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<set>
#include<queue>
using namespace std;

int main()
{
  vector<int> ans;
  for(int i=0;i<12;i++)
    ans.push_back(i);
  ans.push_back(0);
  int n;
  for(;cin>>n,n!=-1;)
    {
      vector<int> p;
      p.push_back(n);
      for(int i=0;i<12;i++)
	{
	  int tmp;
	  cin>>tmp;
	  p.push_back(tmp);
	}
      set<vector<int> >hash;
      queue<pair<vector<int>,int> >qu;
      qu.push(make_pair(p,0));
      int anscnt=-1;
      int dx[]={0,1,1,2,2,3,4,5,5,6,6 ,7,7 ,9 ,10,10};
      int dy[]={2,2,5,3,6,7,5,6,9,7,10,8,11,10,11,12};
      set< vector<int> >t1;
      while(!qu.empty())
	{
	  vector<int > data=qu.front().first;
	  int cnt=qu.front().second;
	  qu.pop();
	  // cout<<"qu: "<<cnt<<endl;
	  if(data==ans)
	    {
	      anscnt=cnt;
	      break;
	    }
	  if(hash.find(data)!=hash.end())
	    continue;
	  hash.insert(data);
	  if(cnt>=10)
	    {
	      t1.insert(data);
	      continue;
	    }
	  for(int i=0;i<16;i++)
	    {
	      int x=dx[i];
	      int y=dy[i];
	      if(data[x]==0 || data[y]==0)
		{
		  swap(data[x],data[y]);
		  if(hash.find(data)==hash.end())
		    qu.push(make_pair(data,cnt+1));
		  swap(data[x],data[y]);
		}
	    }
	}
      if(anscnt==-1)
	{
	  set<vector<int> >hash;
	  queue<pair<vector<int>,int> >qu;
	  qu.push(make_pair(ans,0));
	  while(!qu.empty())
	    {
	      vector<int > data=qu.front().first;
	      int cnt=qu.front().second;
	      qu.pop();
	      // cout<<"qu: "<<cnt<<endl;
	      if(t1.find(data)!=t1.end())
		{
		  anscnt=10+cnt;
		  break;
		}
	      if(hash.find(data)!=hash.end())
		continue;
	      hash.insert(data);
	      if(cnt>=10)
		continue;
	      for(int i=0;i<16;i++)
		{
		  int x=dx[i];
		  int y=dy[i];
		  if(data[x]==0 || data[y]==0)
		    {
		      swap(data[x],data[y]);
		      if(hash.find(data)==hash.end())
			qu.push(make_pair(data,cnt+1));
		      swap(data[x],data[y]);
		    }
		}
	    }
	}

      if(anscnt==-1)
	cout<<"NA"<<endl;
      else
	cout<<anscnt<<endl;
    }
}