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 <vector>

using namespace std;
 
struct P {
    int x, y;
    P(int x, int y) : x{x}, y{y} {}
};
 
int limit;
vector<int> v;

constexpr int X[] = {2, 1, 2, 3, 0, 1, 2, 3, 4, 1, 2, 3, 2};
constexpr int Y[] = {0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4};
 
int getPos(P p)
{
    switch (p.y) {
        case 0:
            return (p.x == 2 ? 0 : -1);
        case 1:
            return (1 <= p.x && p.x <= 3 ? p.x : -1);
        case 2:
            return (p.x <= 4 ? p.x + 4 : -1); 
        case 3:
            return (1 <= p.x && p.x <= 3 ? p.x + 8 : -1);
        case 4:
            return (p.x == 2 ? 12 : -1);
    }
    return -1;
}
 
int getMD()
{
    int sum = 0;
    for (int i = 0; i < 13; i++) {
        if (v[i] == 0) continue;
        P np{X[i], Y[i]};
        P tp{X[v[i]], Y[v[i]]};
        sum += abs(np.x - tp.x) + abs(np.y - tp.y);
    }
    return sum;
}
 
constexpr int dx[] = {-1, 0, 1, 0};
constexpr int dy[] = {0, -1, 0, 1};
 
bool dfs(const int* sp, int step)
{
    int md = getMD();
    if (md == 0) return 1;
    if (md + step > limit) {
        return 0;
    }
    
    for (int i = 0; i < 2; i++) {
        int x = X[sp[i]], y = Y[sp[i]];
        for (int j = 0; j < 4; j++) {
            int nx = x + dx[j], ny = y + dy[j];
            P np{nx, ny};
            
            int next = getPos(np);
            if (next == -1) continue;
            
            int nsp1[] = {next, sp[1]}, nsp2[] = {sp[0], next};
            
            swap(v[sp[i]], v[next]);
            if (i == 0 && dfs(nsp1, step + 1)) {
                return 1;
            }
            if (i == 1 && dfs(nsp2, step + 1)) {
                return 1;
            }
            swap(v[sp[i]], v[next]);
        }
    }
    return 0;
}
 
int main()
{
    int x;
    while (cin >> x, x != -1) {
        int sp[2];
        v.resize(13); v[0] = x;
        for (int i = 1; i < 13; i++) {
            cin >> v[i];
        }

        for (int i = 0, j = 0; i < 13; i++) {
            if (v[i] == 0) {
                sp[j++] = i;
            }
        }

        bool found = 0;
        constexpr int LIMIT = 20;
        for (limit = 0; limit <= LIMIT; limit++) {
            if (dfs(sp, 0)) {
                cout << limit << endl;
                found = 1;
                break;
            }
        }
        if (!found) {
            cout << "NA" << endl;
        }
    }
    return 0;
}

C++: #include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <map>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
class NODE{
public:
	vector<int> data;
	int depth;
	int e[2];
	NODE(int a[13],int d,int E[2]){
		data.resize(13);
		rep(i,13)data[i] = a[i];
		depth = d;
		rep(i,2)e[i] = E[i];
	}
	NODE(){
		depth = 0;
		data.resize(13);
	}
};

int di[13][10] = {
	{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},
	{3,6,7,11,-1},
	{7-1},
	{5,10,-1},
	{6,9,11,12,-1},
	{7,10,-1},
	{10,-1}
};
int rx[] = {3,2,3,4,1,2,3,4,5,2,3,4,3};
int ry[] = {1,2,2,2,3,3,3,3,3,4,4,4,5};

int main(){
	while(1){
		int ret = 21;
		NODE fst; int cnt = 0;
		rep(i,13){
			if(cin >>fst.data[i] , fst.data[i] != -1){
				if(fst.data[i] == 0){
					fst.e[cnt] = i;
					cnt++;
				}
			}else{
				return 0;
			}
		}
		map< vector<int> , int > done;
		
		queue<NODE> Q;
		Q.push(fst);
		done[Q.front().data] = 0;
		
		while(Q.size()){
			NODE q = Q.front(); Q.pop();

			int mndist = 0;
			rep(i,13)mndist += abs(rx[q.data[i]]-rx[i]) + abs(ry[q.data[i]]-ry[i]);
			if(mndist + q.depth > 23)continue;
			
			
			if( q.data[0] == 0 && q.data[1] == 1 && q.data[2] == 2 && q.data[3] == 3 && q.data[4] == 4 && q.data[5] == 5 && q.data[6] == 6 && q.data[7] == 7 &&
					q.data[8] == 8 && q.data[9] == 9 && q.data[10]==10 && q.data[11]==11 && q.data[12]==0
			){
				cout << q.depth << endl;
				goto jmp;
			}

			rep(o,2){
				for(int i=0;di[q.e[o]][i] != -1;i++){
					NODE next = q;
					next.e[o] = next.data[di[q.e[o]][i]];
					swap(next.data[q.e[o]] , next.data[di[q.e[o]][i]]);
					next.depth = q.depth + 1;
					
					if( done.find(next.data) == done.end() ){
						done[next.data] = next.depth;
						if( q.depth < 21)Q.push(next);
					}
				}
			}
		}
		cout << "NA" << endl;
		jmp:;
	}
}