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 <vector>
#include <string>
#include <queue>
#include <set>
using namespace std;

const int INF = 1 << 28;

int main()
{
  vector<vector<int> > table(13);
  table[0].push_back(2);
  table[1].push_back(2);
  table[1].push_back(5);
  table[2].push_back(0);
  table[2].push_back(1);
  table[2].push_back(3);
  table[2].push_back(6);
  table[3].push_back(2);
  table[3].push_back(7);
  table[4].push_back(5);
  table[5].push_back(1);
  table[5].push_back(4);
  table[5].push_back(6);
  table[5].push_back(9);
  table[6].push_back(2);
  table[6].push_back(5);
  table[6].push_back(7);
  table[6].push_back(10);
  table[7].push_back(3);
  table[7].push_back(6);
  table[7].push_back(8);
  table[7].push_back(11);
  table[8].push_back(7);
  table[9].push_back(5);
  table[9].push_back(10);
  table[10].push_back(6);
  table[10].push_back(9);
  table[10].push_back(11);
  table[10].push_back(12);
  table[11].push_back(7);
  table[11].push_back(10);
  table[12].push_back(10);

  vector<vector<int> > MH(13, vector<int>(13, INF));
  for (unsigned int i = 0; i < table.size(); ++i) {
    for (unsigned int j = 0; j < table[i].size(); ++j)
      MH[i][table[i][j]] = 1;
  }

  for (int i = 0; i < 13; ++i)
    MH[i][i] = 0;

  for (int k = 0; k < 13; ++k) {
    for (int i = 0; i < 13; ++i) {
      for (int j = 0; j < 13; ++j)
	MH[i][j] = min(MH[i][j], MH[i][k]+MH[k][j]);
    }
  }

  vector<int> p(13);
  while (cin >> p[0]) {
    if (p[0] == -1)
      break;

    for (unsigned int i = 1; i < p.size(); ++i)
      cin >> p[i];

    string s;
    const string g = "0123456789AB0";
    for (unsigned int i = 0; i < p.size(); ++i) {
      if (p[i] == 10)
	s += "A";
      else if (p[i] == 11)
	s += "B";
      else
	s += ('0' + p[i]);
    }

    int ans = -1;
    queue<pair<int, string> > que;
    que.push(make_pair(0, s));
    set<string> visited;
    while (!que.empty()) {
      const pair<int, string> st = que.front();
      que.pop();

      if (st.first > 20)
	continue;

      if (st.second == g) {
	ans = st.first;
	break;
      }

      visited.insert(st.second);
      vector<int> zero;
      for (unsigned int i = 0; i < st.second.size(); ++i) {
	if (st.second[i] == '0')
	  zero.push_back(i);
      }

      for (unsigned int i = 0; i < zero.size(); ++i) {
	for (unsigned int j = 0; j < table[zero[i]].size(); ++j) {
	  s = st.second;
	  swap(s[zero[i]], s[table[zero[i]][j]]);

	  int cost = 0;
	  for (unsigned int k = 0; k < s.size(); ++k) {
	    if (s[k] == '0')
	      cost += min(MH[0][k], MH[12][k]);
	    else if (s[k] == 'A')
	      cost += MH[10][k];
	    else if (s[k] == 'B')
	      cost += MH[11][k];
	    else
	      cost += MH[s[k]-'0'][k];
	  }
	  if (cost + st.first > 20)
	    continue;

	  if (visited.find(s) == visited.end()) {
	    visited.insert(s);
	    que.push(make_pair(st.first+1, s));
	  }
	}
      }
    }

    if (ans == -1)
      cout << "NA" << endl;
    else
      cout << ans << endl;
  }
  return 0;
}