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){ //枝刈り大事だな
  static int dist[] = { 0, 2, 1, 2, 4, 3, 2, 3, 4, 2, 1, 2, 0};
  static int fuee[] = { 2, 0, 1, 2, 2, 1, 2, 3, 4, 2, 3, 4, 4};
 
  if(cnt > 20) return true;
  int foo = 0;
  for(int i = 0; i < 13; i++){
    if(str[i] == '0') foo += dist[i];
    if(str[i] == '1') foo += fuee[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 <map>
#include <queue>
#include <cstdlib>
#include <vector>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)

int to[13][5] = {
	{2,-1},
	{2,5,-1},
	{0,1,3,6,-1},
	{2,7,-1},
	{5,-1},
	{1,4,6,9,-1},
	{2,5,7,10,-1},
	{3,6,8,11,-1},
	{7,-1},
	{5,10,-1},
	{6,9,11,12},
	{7,10,-1},
	{10,-1}
};
int solve(vector<int> data){
	queue< vector<int> > Q;
	map<vector<int>,int> done;
	Q.push(data);
	done[Q.front()] = 0;
	
	while(Q.size()){
		vector<int> q = Q.front(); Q.pop();
		int dif = 0;
		rep(i,13)if(q[i])dif += abs(i-q[i]);
		if(dif==0)return done[q];
		if(dif/2+done[q]>=20)continue;
		int curcost = done[q];
		rep(x,13){
			if(q[x] == 0){
				rep(i,5){
					if(!~to[x][i])break;
					swap(q[x],q[to[x][i]]);
					if(done.find(q) == done.end() ){
						done[q] = curcost+1;
						Q.push(q);
					}
					swap(q[x],q[to[x][i]]);
				}
			}
		}
	}
	return 21;
}
int main(){
	vector<int> data(13);
	while(1){
		rep(i,13)if(!(cin >> data[i]))return 0;
		int ans = solve(data);
		if(ans > 20)cout << "NA" << endl;
		else cout << ans << endl;
	}
}

C++: #include<stdio.h>
#include<map>
#include<queue>
typedef long long L;
typedef std::map<L,int>M;
M m;
L S(L l,int a,int b)
{
	L c=(l>>(a*4))&15;
	l&=~(15LL<<(a*4));
	L d=(l>>(b*4))&15;
	l&=~(15LL<<(b*4));
	return l|(c<<(b*4))|(d<<(a*4));
}

struct I{int operator()(L l,int x)
{
	if(m.find(l)!=m.end())return -2;
	m[l]=x;
	return -1;
}};
struct E
{
	M inm;
	int operator()(L l,int x)
	{
		M::iterator ite=m.find(l);
		if(ite!=m.end())return ite->second+x;
		else if(inm.find(l)!=inm.end())return -2;
		inm[l]=x;
		return -1;
	}
};
template<class T>
int F(L init,T func)
{
	const int di[13][4]={
		{3},
		{3,6},
		{1,2,4,7},
		{3,8},
		{6},
		{2,5,7,10},
		{3,6,8,11},
		{4,7,9,12},
		{8},
		{6,11},
		{7,10,12,13},
		{8,11},
		{11}};
	M::iterator ite;
	std::queue<L>q;
	q.push(init);
	q.push(-1);
	int i,j,k;
	for(int x=0;x<=10;)
	{
		L l=q.front();
		q.pop();
		if(l<0)
		{
			q.push(l);
			++x;
			continue;
		}
		int res=func(l,x);
		if(res==-2)
			continue;
		if(res>=0)
			return res;
		int a[2];
		for(i=j=0;i<13;++i)
			if( !(l&(15LL<<(i*4))) )
				a[j++]=i;
		for(k=0;k<2;++k)
			for(i=0;i<4;++i)
			{
				int c=di[a[k]][i];
				if(c)
				{
					L t=S(l,a[k],c-1);
					q.push(t);
				}
				else break;
			}
	}
	return -1;
}
int main()
{
	F(0xBA9876543210LL,I());
	for(;;)
	{
		L l=0,x;
		for(int i=0;i<13;++i)
		{
			if(scanf("%lld",&x),x<0)return 0;
			l|=(x<<(i*4));
		}
		x=F(l,E());
		x<0?puts("NA"):printf("%lld\n",x);
	}
}