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<bits/stdc++.h>
using namespace std;
 
typedef long long int64;
const int INF = 1 << 30;
 
vector< int > edge[13];
map< string, int > memo;

bool back(string str, int cnt){
  static int dist[] = { 0, 2, 1, 2, 4, 3, 2, 3, 4, 2, 1, 2, 0};

  if(cnt > 20) return true;
  int foo = 0;
  for(int i = 0; i < 13; i++){
    if(str[i] == '0') foo += dist[i];
  }
  return cnt + foo > 20;
}


int bfs(string mas){

  queue< string > que;
  map< string , int > used;
  que.push( mas );
  memo[mas] = 0;
  while(!que.empty()){

    string p = que.front(); que.pop();
    if(back( p, memo[p])) break;
    if(p == "0123456789AB0") return memo[p];

    for(int i = 0; i < 13; i++){
      if(p[i] == '0') {
        for(int j = 0; j < edge[i].size(); j++){
          string next = p;
          swap( next[i], next[edge[i][j]]);
          if(memo.find(next) != memo.end()) continue;
          que.push( next );
          memo[next] = memo[p] + 1;
        }
      }
    }
  }
  return -1;
}

int main(){
  vector< int > mas(13);

  edge[0].push_back(2);
  edge[1].push_back(2); edge[1].push_back(4);
  edge[2].push_back(0); edge[2].push_back(1); edge[2].push_back(3); edge[2].push_back(6);
  edge[3].push_back(2); edge[3].push_back(7);
  edge[4].push_back(5);
  edge[5].push_back(1); edge[5].push_back(4); edge[5].push_back(6); edge[5].push_back(9);
  edge[6].push_back(2); edge[6].push_back(5); edge[6].push_back(7); edge[6].push_back(10);
  edge[7].push_back(3); edge[7].push_back(6); edge[7].push_back(8); edge[7].push_back(11);
  edge[8].push_back(7);
  edge[9].push_back(5); edge[9].push_back(10);
  edge[10].push_back(6); edge[10].push_back(9); edge[10].push_back(11); edge[10].push_back(12);
  edge[11].push_back(7); edge[11].push_back(10);
  edge[12].push_back(10);

  while(cin >> mas[0], mas[0] != -1){
    for(int i = 1; i < 13; i++){
      cin >> mas[i];
    }

    string start = "";
    for(int i = 0; i < 13; i++){
      if(mas[i] >= 10) start += (char)(mas[i] - 10 + 'A');
      else start += mas[i] + '0';
    }
    int ret = bfs(start);
    if(~ret) cout << ret << endl;
    else cout << "NA" << endl;

    memo.clear();
  }
}

C++: #include<iostream>
#include<queue>
#include<map>
#include<vector>
using namespace std;
int px[13]={0,1,1,1,2,2,2,2,2,3,3,3,4},py[13]={2,1,2,3,0,1,2,3,4,1,2,3,2};
int xx[12]={0,1,1,1,2,2,2,2,2,3,3,3},yy[12]={0,1,2,3,0,1,2,3,4,1,2,3};
struct board{
	int p[13],a,b;
	bool operator<(const board&a)const
	{
		for(int i=0;i<13;i++)
		{
			if(p[i]!=a.p[i])return p[i]<a.p[i];
		}
		return false;
	}
	int distance()const
	{
		int ret=0;
		for(int i=0;i<13;i++)
		{
			if(p[i]==0)continue;
			ret+=abs(px[i]-xx[p[i]])+abs(py[i]-yy[p[i]]);
		}
		return ret;
	}
};
vector<int>D[13];
main()
{
	D[0].push_back(2);
	D[1].push_back(2);
	D[1].push_back(5);
	D[2].push_back(0);
	D[2].push_back(1);
	D[2].push_back(3);
	D[2].push_back(6);
	D[3].push_back(2);
	D[3].push_back(7);
	D[4].push_back(5);
	D[5].push_back(1);
	D[5].push_back(4);
	D[5].push_back(6);
	D[5].push_back(9);
	D[6].push_back(2);
	D[6].push_back(5);
	D[6].push_back(7);
	D[6].push_back(10);
	D[7].push_back(3);
	D[7].push_back(6);
	D[7].push_back(8);
	D[7].push_back(11);
	D[8].push_back(7);
	D[9].push_back(5);
	D[9].push_back(10);
	D[10].push_back(6);
	D[10].push_back(9);
	D[10].push_back(11);
	D[10].push_back(12);
	D[11].push_back(7);
	D[11].push_back(10);
	D[12].push_back(10);
	while(true)
	{
		board start;
		cin>>start.p[0];
		if(start.p[0]<0)break;
		for(int i=1;i<13;i++)cin>>start.p[i];
		start.a=start.b=-1;
		for(int i=0;i<13;i++)
		{
			if(start.p[i]==0)
			{
				if(start.a<0)start.a=i;
				else start.b=i;
			}
		}
		board goal;
		for(int i=0;i<12;i++)goal.p[i]=i;
		goal.p[12]=0;
		queue<board>P;
		P.push(start);
		map<board,int>M;
		M[start]=0;
		int ans=-1;
		while(!P.empty())
		{
			board now=P.front();P.pop();
			int c=M[now];
			if(c+now.distance()>20)continue;
			if(!(now<goal||goal<now))
			{
				ans=c;
				break;
			}
			for(int v:D[now.a])
			{
				int x=now.a,y=v;
				swap(now.p[x],now.p[y]);
				now.a=y;
				if(M.find(now)==M.end())
				{
					M[now]=c+1;
					P.push(now);
				}
				swap(now.p[x],now.p[y]);
				now.a=x;
			}
			for(int v:D[now.b])
			{
				int x=now.b,y=v;
				swap(now.p[x],now.p[y]);
				now.b=y;
				if(M.find(now)==M.end())
				{
					M[now]=c+1;
					P.push(now);
				}
				swap(now.p[x],now.p[y]);
				now.b=x;
			}
		}
		if(ans<0)cout<<"NA"<<endl;
		else cout<<ans<<endl;
	}
}