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;

int fie[5][5];
int o_fie[5][5]={
    -1,-1,0,-1,-1,
    -1,1,2,3,-1,
    4,5,6,7,8,
    -1,9,10,11,-1
    -1,-1,0,-1,-1,
};

int ox[12],oy[12],zx[2],zy[2],zcnt;
int res;
bool flag;

int dx[4]={1,0,-1,0};
int dy[4]={0,1,0,-1};

void dfs(int v,int dist,int pd,int pu){
    if(dist==0){
        flag=true;
        res=min(res,v);
        return;
    }
    for(int i=0;i<4;i++){
        for(int j=0;j<2;j++){
            if(pu==j && (pd+2)%4==i)continue;
            int nx=zx[j]+dx[i],ny=zy[j]+dy[i];
            if(nx>=0 && nx<5 && ny>=0 && ny<5){
                if(fie[nx][ny]<=0)continue;
                int ch=fie[nx][ny];
                int ndist=dist;
                ndist-=abs(ox[ch]-nx)+abs(oy[ch]-ny);
                swap(fie[nx][ny],fie[zx[j]][zy[j]]);
                ndist+=abs(ox[ch]-zx[j])+abs(oy[ch]-zy[j]);
                zx[j]+=dx[i];
                zy[j]+=dy[i];
                if(v+1+ndist<=res)dfs(v+1,ndist,i,j);
                zx[j]-=dx[i];
                zy[j]-=dy[i];
                swap(fie[nx][ny],fie[zx[j]][zy[j]]);
            }
        }
    }
}
int dist;

int main(void){
    for(int i=0;i<5;i++){
        for(int j=abs(2-i);j<=4-abs(2-i);j++){
            ox[o_fie[i][j]]=j;
            oy[o_fie[i][j]]=i;
        }
    }
    while(1){
        memset(fie,-1,sizeof(fie));
        dist=0;
        zcnt=0;
        for(int i=0;i<5;i++){
            for(int j=abs(2-i);j<=4-abs(2-i);j++){
                scanf("%d",&fie[j][i]);
                if(fie[j][i]==-1)return 0;
            }
        }
        for(int i=0;i<5;i++){
            for(int j=abs(2-i);j<=4-abs(2-i);j++){
                int v=fie[j][i];
                if(v==0){
                    zx[zcnt]=j;
                    zy[zcnt++]=i;
                }else dist+=abs(ox[v]-j)+abs(oy[v]-i);
            }
        }
        if(dist>20){
            printf("NA\n");
        }else{
            int i=0;
            flag=false;
            res=20;
            dfs(0,dist,-1,-1);
            if(flag){
                printf("%d\n",res);
            }
            if(!flag)printf("NA\n");
        }
    }
    return 0;
}