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;

const int INF = 1<<28;
const int H = 5;
const int W = 5;

struct State {
  int g[H][W];
  int x[2], y[2];
  bool operator < (const State &s) const {
    for(int i = 0, k = 0; i < H; ++i) {
      for(int j = abs(2-i); j < W-abs(2-i); ++j) {
        if(g[i][j] != s.g[i][j]) return g[i][j] < s.g[i][j];
      }
    }
    return false;
  }
  bool operator == (const State &s) const {
    return !(*this < s) && !(s < *this);
  }
};

map<State,int> bfs1(State src) {
  const static int dx[4] = {1,0,-1,0};
  const static int dy[4] = {0,1,0,-1};
  map<State,int> cost;
  queue<State> que;
  cost[src] = 0;
  que.push(src);
  while(que.size()) {
    const State s = que.front();
    que.pop();
    if(cost[s] == 10) continue;
    for(int k = 0; k < 2; ++k) {
      for(int i = 0; i < 4; ++i) {
        int nx = s.x[k] + dx[i];
        int ny = s.y[k] + dy[i];
        if(nx < 0 || nx >= W) continue;
        if(ny < 0 || ny >= H) continue;
        if(s.g[ny][nx] <= 0) continue;
        State t = s;
        swap(t.g[t.y[k]][t.x[k]], t.g[ny][nx]);
        t.x[k] = nx;
        t.y[k] = ny;
        if(cost.count(t)) continue;
        cost[t] = cost[s] + 1;
        que.push(t);
      }
    }
  }
  return cost;
}

int bfs2(State src, map<State,int> rcost) {
  const static int dx[4] = {1,0,-1,0};
  const static int dy[4] = {0,1,0,-1};
  if(rcost.count(src)) return rcost[src];
  map<State,int> cost;
  queue<State> que;
  cost[src] = 0;
  que.push(src);
  int res = INF;
  while(que.size()) {
    const State s = que.front();
    que.pop();
    if(cost[s] == 10) continue;
    for(int k = 0; k < 2; ++k) {
      for(int i = 0; i < 4; ++i) {
        int nx = s.x[k] + dx[i];
        int ny = s.y[k] + dy[i];
        if(nx < 0 || nx >= W) continue;
        if(ny < 0 || ny >= H) continue;
        if(s.g[ny][nx] <= 0) continue;
        State t = s;
        swap(t.g[t.y[k]][t.x[k]], t.g[ny][nx]);
        t.x[k] = nx;
        t.y[k] = ny;
        if(cost.count(t)) continue;
        cost[t] = cost[s] + 1;
        que.push(t);
        if(rcost.count(t)) {
          res = min(res, cost[t] + rcost[t]);
        }
      }
    }
  }
  return res;
}

int main() {
  State src, dst;
  fill(src.g[0], src.g[H], -1);
  fill(dst.g[0], dst.g[H], -1);
  for(int i = 0, k = 0, t = 0; i < H; ++i) {
    for(int j = abs(2-i); j < W-abs(2-i); ++j) {
      dst.g[i][j] = t % 12;
      ++t;
      if(dst.g[i][j] == 0) {
        dst.x[k] = j;
        dst.y[k] = j;
        ++k;
      }
    }
  }
  while(1) {
    for(int i = 0, k = 0; i < H; ++i) {
      for(int j = abs(2-i); j < W-abs(2-i); ++j) {
        cin >> src.g[i][j];
        if(src.g[i][j] == -1) return 0;
        if(src.g[i][j] == 0) {
          src.x[k] = j;
          src.y[k] = i;
          ++k;
        }
      }
    }
    int res = bfs2(src, bfs1(dst));
    if(res == INF) cout << "NA" << endl;
    else cout << res << endl;
  }
  return 0;
}

C++: #include<bits/stdc++.h>
#define rep(i,n)for(int i=0;i<(n);i++)
using namespace std;

int cx[]{ 0,1,1,1,2,2,2,2,2,3,3,3,4 }, cy[]{ 2,1,2,3,0,1,2,3,4,1,2,3,2 };
int dx[]{ 1,-1,0,0 }, dy[]{ 0,0,1,-1 };
int d[5][5], lim, D, x[2], y[2];
bool dfs(int p) {
	if (D == 0)return true;
	if (p + D > lim)return false;
	rep(j, 2)rep(i, 4) {
		int nx = x[j] + dx[i], ny = y[j] + dy[i];
		if (nx < 0 || 5 <= nx || ny < 0 || 5 <= ny || !d[nx][ny])return false;
		int a = abs(cx[d[nx][ny]] - nx) + abs(cy[d[nx][ny]] - ny);
		int b = abs(cx[d[nx][ny]] - x[j]) + abs(cy[d[nx][ny]] - y[j]);
		D += b - a; swap(d[x[j]][y[j]], d[nx][ny]); swap(x[j], nx); swap(y[j], ny);
		if (dfs(p + 1))return true;
		D -= b - a; swap(d[x[j]][y[j]], d[nx][ny]); swap(x[j], nx); swap(y[j], ny);
	}
	return false;
}
int main() {
	while (1) {
		D = 0; int p = 0;
		rep(i, 13) {
			scanf("%d", &d[cx[i]][cy[i]]);
			if (d[cx[i]][cy[i]] == -1)return 0;
			if (d[cx[i]][cy[i]] == 0) {
				x[p] = cx[i]; y[p++] = cy[i];
			}
			else D += abs(cx[i] - cx[d[cx[i]][cy[i]]]) + abs(cy[i] - cy[d[cx[i]][cy[i]]]);
		}
		for (lim = 0; lim <= 20; lim++) {
			if (dfs(0)) {
				printf("%d\n", lim); goto g;
			}
		}
		puts("NA");
	g:;
	}
}