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 <algorithm>
#include <vector>
#include <cstring>
#include <cstdio>
#include <climits>

using namespace std;

#define REP(i,a,n) for(int i=(a); i<(int)(n); i++)
#define rep(i,n) REP(i,0,n)
#define LIM 20
#define DEB 0

/*
  1 = [2][2]
  2 = [2][3]
  3 = [2][4]
  4 = [3][1]
  5 = [3][2]
  6 = [3][3]
  7 = [3][4]
  8 = [3][5]
  9 = [4][2]
  10= [4][3]
  11= [4][4]
*/
int board[7][7]; //1base
int ans;
int sx[2], sy[2];
static const int dx[] = {0,0,1,-1};
static const int dy[] = {1,-1,0,0};

/*
(y,x)
 */
int calc(int y, int x){
    switch(board[y][x]){
    case 1: return abs(2-y)+abs(2-x);
    case 2: return abs(2-y)+abs(3-x);
    case 3: return abs(2-y)+abs(4-x);
    case 4: return abs(3-y)+abs(1-x);
    case 5: return abs(3-y)+abs(2-x);
    case 6: return abs(3-y)+abs(3-x);
    case 7: return abs(3-y)+abs(4-x);
    case 8: return abs(3-y)+abs(5-x);
    case 9: return abs(4-y)+abs(2-x);
    case 10: return abs(4-y)+abs(3-x);
    case 11: return abs(4-y)+abs(4-x);
    }
    return -1;
}
int dist(void){
    int ret = 0;
    if( board[1][3] ) ret += calc(1,3);
    rep(i,3) if( board[2][2+i] ) ret += calc(2,2+i);
    rep(i,5) if( board[3][1+i] ) ret += calc(3,1+i);
    rep(i,3) if( board[4][2+i] ) ret += calc(4,2+i);
    if( board[5][3] ) ret += calc(5,3);
    return ret;
}
bool isgoal(void){
    if( board[1][3]!=0 ) return false;
    rep(i,3) if( board[2][2+i]!=i+1 ) return false;
    rep(i,5) if( board[3][1+i]!=i+4 ) return false;
    rep(i,3) if( board[4][2+i]!=i+9 ) return false;
    if( board[5][3]!=0 ) return false;
    return true;
}

void dfs(int cnt, int py, int px){
    if( ans<=cnt ) return;
    if( isgoal() ){
        ans = cnt;
        return;
    }
    if( cnt+dist()>LIM ) return;
#if DEB
    //printf("cnt:%d  (%d,%d),(%d,%d)\n",cnt, sx[0], sy[0], sx[1], sy[1]);
#endif
    rep(i,2){
        rep(k,4){
            int tx = sx[i] + dx[k];
            int ty = sy[i] + dy[k];
            if( board[ty][tx]==-1 || ty==py&&tx==px ) continue;
            swap(board[sy[i]][sx[i]], board[ty][tx]);
            swap(sx[i], tx); swap(sy[i],ty);
            dfs(cnt+1, ty, tx); // ツ個ウツづ個スツペツーツスツ暗環置
            swap(sx[i], tx); swap(sy[i],ty);
            swap(board[sy[i]][sx[i]] ,board[ty][tx]);
        }
    }
}

int main(){
    for(;;){
        memset(board, -1, sizeof(board));
        ans = 21;
        int sz = 0;

        scanf("%d",&board[1][3]); if( board[1][3]==-1 ) break;
        rep(i,3) scanf("%d",&board[2][2+i]);
        rep(i,5) scanf("%d",&board[3][1+i]);
        rep(i,3) scanf("%d",&board[4][2+i]);
        scanf("%d",&board[5][3]);

        // find space
        if( board[1][3]==0 ){ sx[sz]=3; sy[sz]=1; sz++; }
        rep(i,3) if( board[2][2+i]==0 ) { sx[sz]=2+i; sy[sz]=2; sz++; }
        rep(i,5) if( board[3][1+i]==0 ) { sx[sz]=1+i; sy[sz]=3; sz++; }
        rep(i,3) if( board[4][2+i]==0 ) { sx[sz]=2+i; sy[sz]=4; sz++; }
        if( board[5][3]==0 ){ sx[sz]=3; sy[sz]=5; sz++; }

#if DEB
        rep(i,7){
            rep(j,7){
                printf("%2d ",board[i][j]);
            }
            puts("");
        }
        rep(i,2){
            printf("(%d,%d),",sx[i], sy[i]);
        }puts("");
        printf("%d\n",dist());
#endif
        
        dfs(0,-1,-1);
        if( ans==21 ) puts("NA"); else printf("%d\n",ans);
    }
    return 0;
}