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 <vector>
using namespace std;

typedef vector <int> VI;
typedef vector <VI> VVI;

VVI goal;
VVI init;

int limit;

const int di[4] = { 0, -1, 0, 1 };
const int dj[4] = { 1, 0, -1,  };

const int T[12][2] = {
	{ 0, 0 },
	{ 2, 2 },
	{ 2, 3 },
	{ 2, 4 },
	{ 3, 1 },
	{ 3, 2 },
	{ 3, 3 },
	{ 3, 4 },
	{ 3, 5 },
	{ 4, 2 },
	{ 4, 3 },
	{ 4, 4 }
};

int getMD( VVI P )
{
	int sum = 0;
	int ti, tj;
	for ( int i = 0; i < 7; i++ ) for ( int j = 0; j < 7; j++ )
	{
		if ( P[j][i] <= 0 )
			continue;

		ti = T[P[j][i]][0];
		tj = T[P[j][i]][1];
		sum += ( max( ti, i ) - min( ti, i ) + max( tj, j ) - min( tj, j ) );
	}
	return sum;
}

bool is_goal( VVI puzzle )
{
	bool ok = true;
	for ( int i = 0; ok && i < 7; i++ ) for ( int j = 0; ok && j < 7; j++ )
	{
		if ( puzzle[j][i] != goal[j][i] )
			ok = false;
	}
	return ok;
}

bool dfs( int depth, VVI now )
{
	if ( is_goal( now ) )
		return true;

	if ( depth + getMD( now ) > limit )
		return false;

	for ( int i = 0; i < 7; i++ ) for ( int j = 0; j < 7; j++ )
	{
		if ( now[j][i] != 0 )
			continue;

		for ( int k = 0; k < 4; k++ )
		{
			VVI v = now;
			int ni = i + di[k];
			int nj = j + dj[k];

			if ( v[nj][ni] <= 0 )
				continue;

			swap( v[j][i], v[nj][ni] );

			if ( dfs( depth+1, v ) )
				return true;

		}
	}

}

int idfs( VVI src )
{
	for ( limit = 0; limit < 20; limit++ )
	{
		if ( dfs( 0, src ) )
			return limit;
	}
	return -1;
}

int main( void )
{
	// S[ÌóÔðìé
	goal = VVI( 7, VI( 7, -1 ) );
	goal[3][1] = 0;
	goal[3][5] = 0;
	for ( int i = 0; i < 3; i++ )
	{
		goal[2+i][2] = 1+i;
		goal[2+i][4] = 9+i;
	}
	for ( int i = 0; i < 5; i++ )
	{
		goal[1+i][3] = 4+i;
	}

	while ( 1 )
	{
		// úóÔÌüÍ
		init = VVI( 7, VI( 7, -1 ) );
		cin >> init[3][1];
		if ( init[3][1] == -1 )
			break;
		for ( int i = 0; i < 3; i++ )
			cin >> init[2+i][2];
		for ( int i = 0; i < 5; i++ )
			cin >> init[1+i][3];
		for ( int i = 0; i < 3; i++ )
			cin >> init[2+i][4];
		cin >> init[3][5];

		int cost = idfs( init );

		if ( cost == -1 )
			cout << "NA" << endl;
		else
			cout << cost << endl;

	}

	return 0;
}

C++: #include <bits/stdc++.h>
using namespace std;
const int pos_x[] = {0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4};
const int pos_y[] = {2, 1, 2, 3, 0, 1, 2, 3, 4, 1, 2, 3, 2};
const int table[][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, -1},
	{7, 10, -1},
	{10, -1},
};

struct Puzzle {
	vector<int> val;
	Puzzle(): val(13){}
	int score(){
		int res = 0;
		for (int i = 0; i < 13; i++){
			if (!val[i]) continue;
			int v = val[i];
			res += abs(pos_x[v] - pos_x[i]);
			res += abs(pos_y[v] - pos_y[i]);
		}
		return res;
	}
	void show(){
		for (int i = 0; i < 13; i++){
			printf("%d ", val[i]);
			if (i == 0 || i == 3 || i == 8 || i == 11 || i == 12){
				puts("");
			}
		}
	}
};

/*inline bool check(Puzzle &p)
{
	for (int i = 1; i <= 11; i++){
		if (p.val[i] != i) return false;
	}
	return true;
}*/

bool search(int d, Puzzle &p)
{
	if (p.score() == 0) return true;
	if (d == 0) return false;
	
	for (int i = 0; i < 13; i++){
		if (p.val[i]) continue;
		for (const int *to = &table[i][0]; ~(*to); to++){
			swap(p.val[i], p.val[*to]);
			//printf("%d %d\n", i, *to);
			//printf("%d\n", p.score());
			if (d - 1 - p.score() >= 0){
				if (search(d - 1, p)) return true;
			}
			swap(p.val[i], p.val[*to]);
		}
	}
	return false;
}

void solve(Puzzle &p)
{
	for (int d = 0; d <= 20; d++){
		if (search(d, p)){
			printf("%d\n", d);
			return;
		}
	}
	puts("NA");
}

int main()
{	
	Puzzle p;
	while (true){
		for (int i = 0; i < 13; i++){
			scanf("%d", &p.val[i]);
			if (p.val[i] == -1) return 0;
		}
		solve(p);
	}
}