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<map>
#include<deque>
#include<cstring>
#include<cstdlib>
using namespace std;
struct board{
	char s[14];
	int z1,z2;
	bool operator<(const board& rhs)const{return strcmp(s,rhs.s)<0;}
};
int main(){
	int d[13][5]={
		{2,-1},			//0
		{2,5,-1},		//1
		{0,1,3,6,-1},	//2
		{2,7,-1},		//3
		{5,-1},			//4
		{1,4,6,9,-1},	//5
		{2,5,7,10,-1},	//6
		{3,6,8,11,-1},	//7
		{7,-1},			//8
		{5,10,-1},		//9
		{6,9,11,12,-1},	//10
		{7,10,-1},		//11
		{10,-1},		//12
	};
	int gx[]={2,1,2,3,0,1,2,3,4,1,2,3,2};
	int gy[]={0,1,1,1,2,2,2,2,2,3,3,3,4};
	board goal;
	strcpy(goal.s,"0123456789:;0");
	for(;;){
		typedef map<board,int>SM;
		SM stepmap;
		deque<board> que;
		board b0;
		b0.z1=b0.z2=-1;
		for(int i=0;i<13;i++){
			int v;
			cin>>v;
			if(v==-1)
				return 0;
			b0.s[i]='0'+v;
			if(v==0){
				if(b0.z1==-1)
					b0.z1=i;
				else
					b0.z2=i;
			}
		}
		b0.s[13]=0;
		que.push_back(b0);
		stepmap[b0]=1;
		while(!que.empty()){
			board b=que.front();
			if(strcmp(b.s,goal.s)==0){
				break;
			}
			que.pop_front();
			int dist=0;
			for(int i=0;i<13;i++){
				int v=b.s[i]-'0';
				if(v){
					dist+=abs(gx[v]-gx[i])+abs(gy[v]-gy[i]);
				}
			}
			int step=stepmap[b];
			if(step-1+dist<=20){
				for(int i=0;d[b.z1][i]!=-1;i++){
					board bn=b;
					bn.z1=d[b.z1][i];
					if(bn.z1!=bn.z2){
						swap(bn.s[b.z1],bn.s[bn.z1]);
						int&ns=stepmap[bn];
						if(!ns){
							ns=step+1;
							que.push_back(bn);
						}
					}
				}
				for(int i=0;d[b.z2][i]!=-1;i++){
					board bn=b;
					bn.z2=d[b.z2][i];
					if(bn.z2!=bn.z1){
						swap(bn.s[b.z2],bn.s[bn.z2]);
						int&ns=stepmap[bn];
						if(!ns){
							ns=step+1;
							que.push_back(bn);
						}
					}
				}
			}
		}
		if(stepmap[goal]==0)
			cout<<"NA "<<endl;
		else
			cout<<stepmap[goal]-1<<endl;
	}
}

C++: #include <iostream>
#include <map>
#include <queue>
#include <cstdlib>
#include <vector>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)

int to[13][5] = {
	{2,-1},
	{2,5,-1},
	{0,1,3,6,-1},
	{2,7,-1},
	{5,-1},
	{1,4,6,9,-1},
	{2,5,7,10,-1},
	{3,6,8,11,-1},
	{7,-1},
	{5,10,-1},
	{6,9,11,12},
	{7,10,-1},
	{10,-1}
};
int solve(vector<int> data){
	queue< vector<int> > Q;
	map<vector<int>,int> done;
	Q.push(data);
	done[Q.front()] = 0;
	
	while(Q.size()){
		vector<int> q = Q.front(); Q.pop();
		int dif = 0;
		rep(i,13)if(q[i])dif += abs(i-q[i]);
		if(dif==0)return done[q];
		if(dif+done[q]>=20)continue;
		int curcost = done[q];
		rep(x,13){
			if(q[x] == 0){
				rep(i,5){
					if(!~to[x][i])break;
					swap(q[x],q[to[x][i]]);
					if(done.find(q) == done.end() ){
						done[q] = curcost+1;
						Q.push(q);
					}
					swap(q[x],q[to[x][i]]);
				}
			}
		}
	}
	return 21;
}
int main(){
	vector<int> data(13);
	while(1){
		rep(i,13)if(!(cin >> data[i]))return 0;
		int ans = solve(data);
		if(ans > 20)cout << "NA" << endl;
		else cout << ans << endl;
	}
}