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 <cstdio>
#include <queue>
#include <set>
#include <map>
#include <cmath>
using namespace std;
typedef unsigned long long ull;
ull B = 1000000003ull;
int a[5]={2,1,0,1,2};
int b[5]={2,3,4,3,2};
int dx[5]={0,1,0,-1};
int dy[5]={1,0,-1,0};
int px[13]={0,1,1,1,2,2,2,2,2,3,3,3,0};
int py[13]={0,1,2,3,0,1,2,3,4,1,2,3,0};
 
struct State
{
    int f[5][5];
    int t;
};
ull hash(State x)
{
    ull t = 1ull;
    ull res = 0;
    for(int i=0;i<5;i++)
    {
        for(int j=a[i];j<=b[i];j++)
        {
            res += x.f[i][j]*t;
            t *= B;
        }
    }
    return res;
}
map<ull,int> mp;
set<ull> used;
bool check(State x)
{
    int cnt=1;
    for(int i=1;i<=3;i++)
    {
        for(int j=a[i];j<=b[i];j++)
        {
            if(x.f[i][j]!=cnt)return false;
            cnt++;
        }
    }
    return true;
}
bool cc(State x)
{
    int res = 0;
    for(int i=0;i<5;i++)
    {
        for(int j=a[i];j<=b[i];j++)
        {
            if(x.f[i][j])
            {
                int k = x.f[i][j];
                res += (abs(px[k]-i)+abs(py[k]-j));
            }
        }
    }
    return (res>20-x.t);
}
int ans = 21;
void bfs(State st)
{
    queue<State> q;
    mp[hash(st)]=0;
    q.push(st);
    while(!q.empty())
    {
        State A = q.front();
        q.pop();
        //cout << "koko" << endl;
        for(int i=0;i<5;i++)
        {
            for(int j=0;j<5;j++)
            {
                if(j<a[i]||b[i]<j)continue;
                if(A.f[i][j]==0)continue;
                for(int k=0;k<4;k++)
                {
                    int nx=i+dx[k],ny=j+dy[k];
                    if(nx<0||nx>=5||ny<0||ny>=5)continue;
                    if(ny<a[nx]||b[nx]<ny)continue;
                    if(A.f[nx][ny]!=0)continue;
                    State B = A;
                    swap(B.f[nx][ny],B.f[i][j]);
                    B.t++;
                    //cout << "a" << endl;
                    if(B.t>8)continue;
                    ull hb = hash(B);
                    if(mp.find(hb)!=mp.end())continue;
                    //cout << hb << endl;
                    mp[hb]=B.t;
                    q.push(B);
                }
            }
        }
    }
    //cout << "owari" << endl;
}
void bfs2(State st)
{
    queue<State> q;
    if(check(st)){ans=0;return;}
    q.push(st);
    while(!q.empty())
    {
        State A = q.front();
        q.pop();
        ull ha=hash(A); 
        if(mp.find(hash(A))!=mp.end()){ans = min(ans,A.t+mp[ha]);continue;}
        for(int i=0;i<5;i++)
        {
            for(int j=0;j<5;j++)
            {
                if(j<a[i]||b[i]<j)continue;
                if(A.f[i][j]==0)continue;
                for(int k=0;k<4;k++)
                {
                    int nx=i+dx[k],ny=j+dy[k];
                    if(nx<0||nx>=5||ny<0||ny>=5)continue;
                    if(ny<a[nx]||b[nx]<ny)continue;
                    if(A.f[nx][ny]!=0)continue;
                    State B = A;
                    swap(B.f[nx][ny],B.f[i][j]);
                    B.t++;
                    if(cc(B))continue;
                    ull hb = hash(B);
                    if(used.find(hb)!=used.end())continue;
                    used.insert(hb);
                    q.push(B);
                }
            }
        }
    }
}
int main()
{
    State end;
    int cnt=1;
    end.t=0;
    for(int i=0;i<5;i++)for(int j=0;j<5;j++)end.f[i][j]=-1;
    end.f[0][2]=0;
    end.f[4][2]=0;
    for(int i=1;i<=3;i++)for(int j=a[i];j<=b[i];j++)end.f[i][j]=cnt++;
    /*for(int i=0;i<5;i++)
    {
        for(int j=a[i];j<=b[i];j++)cout << end.f[i][j] << ' ';
        cout << endl;
    }*/
    bfs(end);
    while(1)
    {
        State st;
        used.clear();
        ans = 21;
        for(int i=0;i<5;i++)for(int j=0;j<5;j++)st.f[i][j]=-1;
        for(int i=0;i<5;i++)
        {
            for(int j=a[i];j<=b[i];j++)
            {
                cin >> st.f[i][j];
                if(st.f[i][j]==-1)goto end;
            }
        }
        st.t=0;
        bfs2(st);
        if(ans>20)printf("NA\n");
        else printf("%d\n",ans);
    }
    end:;
    return 0;
}