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<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,13);

	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,7);

		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;
}

C++: #include <iostream>
#include <cmath>
#include <queue>
#include <set>
using namespace std;

int a[13];
bool m[13][13];
int pr[] = {1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5};
int pc[] = {3, 2, 3, 4, 1, 2, 3, 4, 5, 2, 3, 4, 3};
long long int g;

typedef pair<int, long long int> P;

long long int encode(int *x) {
  long long int t = 0;
  for (int i=0; i<13; ++i) {
    t <<= 4;
    t |= x[i];
  }
  return t;
}

void decode(long long int s, int *x) {
  for (int i=12; i>=0; --i) {
    x[i] = (int)(s & 0xf);
    s >>= 4;
  }
}

int manhattan(int *x) {
  int y = 0;
  for (int i=0; i<13; ++i) {
    if (!x[i]) {
      continue;
    }
    y += abs(pr[x[i]] - pr[i]);
    y += abs(pc[x[i]] - pc[i]);
  }
  return y;
}

void init() {
  a[0] = a[12] = 0;
  for (int i=1; i<12; ++i) {
    a[i] = i;
  }
  g = encode(a);

  for (int i=0; i<13; ++i) {
    int r1 = pr[i];
    int c1 = pc[i];
    m[i][i] = false;
    for (int j=i+1; j<13; ++j) {
      int r2 = pr[j];
      int c2 = pc[j];
      if (((r1 == r2) && (c1 == c2 + 1 || c1 == c2 - 1))
          || ((c1 == c2) && (r1 == r2 + 1 || r1 == r2 - 1))) {
        m[i][j] = m[j][i] = true;
      } else {
        m[i][j] = m[j][i] = false;
      }
    }
  }
}

bool input() {
  int t;
  for (int i=0; i<13; ++i) {
    cin >> t;
    if (!i && t == -1) {
      return false;
    }
    a[i] = t;
  }
  return true;
}

struct Comparator {
  bool operator()(const P l, const P r) const {
    return l > r;
  }
};

int solve() {
  priority_queue<P, vector<P>, Comparator> q;
  set<long long int> u;

  long long int t;
  t = encode(a);
  q.push(make_pair(manhattan(a), t));

  while (!q.empty()) {
    P p = q.top();
    q.pop();

    if (u.find(p.second) != u.end()) {
      continue;
    }
    u.insert(p.second);

    if (p.second == g) {
      return p.first;
    }

    decode(p.second, a);
    int x = manhattan(a);
    int y = p.first - x;
    if (y >= 20) {
      break;
    }
    for (int i=0; i<13; ++i) {
      if (a[i]) {
        continue;
      }
      for (int j=0; j<13; ++j) {
        if (!m[i][j]) {
          continue;
        }
        a[i] = a[j];
        a[j] = 0;
        int z = manhattan(a);
        q.push(make_pair(y + 1 + z, encode(a)));
        a[j] = a[i];
        a[i] = 0;
      }
    }
  }
  return -1;
}

int main() {
  int ans;
  init();
  while (1) {
    if (!input()) {
      break;
    }
    ans = solve();
    if (ans >= 0) {
      cout << ans << endl;
    } else {
      cout << "NA" << endl;
    }
  }
  return 0;
}