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<stdio.h>
#include<map>
#include<queue>
typedef long long L;
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));
}
int main()
{
	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}};
	typedef std::map<L,int>M;
	M m;
	M::iterator ite;
	std::queue<L>q;
	q.push(0xBA9876543210);
	q.push(-1);
	int i,j,k;
	for(int x=0;x<=20;)
	{
		L l=q.front();
		q.pop();
		if(l<0)
		{
			q.push(l);
			++x;
			continue;
		}
		ite=m.find(l);
		if(ite!=m.end())continue;
		m[l]=x;
		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;
			}
	}
	for(;;)
	{
		L l=0,x;
		for(i=0;i<13;++i)
		{
			if(scanf("%lld",&x),x<0)return 0;
			l|=(x<<(i*4));
		}
		ite=m.find(l);
		ite==m.end()?puts("NA"):printf("%d\n",ite->second);
	}
}

C++: #include <iostream>
#include <string>
#include <vector>
#include <queue>
#include <map>
using namespace std;

string s = "0123456789AB";
string goal = "0123456789AB0";

vector<vector<int>> adj = {
    {2},
    {2,5},
    {0,1,3,6},
    {2,7},
    {5},
    {1,4,6,9},
    {2,5,7,10},
    {3,6,8,11},
    {7},
    {5,10},
    {6,9,11,12},
    {7,10},
    {10}
};

int solve(string stat) {
    if (stat == goal) return 0;
    map<string, int> dist;
    dist[stat] = 0;
    queue<string> q;
    q.push(stat);
    while ( ! q.empty()) {
        string s = q.front();
        q.pop();
        for (int i=0; i<13; ++i) {
            if (s[i] != '0') continue;
            for (int j : adj[i]) {
                string next = s;
                next[i] = s[j];
                next[j] = s[i];
                int diff = 0;
                for (int k=0; k<13; ++k) {
                    diff += next[k] != goal[k];
                }
                if ( ! diff) {
                    return dist[s] + 1;
                }
                if (dist.find(next) == dist.end()) {
                    dist[next] = dist[s] + 1;
                    if (dist[next] + diff <= 20) {
                        q.push(next);
                    }
                }
            }
        }
    }
    return 21;
}

int main() {
    while (1) {
        string stat = "";
        int k;
        for (int i=0; i<13; ++i) {
            if (cin >> k && !~k) return 0;
            stat += s[k];
        }
        int ans = solve(stat);
        if (ans <= 20) {
            cout << ans << endl;
            continue;
        }
        cout << "NA" << endl;
    }
    return 0;
}

C++: #include <iostream>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <sstream>
#include <algorithm>
#include <numeric>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cassert>

#define rep(i,n) for(int i=0;i<n;i++)
#define rp(i,c) rep(i,(c).size())
#define fr(i,c) for(__typeof((c).begin()) i=(c).begin();i!=(c).end();i++)
#define mp make_pair
#define pb push_back
#define all(c) (c).begin(),(c).end()
#define dbg(x) cerr<<#x<<" = "<<(x)<<endl

using namespace std;

typedef long long ll;
typedef vector<int> vi;
typedef pair<int,int> pi;
const int inf=1<<28;
const double INF=1e10,EPS=1e-9;

int dx[]={-1,0,1,0},dy[]={0,-1,0,1};
int gx[]={0,1,2,3,0,1,2,3,4,1,2,3},gy[]={0,1,1,1,2,2,2,2,2,3,3,3};

struct S{
	int p[5][5];
	int zx[2],zy[2];
	int md;
	S(){}
	S(int a[5][5])
	{
		md=0;
		zx[0]=-1;
		rep(i,5)rep(j,5)
		{
			p[i][j]=a[i][j];
			if(a[i][j]==0)
			{
				if(zx[0]==-1)zy[0]=i,zx[0]=j;
				else zy[1]=i,zx[1]=j;
			}
			if(abs(i-2)+abs(j-2)<=2&&p[i][j])
			md+=abs(gy[p[i][j]]-i)+abs(gx[p[i][j]]-j);
		}
	}
	bool swp(int z,int d)
	{
		int y=zy[z],x=zx[z],nx=x+dx[d],ny=y+dy[d];
		if(abs(nx-2)+abs(ny-2)>2||p[y][x]==p[ny][nx])return 0;
		
		md+=abs(gy[p[ny][nx]]-y)+abs(gx[p[ny][nx]]-x);
		md-=abs(gy[p[ny][nx]]-ny)+abs(gx[p[ny][nx]]-nx);
		swap(p[y][x],p[ny][nx]);
		zy[z]+=dy[d]; zx[z]+=dx[d];
		return 1;
	}
};
S pz; int lim;
bool dfs(int c)
{
	if(pz.md==0)return 1;
	rep(i,2)rep(d,4)
	{
		if(!pz.swp(i,d))continue;
		if(pz.md+c+1<=lim&&dfs(c+1))return 1;
		pz.swp(i,d+2&3);
	}
	return 0;
}
int main()
{
	int t;
	while(scanf("%d",&t),~t)
	{
		int p[5][5];
		rep(i,5)rep(j,5)p[i][j]=-1;
		p[0][2]=t;
		rep(i,3)scanf("%d",p[1]+i+1);
		rep(i,5)scanf("%d",p[2]+i);
		rep(i,3)scanf("%d",p[3]+i+1);
		scanf("%d",p[4]+2);
		
		for(lim=0;lim<=20;lim++)
		{
			pz=S(p);
			if(!dfs(0))continue;
			printf("%d\n",lim); goto END;
		}
		puts("NA"); END:;
	}
	return 0;
}