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 <cstdio>
#include <cstdlib>
#include <cmath>
#include <climits>
#include <cfloat>
#include <map>
#include <utility>
#include <set>
#include <iostream>
#include <memory>
#include <string>
#include <vector>
#include <algorithm>
#include <functional>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <cstring>
#include <sstream>
#include <cassert>
#include <list>
using namespace std;
static const double EPS = 1e-10;
typedef long long ll;
typedef pair<int,int> PI;
typedef vector<int> vi;
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif
#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()
#define mp(a,b) make_pair(a,b)
#define pb(a) push_back(a)
#define F first
#define S second
template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }

int dx[]={0,1,0,-1},dy[]={1,0,-1,0};

typedef struct{
  vector<int> in;
  int s1,s2;
}state;

vector<int> se[13];

void pr(vector<int> in){
  if(in.size()!=13)return;

  printf("      %3d\n",in[0]);
  printf("   %3d%3d%3d\n",in[1],in[2],in[3]);
  printf("%3d%3d%3d%3d%3d\n",in[4],in[5],in[6],in[7],in[8]);
  printf("   %3d%3d%3d\n",in[9],in[10],in[11]);
  printf("      %3d\n",in[12]);
  puts("");
}

main(){
  int p;
  vector<int> goal(13);
  rep(i,11)goal[i+1]=i+1;
  //cout<<print_array(goal)<<endl;

  se[0].pb(2);
  se[1].pb(2);
  se[1].pb(5);
  se[2].pb(0);
  se[2].pb(1);
  se[2].pb(3);
  se[2].pb(6);
  se[3].pb(2);
  se[3].pb(7);
  se[4].pb(5);
  se[5].pb(1);
  se[5].pb(4);
  se[5].pb(6);
  se[5].pb(9);
  se[6].pb(2);
  se[6].pb(5);
  se[6].pb(7);
  se[6].pb(10);
  se[7].pb(3);
  se[7].pb(6);
  se[7].pb(8);
  se[7].pb(11);
  se[8].pb(7);
  se[9].pb(5);
  se[9].pb(10);
  se[10].pb(6);
  se[10].pb(9);
  se[10].pb(11);
  se[10].pb(12);
  se[11].pb(7);
  se[11].pb(10);
  se[12].pb(10);
  
  while(cin>>p){
    if(p==-1)break;
    vector<int> in;
    in.pb(p);
    rep(i,12){
      cin>>p;
      in.pb(p);
    }

    set<vector<int> > app;

    queue<pair<int,vector<int> > > Q;
    app.insert(in);
    Q.push(mp(0,in));
    int ans=21;

    while(!Q.empty()){
      vector<int> cvec=Q.front().S;
      int ccost=Q.front().F;
      Q.pop();
      //cout<<print_array(cvec)<<endl;
      //pr(cvec);
      if(ccost>3)break;
      if(ccost>20)break;
      if(cvec==goal){
	ans=ccost;
	break;
      }
      rep(i,cvec.size()){
	if(!cvec[i]){
	  rep(j,se[i].size()){
	    if(cvec[se[i][j]]){
	      swap(cvec[se[i][j]],cvec[i]);
	      if(!app.count(cvec)){
		app.insert(cvec);
		Q.push(mp(ccost+1,cvec));
	      }
	      swap(cvec[se[i][j]],cvec[i]);
	    }
	  }
	}
      }
    }
    if(ans==21)cout<<"NA"<<endl;
    else cout<<ans<<endl;
  }
}

C++: #include<iostream>
#include<vector>
#include<queue>
#include<map>
#include<cmath>
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;
  for(int i=0;i<25;i++){
    if(s[i]!='x'){
      int m=20;
      for(int j=0;j<25;j++){
	if(s[i]==ans[j]){
	  int a = abs(i-j);
	  int tmp = a/5 + a%5;
	  m = min(m,tmp);
	  if(s[i]!='o')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> q1;
    q1.push(board(score(s),0,s));

    map<string,bool> m1;
    m1[s] = 0;
    while(q1.size()){
      board p = q1.top();q1.pop();
      int dx[] = {-5,1,5,-1};
      //cout << p.h << " " << p.c << " " << p.s << endl;
      cost = p.c;
      if(p.s == ans)break;
      if(cost>20)break;
      if(p.h/2+p.c > 20){
	cost = 21;
	break;
      }
      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(!m1[str]){
	      q1.push(board(score(str),cost+1,str));
	      m1[str] = cost+1;
	    }
	  }
	}
      }
    }



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