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 <cstdio>
#include <cstring>
#include <algorithm>
#include <string>
#include <cmath>
#include <stack>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <list>
#include <iostream>
#include <sstream>
#include <climits>
#include <cfloat>
#include <complex>

using namespace std;

typedef long long ll;

ll encode(int* state)
{
	ll res = 0;
	for (int i = 0; i < 13; ++i)
		res = res << 4 | state[i];
	return res;
}
void decode(int* d, ll e)
{
	for (int i = 12; i >= 0; --i, e >>= 4)
		d[i] = e & 15;
}
void p(ll s)
{
	int d[13];
	decode(d, s);
	for (int i = 0; i < 13; ++i)
		printf("%d ", d[i]);
	printf("\n");
}

int main()
{
	map<ll, int> minSteps;
	int dir[] = { -1, 1, -2, 2, -4, 4 };
	map<int, bool> ok[3];

	int o[][9] = {
		{ 1, 2, 4, 5, 6, 7, 9, 10, -1 },
		{ 0, 10, -1 },
		{ 1, 2, 3, 5, 6, 7, -1 }
	};
	for (int i = 0; i < 3; ++i)
		for (int j = 0; o[i][j] != -1; ++j)
			ok[i][o[i][j]] = true;

	int initial[] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0 };
	ll t = encode(initial);
	minSteps[t] = 0;
	queue<ll> q;
	q.push(t);

	while (!q.empty())
	{
		ll e = q.front();
		q.pop();
		int d[13];
		decode(d, e);

		int zero_pos[2];
		for (int i = 0, j = 0; j < 2; ++i)
			if (!d[i])
				zero_pos[j++] = i;

		for (int i = 0; i < 2; ++i)
		{
			for (int j = 0; j < 6; ++j)
			{
				int a = zero_pos[i];
				int b = a + dir[j];
				if (a > b)
					swap(a, b);
				if (a < 0 || b > 12 || !d[a] && !d[b] || !ok[j/2][a])
					continue;

				int copy[13];
				memcpy(copy, d, sizeof(copy));
				swap(copy[a], copy[b]);
				ll next = encode(copy);

				if (!minSteps.count(next) && minSteps[e] < 10)
				{
					minSteps[next] = minSteps[e] + 1;
					q.push(next);
				}
			}
		}
	}

	while (true)
	{
		int d[13];
		for (int i = 0; i < 13; ++i)
			scanf("%d", d + i);
		if (d[0] == -1)
			break;

		int ans = -1;
		ll s = encode(d);
		if (minSteps.count(s))
			ans = minSteps[s];
		else
		{
			map<ll, int> c;
			c[s] = 0;
			q.push(s);
			while (!q.empty())
			{
				ll e = q.front();
				q.pop();
				int d[13];
				decode(d, e);

				int zero_pos[2];
				for (int i = 0, j = 0; j < 2; ++i)
					if (!d[i])
						zero_pos[j++] = i;

				for (int i = 0; i < 2; ++i)
				{
					for (int j = 0; j < 6; ++j)
					{
						int a = zero_pos[i];
						int b = a + dir[j];
						if (a > b)
							swap(a, b);
						if (a < 0 || b > 12 || !d[a] && !d[b] || !ok[j/2][a])
							continue;

						int copy[13];
						memcpy(copy, d, sizeof(copy));
						swap(copy[a], copy[b]);
						ll next = encode(copy);

						if (minSteps.count(next))
						{
							ans = 10 + c[e] + 1;
							goto End;
						}
						if (!c.count(next) && c[e] < 10)
						{
							c[next] = c[e] + 1;
							q.push(next);
						}
					}
				}
			}
		}
End:
		if (ans != -1)
			printf("%d\n", ans);
		else
			puts("NA");
	}

	return 0;
}

C++: #include <iostream>
#include <queue>
#include <set>
using namespace std;
typedef long long ll;

ll mov[13][4] = {
	{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},
};

ll sw(ll l, int i, int j) {
	int a, b;
	a = (l >> (4 * i)) & 0xfL;
	b = (l >> (4 * j)) & 0xfL;

	l &= ~(0xfL << (4*i));
	l &= ~(0xfL << (4*j));

	l |= (ll)b << (4 * i);
	l |= (ll)a << (4 * j);

	return l;
}

int main() {
	while(1) {
		ll in = 0;
		for(int i = 0; i < 13; i++) {
			int tmpin;
			cin >> tmpin;
			if(tmpin < 0)
				return 0;
			in |= ((ll)tmpin << (4*i));
		}

		queue<ll> q;
		set<ll> s;
		q.push(in);
		s.insert(in);
		int ans = -1;
		// debug
		int failcount = 0;
		for(int i = 0; i <= 20; i++) {
			queue<ll> next;
			while(!q.empty()) {
				ll l = q.front(); q.pop();
				if(l == 0xba9876543210) {
					ans = i;
					goto OUTPUT_ANSWER;
				}
				else {
					int cnt = 0;
					for(int j = 0; j < 13; j++) {
						ll t = 0xba9876543210;
						if(((l >> 4*j) & 0xfL) != ((t >> 4*j) & 0xfL)) {
							cnt++;
						}
					}
					if(cnt > 20 - (i + 3))
						continue;
				}

				for(int j = 0; j < 13; j++) {
					if(((l >> (4*j)) & 0xfL) == 0) {
						for(int k = 0; k < 4; k++) {
							ll p;
							if(mov[j][k] < 0)
								break;
							p = sw(l, j, mov[j][k]);
							if(s.find(p) == s.end()) {
								s.insert(p);
								next.push(p);
							}
							else {
								failcount++;
							}
						}
					}
				}
			}
			q = next;
		}

OUTPUT_ANSWER:;
		if(ans < 0)
			cout << "NA" << endl;
		else
			cout << ans << endl;
//		cout << failcount << endl;
	}
}