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

C++: #include <bits/stdc++.h>

using namespace std;

#define int long long
#define FR first
#define SC second
#define all(v) (v).begin(), (v).end()
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define reps(i, f, n) for(int i = (int)(f); i < (int)(n); i++)
#define each(a, b) for(auto& a : b)

typedef pair<int, int> P;

const int inf = 1LL << 55;

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

vector<int> ans = {0,1,2,3,4,5,6,7,8,9,10,11,0};

vector<int> x = {2,1,2,3,0,1,2,3,4,1,2,3,2};
vector<int> y = {0,1,1,1,2,2,2,2,2,3,3,3,4};

signed main()
{
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(12);

  int p;
  while(cin >> p, ~p) {
    vector<int> pzl; pzl.push_back(p);
    rep(i, 12) cin >> p, pzl.push_back(p);
    map<vector<int>, int> d;
    queue< vector<int> > que;
    que.push(pzl);
    d[pzl] = 0;
    bool flag = false;
    while(!que.empty() && !flag) {
      auto v = que.front(); que.pop();
      int e = 0;
      rep(i, v.size()) if(v[i]) {
	e += abs(x[i]-x[v[i]]) + abs(y[i]-y[v[i]]);
      }
      if(e == 0) {
	cout << d[v] << endl;
	flag = true;
	break;
      }
      if(e + d[v] > 20) continue;
      rep(i, v.size()) {
	if(v[i]) continue;
	rep(j, to[i].size()) {
	  int c = d[v];
	  swap(v[i], v[to[i][j]]);
	  if(!d.count(v)) {
	    que.push(v);
	    d[v] = c + 1;
	  }
	  swap(v[i], v[to[i][j]]);
	}
      }
    }
    if(!flag) cout << "NA" << endl;
  }
  
  return 0;
}

C++: #include <iostream>
#include <stdlib.h>
using namespace std;

int p[5][5],x[11]={1,2,3,0,1,2,3,4,1,2,3},y[11]={1,1,1,2,2,2,2,2,3,3,3},s,sx[2],sy[2]
    ,mx[4]={1,0,-1,0},my[4]={0,-1,0,1},lt;
int search(int t,int mx2,int my2,int mc) {
	int a,i,j,x2,y2,s2;
	if (s==0) { if (lt>t) lt=t; return 1;}
	  for (i=0;i<2;i++) for (j=0;j<4;j++) {
	  x2=sx[i]+mx[j]; y2=sy[i]+my[j];
	  if (x2<0 || x2>4 || y2<0 || y2>4) continue;
	  if (p[y2][x2]<1 || ( mc==i  && mx2==-mx[j] && my2==-my[j])) continue;
	  s2=abs(x2-x[p[y2][x2]-1])+abs(y2-y[p[y2][x2]-1])-abs(sx[i]-x[p[y2][x2]-1])-abs(sy[i]-y[p[y2][x2]-1]);
	  if (s+s2>lt-t) continue;
	  p[sy[i]][sx[i]]=p[y2][x2]; p[y2][x2]=0;  s+=s2; 
	  sx[i]=x2; sy[i]=y2;
	  a=search(t+1,mx[j],my[j],i);
	  sx[i]=x2-mx[j]; sy[i]=y2-my[j];
	  p[y2][x2]=p[sy[i]][sx[i]]; p[sy[i]][sx[i]]=0; s-=s2;
	  if (a==1) return 0;
  }
  return 0;
}

int main() {
  int i,j,k;
  for (i=0;i<5;i++) for (j=0;j<5;j++) p[i][j]=-1;
  while (cin >> p[0][2] && p[0][2]!=-1) {
	  cin >> p[1][1] >> p[1][2] >> p[1][3];
	  cin >> p[2][0] >> p[2][1] >> p[2][2] >> p[2][3] >> p[2][4];
	  cin >> p[3][1] >> p[3][2] >> p[3][3];
	  cin >> p[4][2]; k=0; s=0;
	  for (i=0;i<5;i++) for (j=0;j<5;j++) {
		  if (p[i][j]==0) { sx[k++]=j; sy[k++]=i;}
		  if (p[i][j]>0) s+=abs(j-x[p[i][j]-1])+abs(i-y[p[i][j]-1]);
		   }
	  lt=21;	   
	  search(0,0,0,0);
	  if (lt==21) cout << "NA" << endl; else cout << lt << endl;
  } 
 return 0;
}