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>
#include<map>
#include<queue>
#include<algorithm>
using namespace std;

const int N = 13;
const vector<vector<int>> NEXT = {
    {2},
    {2, 5},
    {0, 1, 3, 6},
    {2, 7},
    {5},
    {1, 4, 6, 9},
    {2, 5, 7, 10},
    {3, 6, 8, 11},
    {7},
    {5, 10},
    {6, 9, 11, 12},
    {7, 10},
    {10},
};

class Node {
public:
    vector<int> puzzle;
    int depth;
    Node(const vector<int>& p, int d) :puzzle(p), depth(d) {}
};

map<vector<int>, int> memo1;
map<vector<int>, int> memo2;

void bfs(const vector<int>& puzzle, map<vector<int>, int>& memo) {
    queue<Node> q;
    q.push(Node(puzzle, 0));
    while(!q.empty()) {
        Node current(q.front()); q.pop();
        if(current.depth > 10) continue;
        if(memo.count(current.puzzle)) continue;
        memo[current.puzzle] = current.depth;
        for(int i = 0; i < N; ++i) {
            if(current.puzzle[i] != 0) continue;
            for(const auto& j: NEXT[i]) {
                vector<int> next(current.puzzle);
                swap(next[i], next[j]);
                q.push(Node(next, current.depth + 1));
            }
        }
    }
}

int main() {
    vector<int> complete = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0};
    vector<int> puzzle(N);
    bfs(complete, memo1);
    while(cin >> puzzle[0], puzzle[0] != -1) {
        for(int i = 1; i < N; ++i) cin >> puzzle[i];
        memo2.clear();
        bfs(puzzle, memo2);
        int answer = 21;
        for(auto& i: memo1) if(memo2.count(get<0>(i))) answer = min(answer, get<1>(i) + memo2[get<0>(i)]);
        if(answer > 20) cout << "NA" << endl;
        else cout << answer << endl;
    }
}

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;
}

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

const int InitialDepth = 13;
map<ll, int> problemSteps;

int start_from_initial(ll current, ll next)
{
	bool newState = minSteps.count(next) == 0;
	if (newState)
		minSteps[next] = minSteps[current] + 1;

	return newState && minSteps[next] < InitialDepth ? 0 : -1;
}
int start_from_problem(ll current, ll next)
{
	bool newState = problemSteps.count(next) == 0;
	if (newState)
		problemSteps[next] = problemSteps[current] + 1;

	if (minSteps.count(next))
		return problemSteps[next] + minSteps[next];

	return newState && problemSteps[next] < 20 - InitialDepth ? 0 : -1;
}
int bfs(ll initial, int (*f)(ll, ll))
{
	queue<ll> q;
	q.push(initial);

	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);

				int r = f(e, next);
				if (r == 0)
					q.push(next);
				else if (r > 0)
					return r;
			}
		}
	}

	return -1;
}

int main()
{
	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;

	bfs(t, start_from_initial);

	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
		{
			problemSteps.clear();
			ans = bfs(s, start_from_problem);
		}

		if (ans != -1)
			printf("%d\n", ans);
		else
			puts("NA");
	}

	return 0;
}