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 <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

int fie[5][5];
int o_fie[5][5]={
	-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,
};

int ox[12],oy[12],zx[2],zy[2],zcnt;
int res;
bool flag;

int dx[4]={1,0,-1,0};
int dy[4]={0,1,0,-1};

void dfs(int v,int dist,int pd,int pu){
	if(dist==0){
		flag=true;
		res=min(res,v);
		return;
	}
	for(int i=0;i<4;i++){
		for(int j=0;j<2;j++){
			if(pu==j && (pd+2)%4==i)continue;
			int nx=zx[j]+dx[i],ny=zy[j]+dy[i];
			if(nx>=0 && nx<5 && ny>=0 && ny<5){
				if(fie[nx][ny]<=0)continue;
				int ch=fie[nx][ny];
				int ndist=dist;
				ndist-=abs(ox[ch]-nx)+abs(oy[ch]-ny);
				swap(fie[nx][ny],fie[zx[j]][zy[j]]);
				ndist+=abs(ox[ch]-zx[j])+abs(oy[ch]-zy[j]);
				zx[j]+=dx[i];
				zy[j]+=dy[i];
				if(v+1+ndist<=res)dfs(v+1,ndist,i,j);
				zx[j]-=dx[i];
				zy[j]-=dy[i];
				swap(fie[nx][ny],fie[zx[j]][zy[j]]);
			}
		}
	}
}
int dist;

int main(void){
	for(int i=0;i<5;i++){
		for(int j=abs(2-i);j<=4-abs(2-i);j++){
			ox[o_fie[i][j]]=j;
			oy[o_fie[i][j]]=i;
		}
	}
	while(1){
		memset(fie,-1,sizeof(fie));
		dist=0;
		zcnt=0;
		for(int i=0;i<5;i++){
			for(int j=abs(2-i);j<=4-abs(2-i);j++){
				scanf("%d",&fie[j][i]);
				if(fie[j][i]==-1)return 0;
			}
		}
		for(int i=0;i<5;i++){
			for(int j=abs(2-i);j<=4-abs(2-i);j++){
				int v=fie[j][i];
				if(v==0){
					zx[zcnt]=j;
					zy[zcnt++]=i;
				}else dist+=abs(ox[v]-j)+abs(oy[v]-i);
			}
		}
		if(dist>20){
			printf("NA\n");
		}else{
			int i=0;
			flag=false;
			res=20;
			dfs(0,dist,-1,-1);
			if(flag){
				printf("%d\n",res);
			}
			if(!flag)printf("NA\n");
		}
	}
	return 0;
}

C++: #include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<map>
#define lol(i,n) for(int i=0;i<n;i++)
#define mod 1000000007
typedef long long ll;
using namespace std;
int dx[13][4]={
  {3,0,0,0},
  {3,6,0,0},
  {1,2,4,6},
  {3,8,0,0},
  {6,0,0,0},
  {2,5,7,10},
  {3,6,8,11},
  {4,7,9,12},
  {8,0,0,0},
  {6,11,0,0},
  {6,10,12,13},
  {8,11,0,0},
  {11,0,0,0}
};
map<ll,int> mp;
ll Compress(int p[]){
  ll ans=0;
  for(int i=0;i<13;i++){
    ans*=13;
    ans+=p[i];
  }
  return ans;
}

int unzip[13];
void Unzip(ll x){
  for(int i=0;i<13;i++){
    unzip[12-i]=x%13;
    x/=13;
  }
}

queue<pair<ll,int> >Q;
void BFS(int p[],int len){
  ll tmp=Compress(p);
  mp[tmp]=len;
  if(len==21)return;
  lol(i,13){
    if(p[i]==0){
      lol(j,4){
	int t=dx[i][j];
	if(t==0)break;
	t--;
	if(p[t]!=0){
	  swap(p[i],p[t]);
	  Q.push(make_pair(Compress(p),len+1));
	  swap(p[i],p[t]);
	}
      }
    }
  }
}
int main(){
  int p[13];
  lol(i,13)p[i]=i;p[12]=0;
  Q.push(make_pair(Compress(p),1));
  while(!Q.empty()){
    ll data=Q.front().first;
    int len=Q.front().second;
    Q.pop();
    if(mp[data]>0)continue;
    Unzip(data);
    BFS(unzip,len);
  }
  while(cin>>p[0]&&p[0]!=-1){
    for(int i=1;i<13;i++)cin>>p[i];
    ll tmp=Compress(p);
    int cost=mp[tmp];
    if(cost==0)cout<<"NA"<<endl;
    else cout<<cost-1<<endl;
  }
  return 0;
}

C++: #include <queue>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
const int lim = 20;
const vector<int> bx = { 0, 4, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3 };
const vector<int> by = { 2, 2, 1, 2, 3, 0, 1, 2, 3, 4, 1, 2, 3 };
struct state {
	vector<int> px, py;
	int cost, rem, last1, last2;
};
bool operator<(const state& s1, const state& s2) {
	return s1.cost + s1.rem != s2.cost + s2.rem ? s1.cost + s1.rem > s2.cost + s2.rem : s1.rem > s2.rem;
}
int eval(vector<int> px, vector<int> py) {
	int ret = 0;
	for (int i = 2; i < 13; ++i) {
		ret += abs(px[i] - bx[i]) + abs(py[i] - by[i]);
	}
	return ret;
}
int main() {
	int x;
	while (cin >> x, x != -1) {
		vector<int> vx(13), vy(13);
		int zc = 0;
		vx[x == 0 ? zc : x + 1] = bx[0];
		vy[x == 0 ? zc : x + 1] = by[0];
		if (x == 0) ++zc;
		for (int i = 1; i < 13; ++i) {
			cin >> x;
			vx[x == 0 ? zc : x + 1] = bx[i == 12 ? 1 : i + 1];
			vy[x == 0 ? zc : x + 1] = by[i == 12 ? 1 : i + 1];
			if (x == 0) ++zc;
		}
		priority_queue<state> que;
		que.push(state{ vx, vy, 0, eval(vx, vy), -1, -1 });
		int ans = -1;
		while (!que.empty()) {
			state u = que.top();
			que.pop();
			if (u.rem == 0) {
				ans = u.cost;
				break;
			}
			for (int i = 0; i < 2; ++i) {
				for (int j = 2; j < 13; ++j) {
					if (i == u.last1 && j == u.last2) continue;
					if (abs(u.px[i] - u.px[j]) + abs(u.py[i] - u.py[j]) == 1) {
						swap(u.px[i], u.px[j]);
						swap(u.py[i], u.py[j]);
						int ev = eval(u.px, u.py);
						if (u.cost + ev + 1 <= lim) {
							que.push(state{ u.px, u.py, u.cost + 1, eval(u.px, u.py), i, j });
						}
						swap(u.px[i], u.px[j]);
						swap(u.py[i], u.py[j]);
					}
				}
			}
		}
		if (ans != -1) cout << ans << endl;
		else cout << "NA" << endl;
	}
	return 0;
}