			}
		}
	}
	void print(ostream &os)
	{
		os << name;
		if (path.empty()) {
			os << "\n  No Solution Possible";
		}
		else {
			for (size_t i = 0; i < path.size() - 1; i++)
			{
				if (i % 9 == 0) {
					os << "\n  ";
				}
				cout << '(' << path[i].first + 1 << ',' << path[i].second + 1 << "),";
			}
			cout << '(' << path.back().first + 1 << ',' << path.back().second + 1 << ")";
		}
		os << endl;
	}
private:
	string name;
	vector<vector<int>> maze;
	size_t EndRow, EndCol;
	Dice dice;
	vector<vector<set<int>>> states;
	vector<pair<size_t, size_t>> path;
	bool movable(size_t row, size_t col, const Dice &dice)
	{
		return maze[row][col] == -1 || maze[row][col] == dice.top;
	}
	bool visiting(const Node &node)
	{
		set<int> &state = states[node.row][node.col];
		bool found = state.find(node.dice.state()) != state.end();
		state.insert(node.dice.state());
		return found;
	}
};

int main()
{
	string name;
	while (cin >> name) {
		if (name == "END") break;
		size_t row, col, sr, sc;
		int top, facing;
		cin >> row >> col >> sr >> sc >> top >> facing;
		vector<vector<int>> maze(row, vector<int>(col, 0));
		for (size_t i = 0; i < row; i++)
		{
			for (size_t j = 0; j < col; j++)
			{
				cin >> maze[i][j];
			}
		}
		Solution solution(name, maze, sr - 1, sc - 1, top, facing);
		solution.print(cout);
	}
	return 0;
}
/*
DICEMAZE1
3 3 1 2 5 1
-1 2 4
5 5 6
6 -1 -1
DICEMAZE2
4 7 2 6 3 6
6 4 6 0 2 6 4
1 2 -1 5 3 6 1
5 3 4 5 6 4 2
4 1 2 0 3 -1 6
DICEMAZE3
3 3 1 1 2 4
2 2 3
4 5 6
-1 -1 -1
END
*/