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 <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;
			}
			cout << u.cost + u.rem << ' ' << u.rem << '\n';
			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;
}

C++: #include<cstdio>
#include<algorithm>
#include<iostream>
#include<queue>
#include<functional>
#include<map>
#include<vector>
using namespace std;
class P{
	public:
	int state[15];
	int cnt;
	P(){}
	P(int a[15],int cnt):cnt(cnt){
		for(int i = 0; i < 15; i++){
			state[i] = a[i];
		}
	}
};
int rules[13][6]={
	{1,2},{2,2,5},{4,0,1,2,3,6},{2,2,7},{1,5},
	{4,1,4,6,9},{4,2,5,7,10},{4,3,6,8,11},{1,7},{3,5,10},
	{4,6,9,11,12},{2,7,10},{1,10},
};
map< string , int >memo;

string getIndex(int *a){
	string tmp="";
	for(int i = 0; i < 12; i++){
		tmp += a[i];
	}
	return tmp;
}

void bfs(){
	int F[] = {0,1,2,3,4,5,6,7,8,9,10,11,0};
	queue < P > Q;
	Q.push(P(F,0));
	while( true ){
		if(Q.size() == 0)break;
		P p = Q.front();Q.pop();
		if(p.cnt > 20)break;
		string index = getIndex(p.state);
		if(memo[index])continue;
		memo[index] = p.cnt;
		for(int i = 0; i < 13; i++){
			if(p.state[i] == 0){
				int zero = p.state[i];
				for(int j = 0; j < rules[zero][0]; j++){
					swap(p.state[i],p.state[rules[i][j+1]]);
					Q.push(P(p.state,p.cnt+1));
					swap(p.state[i],p.state[rules[i][j+1]]);
				}
			}
		}
	}
}
int main(){
	bfs();
	int input[15];
	while(true){
	    scanf("%d",&input[0]);
	    if(input[0] == -1)break;
		for(int i = 1; i < 13; i++){
			scanf("%d",&input[i]);
		}
		string index = getIndex(input);
		if(memo[index])printf("%d\n",memo[index]);
		else puts("NA");
	}
	return 0;
}

C++: //35
#include<iostream>
#include<vector>
#include<set>
#include<algorithm>
#include<queue>

using namespace std;

struct S{
  vector<int> v;
  int t;
};

int main(){
  for(;;){
    vector<int> v(13);
    cin>>v[2]>>v[1]>>v[4]>>v[7]>>v[0]>>v[3]>>v[6]>>v[9]>>v[12]>>v[5]>>v[8]>>v[11]>>v[10];
    if(v[2]==-1)return 0;
    queue<S> que;
    S is={v,0};
    que.push(is);
    set<vector<int> > p;
    while(!que.empty()&&que.front().t<=20){
      S  c=que.front();
      int g[]={4,1,0,5,2,9,6,3,10,7,0,11,8};
      if(c.v==vector<int>(g,g+13))break;
      que.pop();
      if(p.count(c.v))continue;
      p.insert(c.v);
      for(int i=0;i<13;i++){
	if(v[i]==0){
	  for(int j=0;j<4;j++){
	    int d[]={-2,3,2,-3};
	    int b[][5]={{0,1,2,7,12},{2,7,12,11,10},{12,11,10,5,0},{10,5,0,1,2}};
	    int k;
	    for(k=0;k<5;k++){
	      if(i==b[j][k])break;
	    }
	    if(k==5){
	      vector<int> n=c.v;
	      swap(n[i],n[i+d[j]]);
	      S ns={n,c.t+1};
	      if(!p.count(n)){
		que.push(ns);
	      }
	    }
	  }
	}
      }
    }
    if(que.empty()||que.front().t>20){
      cout<<"NA"<<endl;
    }else{
      cout<<que.front().t<<endl;
    }
  }
  return 0;
}