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<vector>
#include<map>
#include<cstdio>
#include<deque>
#include<cmath>
#include<algorithm>
#define F first
#define S second
#define pb push_back
using namespace std;
typedef pair<int,int> P;
typedef pair<P,P> PP;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<P> VP;
typedef pair<VVI,VP> VVIVP;
 
 
map<VVI,int> memo,bidirectional;
VVI final;
VP ini;
int dx[4] = {0,1,0,-1};
int dy[4] = {1,0,-1,0};
 
P Fpos[] = {P(0,0),P(1,1),P(2,1),P(3,1),P(0,2),P(1,2),P(2,2),P(3,2),P(4,2),P(1,3),P(2,3),P(3,3)};
 
 
class Puzzle
{
public:
  VVI state;
  int Manhattan;
  VP vp;
 
  Puzzle():Manhattan(0){}
  Puzzle(VVI s)
  {
    vp.clear();
    state = s;
    Manhattan_calc(false);
  }
 
  void Manhattan_calc(bool b)
  {
    Manhattan = 0; 
    for(int i=0;i<5;i++)
      for(int j=0;j<state[i].size();j++)
    if(state[i][j] != 0 && state[i][j] != -1)
      Manhattan += abs(j-Fpos[state[i][j]].F) + abs(i-Fpos[state[i][j]].S);
    else if(state[i][j] == 0 && !b)// bがfalseなら初期化
      vp.push_back(P(j,i)); 
  }
 
  void print()
  {
   
    for(int i=0;i<state.size();i++)
      {
    for(int j=0;j<state[i].size();j++)
      {
        if(state[i][j] == -1)
          cout << "  ";
        else
          cout << state[i][j] << " ";
      }
    cout << endl;
      }
    cout << endl;
  }
};
 
bool Input(VVI& puzzle)
{
  puzzle.clear();
  puzzle.resize(5);
  puzzle[0].resize(3),puzzle[1].resize(4),puzzle[2].resize(5),puzzle[3].resize(4),puzzle[4].resize(3);
  puzzle[0][0] = puzzle[0][1] = puzzle[1][0] = puzzle[3][0] = puzzle[4][0] = puzzle[4][1] = -1;
  
  scanf("%d",&puzzle[0][2]);
  if(puzzle[0][2] == -1)
    return false; 
  scanf("%d %d %d",&puzzle[1][1],&puzzle[1][2],&puzzle[1][3]);
  scanf("%d %d %d %d %d",&puzzle[2][0],&puzzle[2][1],&puzzle[2][2],&puzzle[2][3],&puzzle[2][4]);
  scanf("%d %d %d",&puzzle[3][1],&puzzle[3][2],&puzzle[3][3]);
  scanf("%d",&puzzle[4][2]);
         
    return true;
}
 
void print(VVI vvi)
{
  cout << "--- print ---" << endl;
  for(int i=0;i<vvi.size();i++)
    {
      for(int j=0;j<vvi[i].size();j++)
    {
      cout << vvi[i][j] << " ";
    }
      cout << endl;
    }
  cout << endl;
}
 
VVI change(VVI vec,P p1,P p11)
{
  int tmp = vec[p1.S][p1.F];
  vec[p1.S][p1.F] = vec[p11.S][p11.F];
  vec[p11.S][p11.F] = tmp;
 
  return vec;
}
 
void Init()
{
  final.resize(5);
  final[0].pb(-1),final[0].pb(-1),final[0].pb(0);
  final[1].pb(-1),final[1].pb(1),final[1].pb(2),final[1].pb(3);
  final[2].pb(4),final[2].pb(5),final[2].pb(6),final[2].pb(7),final[2].pb(8);
  final[3].pb(-1),final[3].pb(9),final[3].pb(10),final[3].pb(11);
  final[4].pb(-1),final[4].pb(-1),final[4].pb(0);
 
  Puzzle puz(final); 
  deque<Puzzle> deq;
  deq.push_back(puz);
  bidirectional[final] = 0;
   
  while(!deq.empty())
    {
      Puzzle p = deq.front(); deq.pop_front();
      int cost = bidirectional[p.state];
     
      if(cost >= 8)
    continue;
 
      for(int i=0;i<2;i++)
    {
      for(int j=0;j<4;j++)
        {
          int nx = p.vp[i].F + dx[j];
          int ny = p.vp[i].S + dy[j];
          if(!(0<=ny && ny<p.state.size() && 0<=nx && nx<p.state[ny].size() && p.state[ny][nx] != -1))
        continue;
          VVI next = change(p.state,p.vp[i],P(nx,ny));
          map<VVI,int>::iterator it = bidirectional.find(next);
          if(it == bidirectional.end() || (it != bidirectional.end() && bidirectional[next] > cost + 1))
        {
          bidirectional[next] = cost + 1;
          deq.push_back(Puzzle(next));
        }
 
        }
 
    }      
 
    }
   
   
}
 
 
int main()
{
  VVI puzzle;
  Init();
  //cout << "here" << endl;
  while(Input(puzzle))
    {
  
      Puzzle puz(puzzle);
      int men = (1<<28);
      deque<Puzzle> deq;
      deq.push_back(puz);
      memo.clear();
      memo[puzzle] = 0;
 
      while(!deq.empty())
    {
      Puzzle p = deq.front(); deq.pop_front();
      int cost = memo[p.state];
      //cout << "cost : " << cost << endl;
      //p.print();
      if(cost + p.Manhattan > min(20,men))
        continue;
 
      if(p.state == final)
        {
          men = min(men,cost);
          continue;
        }
      else if(bidirectional.find(p.state) != bidirectional.end() && cost + bidirectional[p.state] <= 20)
        {
          men = min(men,cost+bidirectional[p.state]);
          continue;
        }
        
      for(int i=0;i<2;i++)
        {
          for(int j=0;j<4;j++)
        {
   
          int nx = p.vp[i].F + dx[j];
          int ny = p.vp[i].S + dy[j];
          if(!(0<=ny && ny<p.state.size() && 0<=nx && nx<p.state[ny].size() && p.state[ny][nx] != -1))
            continue;
 
          VVI next = change(p.state,p.vp[i],P(nx,ny));
          map<VVI,int>::iterator it = memo.find(next);
          if(it == memo.end() || (it != memo.end() &&  memo[next] > cost + 1) )
            {
              memo[next] = cost + 1;
              deq.push_back(Puzzle(next));
            }
 
        }
        }
 
 
    }
      if(men == (1<<28))
    cout << "NA" << endl;
      else
    cout << men << endl;
    }  
 
     
  return 0;
}