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 <cstdio>
#include <vector>
#include <map>
#include <string>
#include <queue>
#include <algorithm>
using namespace std;

typedef pair<int,int> P;
const int INF = 1e+8;
const int f1[25] = {
	-1,-1, 0,-1,-1,
	-1, 1, 2, 3,-1,
	 4, 5, 6, 7, 8,
	-1, 9,10,11,-1,
	-1,-1,12,-1,-1,
};
const int f2[13] = {2,6,7,8,10,11,12,13,14,16,17,18,22};
const int dx[4] = { 0,-1,+1, 0};
const int dy[4] = {-1, 0, 0,+1};

// パズル
struct Pazzle{
	string v;
	Pazzle(){v = "*************"; }
	void at(int i, int p){
		v[i] = p;
	}
	// 空白の位置を返す. (k は 0 or 1)
	int search(int k){
		int a = 0;
		for(int i=0 ; i < 13 ; i++ ){
			if( v[i] == 0 ){
				if( k == 0 ){
					return i;
				}else{
					if( a == 0 ) a++;
					else return i;
				}
			}
		}
		return -1;
	}
	// 合っている数
	int to_g(){
		int res = 13;
		for(int i=0 ; i < 12 ; i++ ){
			if( i != v[i] ) res--;
		}
		if( v[12] != 0 ) res--;
		return res;
	}
	// 空白 k (0 or 1) を 方向 dir に動かす.
	// 動かせる時は true, 動かせなかったときは false を返す.
	bool move(int dir, int k){
		if( dir < 0 || 4 <= dir || k < 0 || 2 <= k ) return false;
		int pos1 = search(k);
		int x = f2[pos1] % 5;
		int y = f2[pos1] / 5;
		int mx = x + dx[dir];
		int my = y + dy[dir];
		if( mx < 0 || my < 0 || 5 <= mx || 5 <= my ) return false;
		int pos2 = f1[my*5+mx];
		if( pos2 == -1 ) return false;
		if( v[pos1] == v[pos2] ) return false;
		swap( v[pos1] , v[pos2] );
		return true;
	}
	// 完成しているかどうか
	bool is_goal(){
		for(int i=0 ; i < 12 ; i++ ){
			if( v[i] != i ) return false;
		}
		return v[12] == 0;
	}
	void debug(){
		printf("[debug]\n");
		for(int y=0 ; y < 5 ; y++ ){
			for(int x=0 ; x < 5 ; x++ ){
				if( f1[y*5+x] == -1 ){
					printf("##");
				}else{
					printf("%2d", (int)v[f1[y*5+x]] );
				}
			}
			printf("\n");
		}
		printf("\n");
	}
};

// (コスト,スタートからの距離,パズルの状態)
// コスト は (合っている数,-スタートからの距離)
struct State{
	Pazzle p;
	int cnt;
	P cost;
	State(int cost_, int cnt_, const Pazzle& p_){
		cost = P(cost_,-cnt_); cnt = cnt_; p = p_;
	}
};
bool operator<(const State& a, const State& b){
	return a.cost < b.cost;
}

int solve(Pazzle p){
	// (コスト,スタートからの距離,パズルの状態) を優先度つきキューへ
	priority_queue<State> q;
	q.push( State(p.to_g(),0,p) );
	
	int res = 21;
	int low = p.to_g() - 3;
	if( low < 0 ) low = 0;
	int foo=0;
	while( !q.empty() ){
		Pazzle p = q.top().p;
		int cnt = q.top().cnt;
		q.pop();
		
		if( p.is_goal() ){
			res = min( res , cnt );
			continue;
		}
		foo++;
		if( 150000 < foo ) break;
		if( low < p.is_goal() ) continue;
		if( res <= cnt + (13-p.is_goal()) ) continue;
		
		for(int k=0 ; k <= 1 ; k++ ){
			for(int i=0 ; i < 4 ; i++ ){
				Pazzle p_ = p;
				if( p_.move(i,k) ){
					q.push( State(p_.to_g(),cnt+1,p_) );
				}
			}
		}
	}
	return res;
}

int main(){
	int p1;
	while( cin >> p1 , p1 != -1 ){
		Pazzle p;
		p.at(0,p1);
		for(int i=1 ; i < 13 ; i++ ){
			cin >> p1;
			p.at(i,p1);
		}
		int ans = solve(p);
		if( ans == 21 ){
			cout << "NA" << endl;
		}else{
			cout << ans << endl;
		}
	}
}

C++: #include <iostream>
#include <string>
#include <vector>
#include <queue>
#include <map>
using namespace std;

string s = "0123456789AB";
string goal = "0123456789AB0";

vector<vector<int>> adj = {
    {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}
};

int solve(string stat) {
    if (stat == goal) return 0;
    map<string, int> dist;
    dist[stat] = 0;
    queue<string> q;
    q.push(stat);
    while ( ! q.empty()) {
        string s = q.front();
        q.pop();
        for (int i=0; i<13; ++i) {
            if (s[i] != '0') continue;
            for (int j : adj[i]) {
                string next = s;
                next[i] = s[j];
                next[j] = s[i];
                int diff = 0;
                for (int k=0; k<13; ++k) {
                    diff += next[k] != goal[k];
                }
                if ( ! diff) {
                    return dist[s] + 1;
                }
                if (dist.find(next) == dist.end()) {
                    dist[next] = dist[s] + 1;
                    if (dist[next] + diff - 2 <= 20) {
                        q.push(next);
                    }
                }
            }
        }
    }
    return 21;
}

int main() {
    while (1) {
        string stat = "";
        int k;
        for (int i=0; i<13; ++i) {
            if (cin >> k && !~k) return 0;
            stat += s[k];
        }
        int ans = solve(stat);
        if (ans <= 20) {
            cout << ans << endl;
            continue;
        }
        cout << "NA" << endl;
    }
    return 0;
}