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};

vector<int> se[13];
int x[]={0,-1,0,1,-2,-1,0,1,2,-1,0,1,0};
int y[]={2,1,1,1,0,0,0,0,0,-1,-1,-1,-2};

void pr(ll in){

  printf("      %3lld\n",in&15);
  printf("   %3lld%3lld%3lld\n",(in>>4)&15,(in>>8)&15,(in>>12)&15);
  printf("%3lld%3lld%3lld%3lld%3lld\n",(in>>16)&15,(in>>20)&15,(in>>24)&15,(in>>28)&15,(in>>32)&15);
  printf("   %3lld%3lld%3lld\n",(in>>36)&15,(in>>40)&15,(in>>44)&15);
  printf("      %3lld\n",(in>>48)&15);
  puts("");
}

int manh(ll in){
  int ret=0;
  rep(i,13){
    int t=(in>>(i*4))&15;

    if(!t){
      int nx=x[t]-x[i],ny=y[t]-y[i];
      int co=abs(nx)+abs(ny);
      nx=x[12]-x[i],ny=y[12]-y[i];
      int k=abs(nx)+abs(ny);
      ret+=min(co,k);
      continue;
    }
    int nx=(x[t]-x[i]),ny=y[t]-y[i];
    ret+=abs(nx)+abs(ny);
  }
  return ret;
}

main(){
  ll p;

  ll goal=0;
  rep(i,11){
    goal|=(i+1LL)<<(4*(i+1));
    //cout<<goal<<endl;
    //pr(goal);
  }
  //pr(goal);

  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;
    ll in=p;

    rep(i,12){
      cin>>p;
      in|=p<<(4*(i+1));
    }

    set<ll> app;

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

    while(!Q.empty()){
      ll cvec=Q.front().S;
      int ccost=Q.front().F;
      Q.pop();
    
      //pr(cvec);

      //if(ccost>3)break;
      if(ccost+manh(cvec)>32)continue;
      if(cvec==goal){
	ans=ccost;
	break;
      }
      rep(i,13){
	ll t=cvec>>(i<<2);
	t=t&15;
	if(!t){
	  rep(j,se[i].size()){
	    t=cvec>>(se[i][j]<<2);
	    t=t&15;
	    if(t){
	      ll nvec=cvec;
	      t=t<<(i<<2);
	      nvec|=t;
	      nvec&=~(15LL<<se[i][j]*4);
	      
	      if(!app.count(nvec)){
		app.insert(nvec);
		Q.push(mp(ccost+1,nvec));
	      }
	    }
	  }
	}
      }
    }
    if(ans==21)cout<<"NA"<<endl;
    else cout<<ans<<endl;
  }
}

C++: #include <iostream>
#include <map>
#include <queue>
#include <cstdlib>
#include <vector>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)

int to[13][5] = {
	{2,-1},
	{2,5,-1},
	{0,1,3,6,-1},
	{2,7,-1},
	{5,-1},
	{1,4,6,9,-1},
	{2,5,7,10,-1},
	{3,6,8,11,-1},
	{7,-1},
	{5,10,-1},
	{6,9,11,12},
	{7,10,-1},
	{10,-1}
};
int solve(vector<int> data){
	queue< vector<int> > Q;
	map<vector<int>,int> done;
	Q.push(data);
	done[Q.front()] = 0;
	
	while(Q.size()){
		vector<int> q = Q.front(); Q.pop();
		int dif = 0;
		rep(i,13)if(q[i])dif += abs(i-q[i]);
		if(dif==0)return done[q];
		if(dif/4+done[q]>=20)continue;
		int curcost = done[q];
		rep(x,13){
			if(q[x] == 0){
				rep(i,5){
					if(!~to[x][i])break;
					swap(q[x],q[to[x][i]]);
					if(done.find(q) == done.end() ){
						done[q] = curcost+1;
						Q.push(q);
					}
					swap(q[x],q[to[x][i]]);
				}
			}
		}
	}
	return 21;
}
int main(){
	vector<int> data(13);
	while(1){
		rep(i,13)if(!(cin >> data[i]))return 0;
		int ans = solve(data);
		if(ans > 20)cout << "NA" << endl;
		else cout << ans << endl;
	}
}