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 <cstring>
#include <algorithm>
#include <string>
#include <cmath>
#include <stack>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <list>
#include <iostream>
#include <sstream>
#include <climits>
#include <cfloat>
#include <complex>

using namespace std;

typedef long long ll;

ll encode(int* state)
{
	ll res = 0;
	for (int i = 0; i < 13; ++i)
		res = res << 4 | state[i];
	return res;
}
void decode(int* d, ll e)
{
	for (int i = 12; i >= 0; --i, e >>= 4)
		d[i] = e & 15;
}
void p(ll s)
{
	int d[13];
	decode(d, s);
	for (int i = 0; i < 13; ++i)
		printf("%d ", d[i]);
	printf("\n");
}
int main()
{
	map<ll, int> minSteps;
	int initial[] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0 };
	ll t = encode(initial);
	minSteps[t] = 0;
	queue<ll> q;
	q.push(t);

	int dir[] = { -1, 1, -2, 2, -4, 4 };
	int o[][9] = {
		{ 1, 2, 4, 5, 6, 7, 9, 10, -1 },
		{ 0, 10, -1 },
		{ 1, 2, 3, 5, 6, 7, -1 }
	};
	map<int, bool> ok[3];
	for (int i = 0; i < 3; ++i)
		for (int j = 0; o[i][j] != -1; ++j)
			ok[i][o[i][j]] = true;

	while (!q.empty())
	{
		ll e = q.front();
		q.pop();
		int d[13];
		decode(d, e);

		int zero_pos[2];
		for (int i = 0, j = 0; j < 2; ++i)
			if (!d[i])
				zero_pos[j++] = i;

		for (int i = 0; i < 2; ++i)
		{
			for (int j = 0; j < 6; ++j)
			{
				int a = zero_pos[i];
				int b = a + dir[j];
				if (a > b)
					swap(a, b);
				if (a < 0 || b > 12 || !d[a] && !d[b] || !ok[j/2][a])
					continue;

				int copy[13];
				memcpy(copy, d, sizeof(copy));
				swap(copy[a], copy[b]);
				ll next = encode(copy);

				if (!minSteps.count(next) && minSteps[e] < 20)
				{
					minSteps[next] = minSteps[e] + 1;
					q.push(next);
				}
			}
		}
	}

	while (true)
	{
		int d[13];
		for (int i = 0; i < 13; ++i)
			scanf("%d", d + i);
		if (d[0] == -1)
			break;
		if (minSteps.count(encode(d)))
			printf("%d\n", minSteps[encode(d)]);
		else
			puts("NA");
	}

	return 0;
}

C++: #include<queue>
#include<map>
#include<algorithm>
#include<iostream>
#include<string>
#include<cstdlib>
#include<cstring>
#include<cmath>
using namespace std;
int p;
string s="";
queue<pair<string,int> > q;
void f(int a,int b){
  char c;
  c=s[a];
  s[a]=s[b];
  s[b]=c;
  q.push(make_pair(s,p+1));
  c=s[a];
  s[a]=s[b];
  s[b]=c;
  return;
}
void g(){
  if(s[0]==0){
    f(0,2);
  }
  if(s[1]==0){
    f(1,2);
    f(1,5);
  }
  if(s[2]==0){
    f(2,0);
    f(2,1);
    f(2,3);
    f(2,6);
  }
  if(s[3]==0){
    f(3,2);
    f(3,7);
  }
  if(s[4]==0){
    f(4,5);
  }
  if(s[5]==0){
    f(5,1);
    f(5,4);
    f(5,6);
    f(5,9);
  }
  if(s[6]==0){
    f(6,2);
    f(6,5);
    f(6,7);
    f(6,10);
  }
  if(s[7]==0){
    f(7,3);
    f(7,6);
    f(7,8);
    f(7,11);
  }
  if(s[8]==0){
    f(8,7);
  }
  if(s[9]==0){
    f(9,5);
    f(9,10);
  }
  if(s[10]==0){
    f(10,6);
    f(10,9);
    f(10,11);
    f(10,12);
  }
  if(s[11]==0){
    f(11,7);
    f(11,10);
  }
  if(s[12]==0){
    f(12,10);
  }
  return;
}
int main(){
  int i;
  int a;
  int mn;
  map<string,int> m,n;
  for(i=0;i<12;i++)
    s+=i;
  s+=(char)0;
  q.push(make_pair(s,1));
  for(;;){
    s=q.front().first;
    p=q.front().second;
    q.pop();
    if(p>11)
      break;
    if(m[s]==0){
      m[s]=p;
      g();
    }
  }
  while(cin>>a&&a!=-1){
    s="";
    s+=a;
    for(i=0;i<12;i++){
      cin>>a;
      s+=a;
    }
    if(m[s])
      cout<<m[s]-1<<endl;
    else{
      mn=21;
      while(q.empty()==0)
	q.pop();
      q.push(make_pair(s,1));
      n.clear();
      for(;;){
	s=q.front().first;
	p=q.front().second;
	q.pop();
	if(p>11)
	  break;
	if(m[s]&&mn>m[s]+p-2)
	  mn=m[s]+p-2;
	if(n[s]==0){
	  n[s]=p;
	  g();
	}
      }
      if(mn==21)
	cout<<"NA"<<endl;
      else
	cout<<mn<<endl;
    }
  }
  return 0;
}