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 > 1) 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 <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;
}*/

set<vector<int> > st;

bool search(int d, Puzzle &p)
{
	if (p.score() == 0) return true;
	if (d == 0) return false;
	if (st.count(p.val)) return false;
	st.insert(p.val);
	
	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++){
		st.clear();
		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);
	}
}