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 <bits/stdc++.h>

using namespace std;

#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
#define fi first
#define se second

template<typename A, typename B> inline bool chmax(A &a, B b) { if (a<b) { a=b; return 1; } return 0; }
template<typename A, typename B> inline bool chmin(A &a, B b) { if (a>b) { a=b; return 1; } return 0; }

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<int, pll> pip;
const ll INF = 1ll<<29;
const ll MOD = 1000000007;
const double EPS  = 1e-9;

int dd[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}
};

int main() {
	queue<string> que;
	map<string, int> d;
	
	string ans = "abcdefghijkla";
	que.push(ans);
	d[ans] = 0;
	
	while (!que.empty()) {
		string now = que.front(); que.pop();
		int cost = d[now];
		
		if (cost > 10) break;
		
		REP(i, 13) if (now[i] == 'a') {
			REP(j, 4) {
				if (dd[i][j] == -1) break;
				
				swap(now[i], now[dd[i][j]]);
				if (d.find(now) == d.end()) {
					d[now] = cost + 1;
					que.push(now);
			}
				swap(now[i], now[dd[i][j]]);
			}
		}
	}
	while (!que.empty()) que.pop();

	int p[13];
	while (cin >> p[0], ~p[0]) {
		FOR(i, 1, 13) cin >> p[i];
		string st = "";
		REP(i, 13) st += p[i] + 'a';
		
		map<string, int> d2;
		que.push(st);
		d2[st] = 0;
		
		while (!que.empty()) {
			string now = que.front(); que.pop();
			int cost = d2[now];
			
			if (cost > 10 || d.find(now) != d.end()) break;
			
			REP(i, 13) if (now[i] == 'a') {
				REP(j, 4) {
					if (dd[i][j] == -1) break;
					
					swap(now[i], now[dd[i][j]]);
					if (d2.find(now) == d2.end()) {
						d2[now] = cost + 1;
						que.push(now);
				}
					swap(now[i], now[dd[i][j]]);
				}
			}
		}
		while (!que.empty()) que.pop();
		
		if (d.find(st) != d.end()) cout << d[st] + d2[st] << endl;
		else puts("NA");
	}
	return 0;
}

C++: #include<iostream> 
#include<algorithm> 

using namespace std;

#define N 5
#define REP(i, n) for ( int i = 0; i < (int)n; i++ )
#define LIMIT 20

// S[ÌÇ±É éÌ©
static const int T[12][2] = {
	{-1, -1},
	{1, 1},
	{1, 2},
	{1, 3},
	{2, 0},
	{2, 1},
	{2, 2},
	{2, 3},
	{2, 4},
	{3, 1},
	{3, 2},
	{3, 3}
};

// S[Ìzu
static const int g[N][N] = {
	{-1, -1,  0, -1, -1},
	{-1,  1,  2,  3, -1},
	{ 4,  5,  6,  7,  8},
	{-1,  9, 10, 11, -1},
	{-1, -1,  0, -1, -1}
};

class Puzzle
{
public:
	int C[N][N], mdist; //manhatta distance
	Puzzle(){}
	
	bool swapAdj( int si, int sj, int ti, int tj )
	{
		if ( ti < 0 || tj < 0 || ti >= N || tj >= N )
			return false;
		if ( C[ti][tj] <= 0 )
			return false;

		swap( C[ti][tj], C[si][sj] );

		int tti = T[C[si][sj]][0];
		int ttj = T[C[si][sj]][1];
		mdist -= max(tti, ti)-min(tti, ti) + max(ttj, tj)-min(ttj, tj);
		mdist += max(tti, si)-min(tti, si) + max(ttj, sj)-min(ttj, sj);
		return true;
	}
	
	bool isGoal()
	{
		REP(i, N) REP(j, N)
			if ( g[i][j] != C[i][j] )
				return false;
		return true;
	}
	
	// get initial manhattan distance
	int getMD()
	{
		int sum = 0;
		int ti, tj;
		REP(i, 5) REP(j, 5)
		{
			if ( C[i][j] <= 0 )
				continue;
			ti = T[C[i][j]][0];
			tj = T[C[i][j]][1];
			sum += (max(ti, i)-min(ti, i) + max(tj, j) - min(tj, j));
		}
		return sum;
	}
};
 
int limit;
 
bool dfs( int depth, Puzzle P )
{
	if ( P.isGoal() )
		return true;
	if ( depth + P.getMD() > limit )
		return false;
	
	static const int di[4] = {0, -1, 0, 1};
	static const int dj[4] = {1, 0, -1, 0};
	
	REP(i, N) REP(j, N)
	{
		if ( P.C[i][j] != 0 )
			continue;

		REP(r, 4)
		{
			Puzzle v = P;
			if ( !v.swapAdj(i, j, i+di[r], j+dj[r]) )
				continue;
			if ( dfs( depth + 1, v ) )
				return true;
		}
	}
	
	return false;
}

int idp(Puzzle source)
{
	for ( limit = 0; limit <= LIMIT; limit++ )
	{
		source.mdist = source.getMD();
		if ( dfs(0, source) )
			return limit;
	}
	return INT_MAX;
}

int main()
{
	Puzzle P;
	int top;
	
	while(1)
	{
		cin >> top;
		if ( top == -1 ) break;
		REP(j, N) P.C[0][j] = -1;
		P.C[0][2] = top;
		for(int i = 1; i < N; i++) REP(j, N)
		{
			if ( (i == 1 || i == 3) && (j == 0 || j == 4 ) )
				P.C[i][j] = -1;
			else if ( i == 4 && j != 2 )
				P.C[i][j] = -1;
			else
				cin >> P.C[i][j];
		}
	
		int cost = idp(P);
		
		if ( cost == INT_MAX )
			cout << "NA" << endl;
		else
			cout << cost << endl;	
	}
	
	return 0;
}