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<algorithm>
#include<vector>
#include<stack>
#include<queue>
#include<cstdio>
#include<climits>
#include<cmath>
#include<cstring>
#include<set>
#include<string>

#define f first
#define s second
#define mp make_pair

#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()

using namespace std;

typedef unsigned int uint;
typedef long long ll;
typedef unsigned long long ull;

struct pzl{
  ull l;
  pzl() : l(0) {}
  pzl(ull a) : l(a) {}
  inline int get(int i) const{
    return (int)((l >> (4*i)) & 0xF);
  }
  inline ull mask(int i) const{
    return l & ((ull)(0xF) << (4*i));
  }
  inline void set(int i, int n){
    l ^= mask(i);
    l |= ((long long)n << (4*i));
  }
  inline void swap(int i, int j){
    int a = get(i), b = get(j);
    set(i,b); set(j,a);
  }
  inline bool operator < (const pzl &a) const{
    return l < a.l;
  }
  inline bool operator == (const pzl &a) const{
    return l == a.l;
  }
  void print(){
    REP(i,13) printf("%2d ",get(i));
    puts("");
  }
};

int main(){
  pzl ans;
  REP(i,12) ans.set(i,i);
  while(true){
    pzl init;
    int a;
    scanf("%d",&a);
    if(a == -1) break;
    init.set(0,a);
    REP(i,12){ scanf("%d",&a); init.set(i+1,a); }
    
    //init.print();
    queue<pair<int,pzl> > q; q.push(mp(0,init));
    set<ull> s;   s.insert(init.l);
    while(q.size()){
      int cnt = q.front().f;
      pzl p   = q.front().s;
      //printf("cnt: %d\n",cnt);
      //p.print();
      if(p == ans){
	printf("%d\n",cnt);
	break;
      }

      q.pop();

      if(cnt >= 20) continue;
      REP(i,13){
	int g = p.get(i);
	if(g == 0){
	  pzl tmp = p;
#define SP(s,q,tmp) do{if(s.find(tmp.l) == s.end()){ s.insert(tmp.l); q.push(mp(cnt+1,tmp)); }}while(false)
	  switch(i){
	  case 0:  tmp.swap(0,2); SP(s,q,tmp); break;
	  case 1:  tmp.swap(1,2); SP(s,q,tmp); tmp = p; tmp.swap(1,5); SP(s,q,tmp); break;
	  case 2:  tmp.swap(2,0); SP(s,q,tmp); tmp = p; tmp.swap(2,1); SP(s,q,tmp); tmp = p; tmp.swap(2,3); SP(s,q,tmp); tmp = p; tmp.swap(2,6); SP(s,q,tmp); break;
	  case 3:  tmp.swap(3,2); SP(s,q,tmp); tmp = p; tmp.swap(3,7); SP(s,q,tmp); break;
	  case 4:  tmp.swap(4,5); SP(s,q,tmp); break;
	  case 5:  tmp.swap(5,1); SP(s,q,tmp); tmp = p; tmp.swap(5,4); SP(s,q,tmp); tmp = p; tmp.swap(5,6); SP(s,q,tmp); tmp = p; tmp.swap(5,9); SP(s,q,tmp); break;
	  case 6:  tmp.swap(6,2); SP(s,q,tmp); tmp = p; tmp.swap(6,5); SP(s,q,tmp); tmp = p; tmp.swap(6,7); SP(s,q,tmp); tmp = p; tmp.swap(6,10);SP(s,q,tmp); break;
	  case 7:  tmp.swap(7,3); SP(s,q,tmp); tmp = p; tmp.swap(7,6); SP(s,q,tmp); tmp = p; tmp.swap(7,8); SP(s,q,tmp); tmp = p; tmp.swap(7,11);SP(s,q,tmp); break;
	  case 8:  tmp.swap(8,7); SP(s,q,tmp); break; 
	  case 9:  tmp.swap(9,5); SP(s,q,tmp); tmp = p; tmp.swap(9,10);SP(s,q,tmp); break;
	  case 10: tmp.swap(10,6);SP(s,q,tmp); tmp = p; tmp.swap(10,9);SP(s,q,tmp); tmp = p;tmp.swap(10,11);SP(s,q,tmp); tmp = p;tmp.swap(10,12);SP(s,q,tmp); break;
	  case 11: tmp.swap(11,7);SP(s,q,tmp); tmp = p;tmp.swap(11,10);SP(s,q,tmp); break;
	  case 12: tmp.swap(12,10);SP(s,q,tmp);break;
	  }
	}
      }
    }
    if(q.empty())
      printf("NA\n");
  }
  return 0;
}