Sliding Game, C++ (gcc)

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/*
19 Sliding Game
You're given a 3x3 board of a tile puzzle, with 8 tiles numbered 1 to 8, and an empty spot. 
You can move any tile adjacent to the empty spot, to the empty spot, creating an empty spot 
where the tile originally was. The goal is to find a series of moves that will solve the board, 
i.e. get [ [1, 2, 3], [4, 5, 6], [7, 8, - ]…
*/

#include <iostream>
#include <vector>
#include <set>
#include <queue>
using namespace std;

vector<string> sliding(vector<vector<int>>& board){
    string target = "123456780"; // "0" means empty space 
    string start =""; 
    for(auto v: board){
        for(auto x: v) 
            start.push_back('0'+x); 
    }
    
    // check a corner case 
    if(start == target) return {"No Action Needed!"}; 
    
    int M = 3;
    int N = 3; 
    int dir[4][2] = {{0,1}, {0,-1},{1,0}, {-1,0}};  
    string s[4] = {"right", "left", "down", "up"}; // meaning 
    set<string> visited; 
    queue<vector<string>> q; // status, step1, step2,...
    visited.insert(start);  //don't forget this 
    q.push({start,{}}); 
    int step = 0; 
    while(q.size()){
        step++;
        int n = q.size(); 
        while(n--){
            auto current = q.front(); q.pop(); 
            string status = current[0];
            // find '0'
            int pos = status.find('0'); 
            int x = pos/N; 
            int y = pos%N; 
            for(int i=0; i<4; i++){
                int dx = x+ dir[i][0];
                int dy = y+ dir[i][1];
                if(dx<0 || dy<0 || dx>=M || dy>=N) continue; // out of range, IMPORTANT!
                int pos2 = dx * N + dy; 
                string t = status; 
                swap(t[pos],t[pos2]); 
                if(visited.count(t)) continue;
                vector<string> v = current; // paths
                v.push_back(s[i]);
                v[0] = t; 
                if(t==target) return v; 
                visited.insert(t); 
                q.push(v); 
            }
        }
    }
    return {"no solution" }; 
}

int main() {
    //vector<vector<int>> board = {{1,2,3}, {4,5,6}, {7,8,0}};
    vector<vector<int>> board = {{0,2,3}, {1,5,6}, {4,7,8}};
    //vector<vector<int>> board = {{3,1,4}, {6,2,0}, {7,5,8}};
    vector<string> res = sliding(board); 
    for(auto x: res) 
        cout << x << endl;
    return 0; 
}

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Compilation time: 1.03 sec, absolute running time: 0.07 sec, cpu time: 0.01 sec, memory peak: 3 Mb, absolute service time: 1,11 sec