八数码问题 Eight Digital Problem

Posted 2020-10-14 冯煜博

八数码问题

利用启发式搜索，找出以下问题的最优解。

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

const int BLANK = 0;
const int R = 3;
const int C = 3;


pair<int, int> find_blank(const vector<vector<int>> &m) {
	for (int r = 0; r < m.size(); r++) {
		for (int c = 0; c < m[r].size(); c++) {
			if (m[r][c] == BLANK) {
				return make_pair(r, c);
			}
		}
	}
	return make_pair(-1, -1);
}

vector<pair<int, int>> address_derive(const pair<int, int> &father) {
	vector<pair<int, int>> addresses;
	const int r = father.first, c = father.second;
	if (r - 1 >= 0) {
		addresses.push_back(make_pair(r - 1, c));
	}
	if (r + 1 < R) {
		addresses.push_back(make_pair(r + 1, c));
	}
	if (c - 1 >= 0) {
		addresses.push_back(make_pair(r, c - 1));
	}
	if (c + 1 < C) {
		addresses.push_back(make_pair(r, c + 1));
	}
	return addresses;
}

vector<vector<vector<int>>> matrix_derive(const vector<vector<int>> &father) {
	vector<vector<vector<int>>> matrices;
	pair<int, int> address = find_blank(father);
	vector<pair<int, int>> addresses = address_derive(address);
	for (const auto e : addresses) {
		int r = e.first, c = e.second;
		vector<vector<int>> son = father;
		swap(son[address.first][address.second], son[r][c]);
		matrices.push_back(son);
	}
	return matrices;
}

int evaluate(const vector<vector<int>> &m, const vector<vector<int>> &goal) {
	int difference = 0;
	for (int r = 0; r < goal.size(); r++) {
		for (int c = 0; c < goal[r].size(); c++) {
			if (goal[r][c] == BLANK) {
				continue;
			}
			difference = m[r][c] != goal[r][c] ? difference + 1 : difference;
		}
	}
	return difference;
}

struct Block {
	int g;
	int h;
	vector<vector<int>> m;
	Block(int g = 0, int h = 0, vector<vector<int>> m = vector<vector<int>>())
		:g(g), h(h), m(m) {};
};

void print(const Block &b) {
	for (const auto r : b.m) {
		for (const auto c : r) {
			cout << c << " ";
		}
		cout << endl;
	}
	cout << b.g << " " << b.h << endl;
	cout << endl;
}

bool in_close(const vector<vector<vector<int>>> &close, const vector<vector<int>> &m) {
	for (auto e : close) {
		if (e == m) {
			return true;
		}
	}
	return false;
}

bool in_open(const vector<Block> &open, const vector<vector<int>> &m) {
	for (auto e : open) {
		if (e.m == m) {
			return true;
		}
	}
	return false;
}

void search(const vector<vector<int>> &begin, const vector<vector<int>> &goal) {
	vector<Block> open;
	vector<vector<vector<int>>> close;
	open.push_back(Block(0, evaluate(begin, goal), begin));
	int g = 0;
	while (open.size()){
		sort(open.begin(), open.end(), [](const Block &lhs, const Block &rhs) {
			return (lhs.g + lhs.h) < (rhs.g + rhs.h);
		});

		Block cur = open.front();
		open.erase(open.begin());
		close.push_back(cur.m);

		print(cur);
		
		if (cur.m == goal) {
			break;
		}

		vector<vector<vector<int>>> matrices = matrix_derive(cur.m);

		for (auto e : matrices) {
			if(!in_open(open, e)){
				if (!in_close(close, e)) {
					open.push_back(Block(cur.g+1, evaluate(e, goal), e));
				}
			}
		}
	}
}

int main() {
	vector<vector<int>> begin = { {2,1,6},{4,0,8},{7,5,3} };
	vector<vector<int>> goal = { {1,2,3}, {8,0,4}, {7,6,5} };

	search(begin, goal);

	return 0;
}