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<queue>
#include<unordered_map>
#define lol(i,n) for(int i=0;i<n;i++)
#define mod 1000000007
typedef long long ll;
using namespace std;
int dx[13][4]={
  {3,0,0,0},
  {3,6,0,0},
  {1,2,4,6},
  {3,8,0,0},
  {6,0,0,0},
  {2,5,7,10},
  {3,6,8,11},
  {4,7,9,12},
  {8,0,0,0},
  {6,11,0,0},
  {6,10,12,13},
  {8,11,0,0},
  {11,0,0,0}
};
unordered_map<ll,int> mp;
ll Compress(int p[]){
  ll ans=0;
  for(int i=0;i<13;i++){
    ans*=13;
    ans+=p[i];
  }
  return ans;
}

int unzip[13];
void Unzip(ll x){
  for(int i=0;i<13;i++){
    unzip[12-i]=x%13;
    x/=13;
  }
}

int beflen=0;
queue<pair<ll,int> >Q;
void BFS(int p[],int len){
  //if(len!=beflen){cout<<len<<endl;beflen=len;}
  ll tmp=Compress(p);
  mp[tmp]=len;
  if(len==17)return;
  lol(i,13){
    if(p[i]==0){
      lol(j,4){
	int t=dx[i][j];
	if(t==0)break;
	t--;
	if(p[t]!=0){
	  swap(p[i],p[t]);
	  tmp=Compress(p);
	  if(mp[tmp]!=0)continue;
	  mp[tmp]=-1;
	  Q.push(make_pair(tmp,len+1));
	  swap(p[i],p[t]);
	}
      }
    }
  }
}

int ans;
void EFS(int p[],int len){
  //if(len!=beflen){cout<<len<<endl;beflen=len;}
  ll tmp=Compress(p);
  if(mp[tmp]>0){
    ans=min(ans,len+mp[tmp]);
    return;
  }
  if(len==5)return;
  lol(i,13){
    if(p[i]==0){
      lol(j,4){
	int t=dx[i][j];
	if(t==0)break;
	t--;
	if(p[t]!=0){
	  swap(p[i],p[t]);
	  tmp=Compress(p);
	  Q.push(make_pair(tmp,len+1));
	  swap(p[i],p[t]);
	}
      }
    }
  }
}
int main(){
  int p[13];
  lol(i,13)p[i]=i;p[12]=0;
  Q.push(make_pair(Compress(p),1));
  while(!Q.empty()){
    ll data=Q.front().first;
    int len=Q.front().second;
    Q.pop();
    if(mp[data]>0)continue;
    Unzip(data);
    BFS(unzip,len);
  }
  while(cin>>p[0]&&p[0]!=-1){
    for(int i=1;i<13;i++)cin>>p[i];
    ans=mod;
    Q.push(make_pair(Compress(p),0));
    while(!Q.empty()){
      ll data=Q.front().first;
      int len=Q.front().second;
      Q.pop();
      Unzip(data);
      EFS(unzip,len);
    }
    if(ans==mod)cout<<"NA"<<endl;
    else cout<<ans-1<<endl;
  }
  return 0;
}

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

string ans;

class board{
public:
  int h,c;
  string s;
  board(int x,int y,string z){ h=x; c=y; s=z;}
  const bool operator<(const board x)const{return (h+c>x.h+x.c) || (h+c==x.h+x.c && c>x.c); }
};

int score(string s){
  int res=0,m;
  for(int i=0;i<25;i++){
    if(s[i]!='x' && s[i]!='o'){
      for(int j=0;j<25;j++){
	if(s[i]==ans[j]){
	  int a = abs(i-j);
	  int tmp = a/5 + a%5;
	  m = tmp;
	  break;
	}
      }
      res += m;
    }
  }
  return res;
}

char trans(int x){
  if(!x)return 'o';
  else return 'a'+x-1;
}

int main(){
  string s;
  ans = "xxoxxxabcxdefghxijkxxxoxx";
  int tmp,cost;

  for(;;){
    cin >> tmp;
    if(tmp<0)break;

    s = "xx";
    s += trans(tmp);
    s += "xxx";
    for(int i=0;i<3;i++){
      cin >> tmp;
      s += trans(tmp);
    }
    s += "x";
    for(int i=0;i<5;i++){
      cin >> tmp;
      s += trans(tmp);
    }
    s += "x";
    for(int i=0;i<3;i++){
      cin >> tmp;
      s+= trans(tmp);
    }
    s += "xxx";
    cin >> tmp;
    s += trans(tmp);
    s += "xx";

    priority_queue<board> q;
    q.push(board(score(s),0,s));

    map<string,bool> m;
    m[s] = 0;
    while(q.size()){
      board p = q.top();q.pop();
      int dx[] = {-5,1,5,-1};
      //cout << p.h << " " << p.c << " " << p.s << endl;
      cost = p.c;
      if(p.s == ans)break;
      if(p.h+cost>20){
	cost = 21;
	break;
      }
      m[p.s] = true;
      for(int i=0;i<25;i++){
	if(p.s[i]=='o'){
	  for(int j=0;j<4;j++){
	    int sx = i + dx[j];
	    string str = p.s;
	    if(sx<0 || 25<=sx)continue;
	    if(str[sx] == 'x' || str[sx] == 'o')continue;
	    swap(str[i],str[sx]);
	    if(!m[str])q.push(board(score(str),cost+1,str));
	  }
	}
      }
    }



    if(cost>20)cout << "NA\n";
    else cout << cost << endl;
  }
}