八數碼問題

利用啟發式搜索，找出以下問題的最優解。

#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;
}

八數碼問題 Eight Digital Problem