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 <sstream> 
#include <iomanip> 
#include <algorithm> 
#include <cmath> 
#include <string> 
#include <vector> 
#include <list> 
#include <queue> 
#include <stack> 
#include <set> 
#include <map> 
#include <bitset> 
#include <numeric> 
#include <climits> 
#include <cfloat> 
using namespace std;

int main()
{
    string goal = "##.##"
                  "#abc#"
                  "defgh"
                  "#ijk#"
                  "##.##";

    vector<int> pos(256);
    for(int i=0; i<25; ++i){
        if(goal[i] != '#' && goal[i] != '.')
            pos[goal[i]] = i;
    }

    int d[] = {5, -5, 1, -1};

    for(;;){
        string s(25, '#');
        for(int i=0; i<25; ++i){
            if(goal[i] == '#')
                continue;
            int a;
            cin >> a;
            if(a == -1)
                return 0;
            if(a == 0)
                s[i] = '.';
            else
                s[i] = 'a' + a - 1;
        }

        if(s == goal){
            cout << 0 << endl;
            continue;
        }

        set<string> history;
        history.insert(s);
        vector<string> curr(1, s);

        int ret = -1;
        for(int i=0; i<20; ++i){
            vector<string> next;
            for(unsigned j=0; j<curr.size(); ++j){
                int len = 0;
                for(int k=0; k<25; ++k){
                    if(curr[j][k] != '#' && curr[j][k] != '.')
                        len += abs(k/5 - pos[curr[j][k]]/5) + abs(k%5 - pos[curr[j][k]]%5);
                }
                if(len > 20 - i)
                    continue;

                for(int k=0; k<25; ++k){
                    if(curr[j][k] != '.')
                        continue;
                    for(int l=0; l<4; ++l){
                        if(l < 2 && (k+d[l] < 0 || k+d[l] >= 25))
                            continue;
                        if(l >= 2 && (k+5) / 5 != (k+d[l]+5) / 5)
                            continue;
                        if(curr[j][k+d[l]] == '#')
                            continue;
                        swap(curr[j][k], curr[j][k+d[l]]);
                        if(history.find(curr[j]) == history.end()){
                            if(curr[j] == goal)
                                ret = i + 1;
                            history.insert(curr[j]);
                            next.push_back(curr[j]);
                        }
                        swap(curr[j][k], curr[j][k+d[l]]);
                    }
                }
            }
            curr.swap(next);
            if(ret != -1)
                break;
        }

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