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 <algorithm>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <numeric>
#include <bitset>
#include <cmath>

static const int MOD = 1000000007;
using ll = long long;
using u32 = unsigned;
using u64 = unsigned long long;
using namespace std;

template<class T> constexpr T INF = ::numeric_limits<T>::max()/32*15+208;

template <class T, class U>
vector<T> make_v(U size, const T& init){ return vector<T>(static_cast<size_t>(size), init); }

template<class... Ts, class U>
auto make_v(U size, Ts... rest) { return vector<decltype(make_v(rest...))>(static_cast<size_t>(size), make_v(rest...)); }

template<class T> void chmin(T &a, const T &b){ a = (a < b ? a : b); }
template<class T> void chmax(T &a, const T &b){ a = (a > b ? a : b); }

int main() {
    vector<vector<int>> G{{2},{2, 5},{0, 1, 3, 6},{2, 7},{5},{1, 4, 6, 9},{2, 5, 7, 10},{3, 6, 8, 11},{7},{5, 10},{6, 9, 11, 12},{7, 10},{10}};
    vector<int> y{0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4}, x{2, 1, 2, 3, 0, 1, 2, 3, 4, 1, 2, 3, 2};
    using P = array<int, 13>;
    P v{};
    iota(v.begin(), v.end(), 0);
    v.back() = 0;
    map<P, int> A;
    auto dfs1 = [&](int a, int b, int cur, auto &&f) -> void {
        if(!A.count(v)) A[v] = cur;
        else chmin(A[v], cur);
        if(cur >= 5) return;
        for (auto &&j : G[a]) {
            if(j != b){
                swap(v[a], v[j]);
                f(j, b, cur+1, f);
                swap(v[a], v[j]);
            }
        }
        for (auto &&j : G[b]) {
            if(j != a){
                swap(v[b], v[j]);
                f(a, j, cur+1, f);
                swap(v[b], v[j]);
            }
        }
        return;
    };
    dfs1(0, 12, 0, dfs1);
    while(cin >> v[0], ~v[0]){
        for (int i = 1; i < 13; ++i) cin >> v[i];
        int ans = 21;
        auto dfs = [&](int cur, auto &&f) -> void {
            if(cur+5 >= ans) return;
            if(A.count(v)) {
                chmin(ans, A[v]+cur);
                return;
            }
            int d = 0, a = -1, b = -1;
            for (int i = 0; i < 13; ++i) {
                if(v[i]) d += abs(y[i]-y[v[i]])+abs(x[i]-x[v[i]]);
                else if(!~a) a = i;
                else b = i;
            }
            if(d+cur >= ans) return;
            for (auto &&j : G[a]) {
                if(j != b){
                    swap(v[a], v[j]);
                    f(cur+1, f);
                    swap(v[a], v[j]);
                }
            }
            for (auto &&j : G[b]) {
                if(j != a){
                    swap(v[b], v[j]);
                    f(cur+1, f);
                    swap(v[b], v[j]);
                }
            }

        };
        dfs(0, dfs);
        if(ans == 21) puts("NA");
        else cout << ans << "\n";
    }
    return 0;
}