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 <cmath>
#include <algorithm>
#include <cfloat>
#include <stack>
#include <queue>
#include <vector>
#include <string>
#include <iostream>
#include <set>
#include <map>
typedef long long int ll;
typedef unsigned long long int ull;
#define BIG_NUM 2000000000
#define MOD 1000000007
#define EPS 0.000000001
using namespace std;

struct Info{
	short table[5][5];
	int space_row1,space_col1,space_row2,space_col2;
};

map<string,bool> MAP;

bool rangeCheck(int row,int col){
	if(row < 0 || row >= 5)return false;

	switch(row){
	case 0:
		if(col == 2)return true;
		break;
	case 1:
		if(col >= 1 && col <= 3)return true;
		break;
	case 2:
		if(col >= 0 && col <= 4)return true;
		break;
	case 3:
		if(col >= 1 && col <= 3)return true;
		break;
	case 4:
		if(col == 2)return true;
		break;
	}
	return false;
}

bool clearFLG;
int ans;
int p[13];
int diff_row[4] = {-1,0,0,1},diff_col[4] = {0,-1,1,0};


void copyInfo(Info& to,Info from){

	for(int row = 0; row <= 4; row++){
		for(int col = 0; col <= 4; col++){
			to.table[row][col] = from.table[row][col];
		}
	}
}


void recursive(Info info,int depth,int max_depth){

	if(clearFLG)return;

	if(depth == max_depth){
		if(info.table[1][1] == 1 && info.table[1][2] == 2 && info.table[1][3] == 3 &&
				info.table[2][0] == 4 && info.table[2][1] == 5 && info.table[2][2] == 6 && info.table[2][3] == 7 && info.table[2][4] == 8 &&
				info.table[3][1] == 9 && info.table[3][2] == 10 && info.table[3][3] == 11){
			clearFLG = true;
		}
		return;
	}

	int adj_row,adj_col;

	for(int i = 0; i < 4; i++){
		adj_row = info.space_row1+diff_row[i];
		adj_col = info.space_col1+diff_col[i];

		if(rangeCheck(adj_row,adj_col) == false || info.table[adj_row][adj_col] == 0)continue;

		Info next_info;
		copyInfo(next_info,info);

		swap(next_info.table[info.space_row1][info.space_col1],next_info.table[adj_row][adj_col]);

		string tmp;
		for(int row = 0; row <= 4; row++){
			for(int col = 0; col <= 4; col++){
				if(rangeCheck(row,col)){
					tmp.append(to_string(next_info.table[row][col])).append(to_string('*'));
				}
			}
		}

		auto at = MAP.find(tmp);
		if(at != MAP.end())continue;

		MAP[tmp] = true;

		next_info.space_row1 = adj_row;
		next_info.space_col1 = adj_col;
		next_info.space_row2 = info.space_row2;
		next_info.space_col2 = info.space_col2;

		recursive(next_info,depth+1,max_depth);
	}

	for(int i = 0; i < 4; i++){
		adj_row = info.space_row2+diff_row[i];
		adj_col = info.space_col2+diff_col[i];

		if(rangeCheck(adj_row,adj_col) == false || info.table[adj_row][adj_col] == 0)continue;

		Info next_info;
		copyInfo(next_info,info);

		swap(next_info.table[info.space_row2][info.space_col2],next_info.table[adj_row][adj_col]);

		string tmp;
		for(int row = 0; row <= 4; row++){
			for(int col = 0; col <= 4; col++){
				if(rangeCheck(row,col)){
					tmp.append(to_string(next_info.table[row][col])).append(to_string('*'));
				}
			}
		}

		auto at = MAP.find(tmp);
		if(at != MAP.end())continue;

		MAP[tmp] = true;

		next_info.space_row1 = info.space_row1;
		next_info.space_col1 = info.space_col1;
		next_info.space_row2 = adj_row;
		next_info.space_col2 = adj_col;

		recursive(next_info,depth+1,max_depth);
	}
}

void func(){

	for(int i = 1; i < 13; i++)scanf("%d",&p[i]);

	Info first;
	first.table[0][2] = p[0];
	for(int i = 1; i <= 3; i++)first.table[1][i] = p[i];
	for(int i = 0; i <= 4; i++)first.table[2][i] = p[4+i];
	for(int i = 1; i <= 3; i++)first.table[3][i] = p[8+i];
	first.table[4][2] = p[12];

	int count = 0;

	for(int row = 0; row <= 4; row++){
		for(int col = 0; col <= 4; col++){
			if(rangeCheck(row,col) == true && first.table[row][col] == 0){
				if(count == 0){
					first.space_row1 = row;
					first.space_col1 = col;
					count++;
				}else{
					first.space_row2 = row;
					first.space_col2 = col;
				}
			}
		}
	}

	clearFLG = false;

	for(int max_depth = 0; max_depth <= 20; max_depth++){
		MAP.clear();

		string tmp;
		for(int row = 0; row <= 4; row++){
			for(int col = 0; col <= 4; col++){
				if(rangeCheck(row,col)){
					tmp.append(to_string(first.table[row][col])).append(to_string('*'));
				}
			}
		}

		MAP[tmp] = true;

		recursive(first,0,max_depth);
		if(clearFLG){
			ans = max_depth;
			break;
		}
	}

	if(clearFLG){
		printf("%d\n",ans);
	}else{
		printf("NA\n");
	}
}

int main(){

	while(true){
		scanf("%d",&p[0]);
		if(p[0] == -1)break;

		func();
	}

	return 0;
}