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<queue>
#include<algorithm>
#include<map>

using namespace std;

const int SIZE = 13;

struct Puzzle{
  short c[SIZE];
  
  void move(int d, int n){
    if(d == 0) moveUp(n);
    if(d == 1) moveDown(n);
    if(d == 2) moveLeft(n);
    if(d == 3) moveRight(n);
  }
  // n = choosed blank number 0(first one) or 1(second one)
  void moveUp(int n){
    int pos = findBlankPosition(n);
    int tmp[] = {-1,-1,0,-1,-1,1,2,3,-1,5,6,7,10};
    
    int npos = tmp[pos];
    if(npos != -1) swap(c[pos],c[npos]);
  }

  void moveDown(int n){
    int pos = findBlankPosition(n);
    int tmp[] = {2,5,6,7,-1,9,10,11,-1,-1,12,-1,-1};
    
    int npos = tmp[pos];
    if(npos != -1) swap(c[pos],c[npos]);
  }

  void moveLeft(int n){
    int pos = findBlankPosition(n);
    int tmp[] = {-1,-1,1,2,-1,4,5,6,7,-1,9,10,-1};
    
    int npos = tmp[pos];
    if(npos != -1) swap(c[pos],c[npos]);
  }

  void moveRight(int n){
    int pos = findBlankPosition(n);
    int tmp[] = {-1,2,3,-1,5,6,7,8,-1,10,11,-1,-1};
    
    int npos = tmp[pos];
    if(npos != -1) swap(c[pos],c[npos]);
  }

  int findBlankPosition(int n){
    for(int i = 0; i < SIZE; i++){
      if(c[i] == 0) n--;
      if(n < 0) return i;
    }
    return -1;
  }

  bool operator < (const Puzzle& p) const {
    for(int i = 0; i < SIZE; i++)
      if(c[i] != p.c[i]) return c[i] < p.c[i];
    return false;
  }
};

Puzzle puz;

bool input(){
  cin >> puz.c[0];
  if(puz.c[0] == -1) return false;
  for(int i = 1; i < SIZE; i++) cin >> puz.c[i];
  return true;
}

void solve(){
  map<Puzzle, int> M;
  M[puz] = 1;
 
  queue<Puzzle> Q;
  Q.push(puz);

  while(!Q.empty()){
    Puzzle now = Q.front(); Q.pop();
  
    for(int i = 0; i < 4; i++)
      for(int j = 0; j < 2; j++){
	Puzzle nex = now;
	nex.move(i,j);
	if(M[nex] > M[now]+1|| M[nex] == 0){
	  M[nex] = M[now]+1;
	  if(M[nex] < 11) Q.push(nex);
	}
      }
  }

  Puzzle tmp;
  for(int i = 0; i < SIZE; i++) tmp.c[i] = i%(SIZE-1);

 
  int ans = 25;
  Q.push(tmp);
  map<Puzzle,int> MG;
  MG[tmp] = 1;
  while(!Q.empty()){
    Puzzle now = Q.front(); Q.pop();
    if(M[now] != 0) ans = min(ans,M[now]+MG[now]-2);
    for(int i = 0; i < 4; i++)
      for(int j = 0; j < 2; j++){
	Puzzle nex = now;
	nex.move(i,j);
      
        if(MG[nex] > MG[now]+1 || MG[nex] == 0){
	  MG[nex] = MG[now]+1;
	  if(MG[nex] < 11) Q.push(nex);
	}
      }
    }
    if(ans <= 20) cout << ans << endl;
    else cout << "NA" << endl;
}

int main(){
  while(input()) solve();
  return 0;
}

C++: #include <iostream>
#include <cstdio>
#include <queue>
#include <set>
#include <cmath>
using namespace std;
typedef unsigned long long ull;
ull B = 1000000007ull;
int a[5]={2,1,0,1,2};
int b[5]={2,3,4,3,2};
int dx[5]={0,1,0,-1};
int dy[5]={1,0,-1,0};
int px[12]={0,1,1,1,2,2,2,2,2,3,3,3};
int py[12]={0,1,2,3,0,1,2,3,4,0,1,2};

struct State
{
	int f[5][5];
	int t;
};
ull hash(State x)
{
	ull t = 1ull;
	ull res = 0;
	for(int i=0;i<5;i++)
	{
		for(int j=a[i];j<=b[i];j++)
		{
			res += x.f[i][j]*t;
			t *= B;
		}
	}
	return res;
}
set<ull> s;
bool check(State x)
{
	int cnt = 1;
	for(int i=1;i<=3;i++)
	{
		for(int j=a[i];j<=b[i];j++)
		{
			if(x.f[i][j]!=cnt)return false;
			cnt++;
		}
	}
	return true;
}
bool cc(State x)
{
	int res = 0;
	for(int i=0;i<5;i++)
	{
		for(int j=a[i];j<=b[i];j++)
		{
			if(x.f[i][j])
			{
				int k = x.f[i][j];
				res += (abs(px[k]-i)+abs(py[k]-j));
			}
		}
	}
	return (res>20);
}
int bfs(State st)
{
	if(check(st))return 0;
	queue<State> q;
	q.push(st);
	while(!q.empty())
	{
		State A = q.front();
		q.pop();
		if(A.t>20)return 21;
		for(int i=0;i<5;i++)
		{
			for(int j=0;j<5;j++)
			{
				if(j<a[i]||b[i]<j)continue;
				if(A.f[i][j]==0)continue;
				for(int k=0;k<4;k++)
				{
					int nx=i+dx[k],ny=j+dy[k];
					if(nx<0||nx>=5||ny<0||ny>=5)continue;
					if(ny<a[nx]||b[nx]<ny)continue;
					if(A.f[nx][ny]!=0)continue;
					State B = A;
					swap(B.f[nx][ny],B.f[i][j]);
					B.t++;
					if(cc(B))continue;
					ull p = hash(B);
					if(s.find(p)!=s.end())continue;
					s.insert(p);
					if(check(B))return B.t;
					q.push(B);
				}
			}
		}
	}
	return 21;
}
int main()
{
	while(1)
	{
		State st;
		s.clear();
		for(int i=0;i<5;i++)for(int j=0;j<5;j++)st.f[i][j]=-1;
		for(int i=0;i<5;i++)
		{
			for(int j=a[i];j<=b[i];j++)
			{
				cin >> st.f[i][j];
				if(st.f[i][j]==-1)goto end;
			}
		}
		st.t=0;
		int ans = bfs(st);
		if(ans>20)printf("NA\n");
		else printf("%d\n",ans);
	}
	end:;
	return 0;
}