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 <set>
#include <queue>

using namespace std;

class State{
public:
   string s;
   int cost;
};

int input;
set<string> visited;

void swap(string &str, int a, int b){
   char tmp = str[a];
   str[a] = str[b];
   str[b] = tmp;
}

int bfs(string str){
   State u, v;
   u.s = str;
   u.cost = 0;
   queue<State> Q;
   Q.push(u);
   while(!Q.empty()){
      u = Q.front(); Q.pop();
      //cout << u.s << ' ' << u.cost << endl;
      if(u.s == "ABCDEFGHIJKLA") return u.cost;
      if(u.s == "ALKJIHGFEDCBA") break;
      if(u.cost >= 20) continue;
      for(int i=0;i<13;i++){
         if(u.s[i] == 'A'){
            v.cost = u.cost + 1;
            switch(i){
               case 0:
                  v.s = u.s;
                  swap(v.s, 0, 2);
                  if(visited.find(v.s) == visited.end()){
                     visited.insert(v.s);
                     Q.push(v);
                  }
                  break;
               case 1:
                  v.s = u.s;
                  swap(v.s, i, 2);
                  if(visited.find(v.s) == visited.end()){
                     visited.insert(v.s);
                     Q.push(v);
                  }
                  v.s = u.s;
                  swap(v.s, i, 5);
                  if(visited.find(v.s) == visited.end()){
                     visited.insert(v.s);
                     Q.push(v);
                  }
                  break;
               case 3:
                  v.s = u.s;
                  swap(v.s, i, 2);
                  if(visited.find(v.s) == visited.end()){
                     visited.insert(v.s);
                     Q.push(v);
                  }
                  v.s = u.s;
                  swap(v.s, i, 7);
                  if(visited.find(v.s) == visited.end()){
                     visited.insert(v.s);
                     Q.push(v);
                  }
                  break;
               case 4:
                  v.s = u.s;
                  swap(v.s, i, 5);
                  if(visited.find(v.s) == visited.end()){
                     visited.insert(v.s);
                     Q.push(v);
                  }
                  break;
               case 8:
                  v.s = u.s;
                  swap(v.s, i, 7);
                  if(visited.find(v.s) == visited.end()){
                     visited.insert(v.s);
                     Q.push(v);
                  }
                  break;
               case 9:
                  v.s = u.s;
                  swap(v.s, i, 5);
                  if(visited.find(v.s) == visited.end()){
                     visited.insert(v.s);
                     Q.push(v);
                  }
                  v.s = u.s;
                  swap(v.s, i, 10);
                  if(visited.find(v.s) == visited.end()){
                     visited.insert(v.s);
                     Q.push(v);
                  }

                  break;
               case 11:
                  v.s = u.s;
                  swap(v.s, i, 7);
                  if(visited.find(v.s) == visited.end()){
                     visited.insert(v.s);
                     Q.push(v);
                  }
                  v.s = u.s;
                  swap(v.s, i, 10);
                  if(visited.find(v.s) == visited.end()){
                     visited.insert(v.s);
                     Q.push(v);
                  }
                  break;
               case 12:
                  v.s = u.s;
                  swap(v.s, i, 10);
                  if(visited.find(v.s) == visited.end()){
                     visited.insert(v.s);
                     Q.push(v);
                  }
                  break;
               default:
                  int ue = 4;
                  int sita = 4;
                  if(i == 2) ue = 2;
                  if(i == 10) sita = 2;
                  v.s = u.s;
                  swap(v.s, i, i-ue);
                  if(visited.find(v.s) == visited.end()){
                     visited.insert(v.s);
                     Q.push(v);
                  }
                  v.s = u.s;
                  swap(v.s, i, i+sita);
                  if(visited.find(v.s) == visited.end()){
                     visited.insert(v.s);
                     Q.push(v);
                  }
                  v.s = u.s;
                  swap(v.s, i, i+1);
                  if(visited.find(v.s) == visited.end()){
                     visited.insert(v.s);
                     Q.push(v);
                  }
                  v.s = u.s;
                  swap(v.s, i, i-1);
                  if(visited.find(v.s) == visited.end()){
                     visited.insert(v.s);
                     Q.push(v);
                  }
                  break;
            }
         }
      }
   }
   return -1;
}

main(){
   while(cin >> input){
      if(input == -1) break;
      string str = "";
      str += ((char)input + 'A');
      for(int i=1;i<13;i++){
         cin >> input;
         str += ((char)input + 'A');
      }
      int ans = bfs(str);
      if(ans == -1){
         cout << "NA" << endl;
      }else{
         cout << ans << endl;
      }
   }
   return 0;

}