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<cmath>
#include<stdio.h>
using namespace std;

#define LIMIT 20

struct Puzzle {
  int cont[25];
  int space[2];
};

int limit;

Puzzle puzzle;

int tx[12]={0,1,2,3,0,1,2,3,4,1,2,3};
int ty[12]={0,1,1,1,2,2,2,2,2,3,3,3};
int dx[4]={0,1,0,-1};
int dy[4]={-1,0,1,0};

int heuris[12][25];

int getHeuristic(){
  int res=0;
  for(int i=0;i<25;i++){
    if(puzzle.cont[i]==-1||puzzle.cont[i]==0)continue;
    res+=heuris[puzzle.cont[i]][i];
  }
  return res;
}

bool dfs(int depth,int prev0,int prev1){
  
  int heuri;
  heuri=getHeuristic();
  /*
  cout<<depth<<' '<<heuri<<endl;
  for(int i=0;i<5;i++){
    for(int j=0;j<5;j++){
      if(puzzle.cont[i*5+j]!=-1)printf("%3d",puzzle.cont[i*5+j]);
      else cout<<"???";
    }
    cout<<endl;
  }
  */
  if(heuri==0){
    cout<<depth<<endl;
    return true;
  }
  if(depth + heuri-1>limit)return false;

  int px,py,nx,ny;
  Puzzle tmp=puzzle;

  py=puzzle.space[0]/5;px=puzzle.space[0]%5;

  for(int i=0;i<4;i++){
    if(max(prev0,i)-min(prev0,i)==2)continue;
    ny=py+dy[i];nx=px+dx[i];
    if(ny<0||ny>=5||nx<0||nx>=5)continue;
    if(puzzle.cont[ny*5+nx]==-1)continue;
    if(puzzle.cont[ny*5+nx]==0)continue;
    puzzle.cont[py*5+px]=puzzle.cont[ny*5+nx];
    puzzle.cont[ny*5+nx]=0;
    puzzle.space[0]=ny*5+nx;
    if(dfs(depth+1,i,-100))return true;
    puzzle=tmp;
  }
  py=puzzle.space[1]/5;px=puzzle.space[1]%5;
  for(int i=0;i<4;i++){
    if(max(prev1,i)-min(prev1,i)==2)continue;
    ny=py+dy[i];nx=px+dx[i];
    if(ny<0||ny>=5||nx<0||nx>=5)continue;
    if(puzzle.cont[ny*5+nx]==-1)continue;
    if(puzzle.cont[ny*5+nx]==0)continue;
    puzzle.cont[py*5+px]=puzzle.cont[ny*5+nx];
    puzzle.cont[ny*5+nx]=0;
    puzzle.space[1]=ny*5+nx;
    if(dfs(depth+1,-100,i))return true;
    puzzle=tmp;
  }
  return false;
}

void solve(){
  Puzzle tmp=puzzle;
  for(limit=getHeuristic();limit<=LIMIT;limit++){
    puzzle=tmp;
    if(dfs(0,-100,-100))return;
  }
  cout<<"NA"<<endl;
}

int main(){
  int x,y,c=0;

  for(int i=1;i<=11;i++){
    for(int j=0;j<25;j++){
      y=j/5;
      x=j%5;
      heuris[i][j]=abs(tx[i]-x)+abs(ty[i]-y);
    }
  }
  /*
  for(int i=1;i<=11;i++){
    for(int j=0;j<5;j++){
      for(int k=0;k<5;k++){
	cout<<heuris[i][j*5+k]<<' ';
      }
      cout<<endl;
    }
    cout<<endl;
  }
  */


  while(1){
    c=0;
    for(int i=0;i<25;i++)puzzle.cont[i]=-1;

    cin>>puzzle.cont[2];
    if(puzzle.cont[2]==-1)break;
    if(puzzle.cont[2]==0)puzzle.space[c++]=2;
    
    
    for(int i=6;i<=8;i++){
      cin>>puzzle.cont[i];
      if(puzzle.cont[i]==0)puzzle.space[c++]=i;
    }
    for(int i=10;i<=14;i++){
      cin>>puzzle.cont[i];
      if(puzzle.cont[i]==0)puzzle.space[c++]=i;
    }
    
    for(int i=16;i<=18;i++){
      cin>>puzzle.cont[i];
      if(puzzle.cont[i]==0)puzzle.space[c++]=i;
    }
    
    cin>>puzzle.cont[22];
    if(puzzle.cont[22]==0)puzzle.space[c++]=22;
    solve();
  }

  return 0;
}

C++: #include<stdio.h>
#include<queue>
#include<algorithm>
#include<set>
using namespace std;
int p[15];
struct wolf{
	int m[13];
};
inline bool operator <(const wolf &a,const wolf &b){
	for(int i=0;i<13;i++)if(a.m[i]!=b.m[i])return a.m[i]<b.m[i];
	return false;
}
int g[13][4]={
{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}
};
int row[]={0,1,1,1,2,2,2,2,2,3,3,3,4};
int col[]={2,1,2,3,0,1,2,3,4,1,2,3,2};
int ABS(int a){return max(a,-a);}
int main(){
	while(scanf("%d",p),~p[0]){
		for(int i=1;i<13;i++)scanf("%d",p+i);
		set<wolf>S;
		wolf st;
		for(int i=0;i<13;i++)st.m[i]=p[i];
		queue<pair<wolf,int> > Q;
		S.insert(st);
		Q.push(make_pair(st,0));
		bool yet=true;
		while(Q.size()){
			wolf at=Q.front().first;
			int cost=Q.front().second;
			Q.pop();
			bool ok=true;
			for(int i=1;i<12;i++)if(at.m[i]!=i)ok=false;
			if(ok){
				yet=false;
				printf("%d\n",cost);
				break;
			}
			int now=cost;
			for(int i=0;i<13;i++)if(at.m[i]){
				now+=ABS(row[i]-row[at.m[i]])+ABS(col[i]-col[at.m[i]]);
			}
			if(now>20)continue;
			for(int i=0;i<13;i++)if(!at.m[i]){
				for(int j=0;j<4;j++)if(~g[i][j]){
					swap(at.m[i],at.m[g[i][j]]);
					if(!S.count(at)){
						S.insert(at);
						Q.push(make_pair(at,cost+1));
					}
					swap(at.m[i],at.m[g[i][j]]);
				}
			}
		}
		if(yet)printf("NA\n");
	}
}