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 <cstdio>
#include <vector>
#include <algorithm>
#include <complex>
#include <cstring>
#include <cstdlib>
#include <string>
#include <cmath>
#include <queue>
#include <set>
using namespace std;

#define REP(i,n) for(int i=0;i<(int)n;++i)
#define FOR(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();++i)
#define ALL(c) (c).begin(), (c).end()
const int INF = 1<<29;

typedef vector<vector<int> > mat;
int dx[] = {0,1,0,-1};
int dy[] = {1,0,-1,0};

mat goal(5, vector<int>(5,-1));
set<mat> mp;

int hogex[12] = {0,1,2,3,0,1,2,3,4,1,2,3};
int hogey[12] = {0,1,1,1,2,2,2,2,2,3,3,3};
int dist(mat a) {
  int res = 0;
  REP(x,5) {
    REP(y,5) {
      if (a[x][y] > 0) {
        res += abs(x-hogex[a[x][y]]) + abs(y-hogey[a[x][y]]);
      }
    }
  }
  return res;
}

int main() {
  goal[2][0] = 0;
  REP(i,3) goal[i+1][1] = i+1;
  REP(i,5) goal[i][2] = i+4;
  REP(i,3) goal[i+1][3] = i+9;
  goal[2][4] = 0;
  
  int a;
  while(cin >> a, a!=-1) {
    mp.clear();
    mat ma(5, vector<int>(5, -1));
    ma[2][0] = a;
    REP(i,3) {
      cin >> a;
      ma[i+1][1] = a;
    }
    REP(i,5) {
      cin >> a;
      ma[i][2] = a;
    }
    REP(i,3) {
      cin >> a;
      ma[i+1][3] = a;
    }
    cin >> a;
    ma[2][4] = a;

    queue<pair<mat, int> > Q;
    Q.push(pair<mat, int>(ma, 0));
    mp.insert(ma);
    bool ff = 0;
    while(!Q.empty()) {
      mat ma2 = Q.front().first;
      int d = Q.front().second;
      Q.pop();
//      cout << d << " " << mp.size() << endl;
      if (d > 20) break;
      if (ma2 == goal) {
        ff = 1;
        cout << d << endl;
        break;
      }
      if (d + dist(ma2) > 20) continue;
      
      vector<int> zx,zy;
      REP(x,5) REP(y,5) {
        if (ma2[x][y] == 0) {
          zx.push_back(x);
          zy.push_back(y);
        }
      }
      REP(i,2) {
        int x = zx[i], y = zy[i];
        REP(k,4) {
          int xx = x + dx[k];
          int yy = y + dy[k];

          if (xx<0 || xx>=5 || yy<0 || yy>=5) continue;
          if (ma2[xx][yy] == -1) continue;

          mat tmp = ma2;
          swap(tmp[x][y], tmp[xx][yy]);
          if (mp.count(tmp)) continue;
          mp.insert(tmp);
          Q.push(make_pair(tmp, d+1));
        }
      }
    }
    if (!ff)
      cout << "NA" << endl;
  }
}

C++: #include<map>
#include<queue>
#include<cstdio>
#include<vector>

#define	pb	push_back

using namespace std;

typedef	vector<int>	vi;

vi mv[13];
long long pow12[13];

void findEmptyPos(long long stat,int *z){
	for(int i=0,j=0;i<13;i++){
		if(stat%12==0)	z[j++]=12-i;
		stat/=12;
	}
}

long long sw(long long stat,int i,int j){
	long long powi=pow12[12-i],powj=pow12[12-j];
	int pi=(stat/powi)%12,pj=(stat/powj)%12;
	return stat+(pj-pi)*powi+(pi-pj)*powj;
}

void bfs(map<long long,int> &f,long long inistat,int stop){
	f[inistat]=0;
	queue<long long> qu;	qu.push(inistat);
	while(!qu.empty()){
		long long stat=qu.front();	qu.pop();
		int cnt=f[stat];
		if(cnt==stop)	break;

		int z[2];	findEmptyPos(stat,z);
		for(int i=0;i<2;i++){
			for(int j=0;j<mv[z[i]].size();j++){
				long long nextstat=sw(stat,z[i],mv[z[i]][j]);
				if(f.count(nextstat)==0){
					qu.push(nextstat);
					f[nextstat]=cnt+1;
				}
			}
		}
	}
}

int main(){
	long long a=1;
	for(int i=0;i<13;i++)	pow12[i]=a,a*=12;

	mv[0].pb(2);
	mv[1].pb(2);	mv[1].pb(5);
	mv[2].pb(0);	mv[2].pb(1);	mv[2].pb(3);	mv[2].pb(6);
	mv[3].pb(2);	mv[3].pb(7);
	mv[4].pb(5);
	mv[5].pb(1);	mv[5].pb(4);	mv[5].pb(6);	mv[5].pb(9);
	mv[6].pb(2);	mv[6].pb(5);	mv[6].pb(7);	mv[6].pb(10);
	mv[7].pb(3);	mv[7].pb(6);	mv[7].pb(8);	mv[7].pb(11);
	mv[8].pb(7);
	mv[9].pb(5);	mv[9].pb(10);
	mv[10].pb(6);	mv[10].pb(9);	mv[10].pb(11);	mv[10].pb(12);
	mv[11].pb(7);	mv[11].pb(10);
	mv[12].pb(10);

	int ans[]={0,1,2,3,4,5,6,7,8,9,10,11,0};
	long long ansstat=0;
	for(int i=0;i<13;i++)	ansstat=ansstat*12+ans[i];

	map<long long,int> f;
	bfs(f,ansstat,12);

	for(long long inistat;scanf("%lld",&inistat),~inistat;){
		for(int i=1,p;i<13;i++)	scanf("%d",&p),inistat=inistat*12+p;
		map<long long,int> g;
		bfs(g,inistat,8);

		int cmin=21;
		map<long long,int>::iterator it;
		for(it=g.begin();it!=g.end();it++){
			long long stat=it->first;
			int cnt=it->second;
			if(f.count(stat))	cmin=min(cmin,cnt+f[stat]);
		}
		if(cmin<=20)	printf("%d\n",cmin);
		else	puts("NA");
	}

	return 0;
}