Go: // BFS

package main

import (
	"bufio"
	"os"
		"fmt"
	"strconv"
	"strings"
)

var scanner = bufio.NewScanner(os.Stdin)

var p = [15]int{}
var g = [13][4]int {
	// -1は存在しないマス目
	{2,-1,-1,-1},
	{2,5,-1,-1},{0,1,3,6},{2,7,-1,-1},
	{5,-1,-1,-1},{1,4,6,9},{2,5,7,10},{3,6,8,11},{7,-1,-1,-1},
	{5,10,-1,-1},{6,9,11,12},{7,10,-1,-1},
	{10,-1,-1,-1},
}

/*
　  ０ １ ２ ３ ４
 0 |／|／|  |／|／|
 1 |／|　|  |　|／|
 2 |　|　|  |　|　|
 3 |／|　|  |　|／|
 4 |／|／|  |／|／|
*/

var row = [13]int{0,1,1,1,2,2,2,2,2,3,3,3,4}
var col = [13]int{2,1,2,3,0,1,2,3,4,1,2,3,2}

type wolf struct {
	m [13]int
}

type pair struct {
	first wolf
	second int
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

func print_board(board [13]int) {
	fmt.Println("--------------------------")
	fmt.Printf("        [%2d]\n", board[0])
	fmt.Printf("    [%2d][%2d][%2d]\n", board[1], board[2], board[3])
	fmt.Printf("[%2d][%2d][%2d][%2d][%2d]\n", board[4], board[5], board[6], board[7], board[8])
	fmt.Printf("    [%2d][%2d][%2d]\n", board[9], board[10], board[11])
	fmt.Printf("        [%2d]\n", board[12])
	fmt.Println("--------------------------")
}

func main() {
	for scanner.Scan() {
		p1, _ := strconv.Atoi(scanner.Text())
		if p1 == -1 {
			break
		}
		p[0]= p1
		scanner.Scan()
		buf1 := strings.Split(scanner.Text(), " ")
		p2, _ := strconv.Atoi(buf1[0])
		p3, _ := strconv.Atoi(buf1[1])
		p4, _ := strconv.Atoi(buf1[2])
		p[1], p[2], p[3] = p2, p3, p4
		scanner.Scan()
		buf2 := strings.Split(scanner.Text(), " ")
		p5, _ := strconv.Atoi(buf2[0])
		p6, _ := strconv.Atoi(buf2[1])
		p7, _ := strconv.Atoi(buf2[2])
		p8, _ := strconv.Atoi(buf2[3])
		p9, _ := strconv.Atoi(buf2[4])
		p[4], p[5], p[6], p[7], p[8] = p5, p6, p7, p8, p9
		scanner.Scan()
		buf3 := strings.Split(scanner.Text(), " ")
		p10, _ := strconv.Atoi(buf3[0])
		p11, _ := strconv.Atoi(buf3[1])
		p12, _ := strconv.Atoi(buf3[2])
		p[9], p[10], p[11] = p10, p11, p12
		scanner.Scan()
		p13, _ := strconv.Atoi(scanner.Text())
		p[12] = p13
		S := make(map[wolf]struct{})
		st := wolf{}
		for i := 0; i < 13; i++ {
			st.m[i] = p[i]
		}
		Q := make([]pair, 0)
		S[st] = struct{}{}
		Q = append(Q, pair{st, 0})
		yet := true
		for len(Q) > 0 {
			at := Q[0].first
			print_board(at.m)
			cost := Q[0].second
			Q = Q[1:]
			ok := true
			for i :=1; i < 12; i++ {
				if at.m[i] != i {
					ok = false
				}
			}
			if ok {
				// print_board(at.m)
				yet = false
				fmt.Println(cost)
				break
			}
			now := cost
			for i := 0; i < 13; i++ {
				if at.m[i] != 0 {
					now += abs(row[i]-row[at.m[i]]) + abs(col[i]-col[at.m[i]])
				}
			}
			if now > 20 {
				continue
			}
			for i := 0; i < 13; i++ {
				if at.m[i] == 0 {
					for j := 0; j < 4; j++ {
						if ^g[i][j] != 0 {
							at.m[i], at.m[g[i][j]] = at.m[g[i][j]], at.m[i]
							if _, ok := S[at]; !ok {
								S[at] = struct{}{}
								Q = append(Q, pair{at, cost+1})
							}
							at.m[i], at.m[g[i][j]] = at.m[g[i][j]], at.m[i]
						}
					}
				}
			}
		}
		if yet {
			fmt.Println("NA")
		}
	}
}

