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 <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 (t-1>=lt) return 0;
	if (s==0) { lt=t-1; 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) 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(1,0,0,0);
	  if (lt==21) cout << "NA" << endl; else cout << lt << 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(sx[i]-x[p[y2][x2]-1])+abs(sy[i]-y[p[y2][x2]-1])-(abs(x2-x[p[y2][x2]-1])+abs(y2-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; k++;}
		  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;
}