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 <bits/stdc++.h>

using namespace std;

#define int long long
#define FR first
#define SC second
#define all(v) (v).begin(), (v).end()
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define reps(i, f, n) for(int i = (int)(f); i < (int)(n); i++)
#define each(a, b) for(auto& a : b)

typedef pair<int, int> P;

const int inf = 1LL << 55;

vector< vector<int> > to = {
  {2},
  {2, 5},
  {0, 1, 3, 6},
  {2, 7},
  {5},
  {1, 4, 6, 9},
  {2, 5, 7, 10},
  {3, 6, 8, 11},
  {7},
  {5, 10},
  {6, 9, 11, 12},
  {7, 10},
  {10}
};

vector<int> ans = {0,1,2,3,4,5,6,7,8,9,10,11,0};

signed main()
{
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(12);

  map<vector<int>, int> D;  
  queue< vector<int> > que;
  que.push(ans);
  D[ans] = 0;
  while(!que.empty()) {
    auto v = que.front(); que.pop();
    if(D[v] >= 10) break;
    rep(i, v.size()) {
      if(v[i]) continue;
      rep(j, to[i].size()) {
	int c = D[v];
	swap(v[i], v[to[i][j]]);
	if(!D.count(v)) {
	  que.push(v);
	  D[v] = c + 1;
	}
	swap(v[i], v[to[i][j]]);
      }
    }
  }
  
  int p;
  while(cin >> p, ~p) {
    vector<int> pzl; pzl.push_back(p);
    rep(i, 12) cin >> p, pzl.push_back(p);
    if(D.count(pzl)) {
      cout << D[pzl] << endl;
      continue;
    }
    map<vector<int>, int> d;
    queue< vector<int> > que;
    que.push(pzl);
    d[pzl] = 0;
    bool flag = false;
    while(!que.empty() && !flag) {
      auto v = que.front(); que.pop();
      if(d[v] >= 10) break;      
      rep(i, v.size()) {
	if(v[i]) continue;
	rep(j, to[i].size()) {
	  int c = d[v];
	  swap(v[i], v[to[i][j]]);
	  if(D.count(v)) {
	    cout << D[v] + c + 1 << endl;
	    flag = true;
	    break;
	  } else if(!d.count(v)) {
	    que.push(v);
	    d[v] = c + 1;
	  }
	  swap(v[i], v[to[i][j]]);
	}
	if(flag) break;
      }
    }
    if(!flag) cout << "NA" << endl;
  }
  return 0;
}