C++: #include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
#include <set>
#include <cstring>
#include <cstdlib>
using namespace std;


const int INF=100000000;
// ®©¹éêði[·éXg
vector<int> d[13];

// »ê¼êÌê©çá¤êÖÚ®·éÌÉKvÈ}nb^£
int mhd[13][13];
const int V=13;

void warshall_floyd(){
    for(int k = 0; k < V; k++)
        for(int i = 0; i < V; i++)
            for(int j = 0; j < V; j++)
                mhd[i][j]=min(mhd[i][j],mhd[i][k]+mhd[k][j]);
}

int main(){

    d[0].push_back(2);

    d[1].push_back(2);
    d[1].push_back(5);

    d[2].push_back(0);
    d[2].push_back(1);
    d[2].push_back(3);
    d[2].push_back(6);

    d[3].push_back(2);
    d[3].push_back(7);

    d[4].push_back(5);

    d[5].push_back(1);
    d[5].push_back(4);
    d[5].push_back(6);
    d[5].push_back(9);

    d[6].push_back(2);
    d[6].push_back(5);
    d[6].push_back(7);
    d[6].push_back(10);

    d[7].push_back(3);
    d[7].push_back(6);
    d[7].push_back(8);
    d[7].push_back(11);

    d[8].push_back(7);

    d[9].push_back(5);
    d[9].push_back(10);

    d[10].push_back(6);
    d[10].push_back(9);
    d[10].push_back(11);
    d[10].push_back(12);

    d[11].push_back(10);
    d[11].push_back(7);

    d[12].push_back(10);

    for(int i = 0; i < 13; i++)
        for(int j = 0; j < 13; j++)
            mhd[i][j]=INF;
    
    for(int i = 0; i < 13; i++){
        mhd[i][i]=0;
        // ¼Ú¹ª éÆ±ëÉRXg1ðãü
        for(int j = 0; j < d[i].size(); j++){
            int to=d[i][j];
            mhd[i][to]=1;
        }
    }

    warshall_floyd();

    while(1){
        set<vector<int> > no;
        vector<int> v;
        int cost=0;
        for(int j = 0; j < 13; j++){
            int t;
            cin>>t;
            if(t==-1)
                return 0;
            v.push_back(t);
            if(t!=0)
                cost+=mhd[t][j];
        }
        // Å©ç»ëÁÄ¢éê
        if(cost==0){
            cout<<0<<endl;
            continue;
        }
        queue<pair<int,vector<int> > > *prv=new queue<pair<int,vector<int> > >();
        queue<pair<int,vector<int> > > *nxt=new queue<pair<int,vector<int> > >();
        prv->push(make_pair(cost,v));
        int cnt=0;
        bool isGoal=false;
        // 20èÜÅTõð©¯é
        while(prv->size()){
            while(prv->size()){
                vector<int> b=prv->front().second;
                int cos=prv->front().first;    
                prv->pop();
                vector<int> emp;
                for(int i = 0; i < b.size(); i++)
                    if(b[i]==0)
                        emp.push_back(i);
                // óÌêðêÂIÑAJÚ·é
                for(int i = 0; i < emp.size(); i++){
                    int num=emp[i];
                    for(int j = 0; j < d[num].size(); j++){
                        // ¡ñg¤board
                        vector<int> bt=b;
                        // Ú®æ
                        int to=d[num][j];
                        if(bt[to]==0)
                            continue;
                        swap(bt[to],bt[num]);
                        if(no.find(bt)!=no.end())
                            continue;
                        no.insert(bt);
                        // Ú®æÌ]¿l(0ÉÈÁ½çI¹)
                        int toCost=cos-mhd[to][b[to]]+mhd[b[to]][num];
                        // goal
                        if(toCost==0){
                            isGoal=true;
                            break;
                        }
                        // »Ýn_©çS[É½Çè¯é©Ç¤©
                        // ³Èç}ëè
                        if(!(toCost>(19-cnt)))
                            nxt->push(make_pair(toCost,bt));
                    }
                    if(isGoal)
                        break;
                }
                if(isGoal)
                    break;
            }
            if(isGoal)
                break;
            swap(prv,nxt);
            cnt++;
            // 20èðz¦Ä¢é
            if(cnt>=20){
                break;
            }
        }
        if(isGoal){
            cout<<cnt+1<<endl;
        }
        else{
            cout<<"NA"<<endl;
        }
        delete prv,nxt;
    }

    return 0;
}