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<vector>
#include<cmath>
using namespace std;
#define MAX_N 20
#define WIDTH 100
int OK[5][5] = { {0,0,1,0,0},{0,1,1,1,0},{1,1,1,1,1},{0,1,1,1,0},{0,0,1,0,0} };
int dx[4] = { 1,0,-1,0 }, dy[4] = { 0,1,0,-1 };
pair<int, vector<vector<int>>> dp[MAX_N + 2][WIDTH], E[WIDTH * 10];

int score(vector<vector<int>>p) {
	int sum = 0; pair<int, int>a[12], b[12]; int CNT = 0;
	for (int i = 0; i < 25; i++) {
		if (p[i / 5][i % 5] >= 1)a[p[i / 5][i % 5]] = make_pair(i / 5, i % 5);
	}
	for (int i = 5; i < 20; i++) {
		if (OK[i / 5][i % 5] == 1) { CNT++; b[CNT] = make_pair(i / 5, i % 5); }
	}
	for (int i = 1; i <= 11; i++) { sum += abs(a[i].first - b[i].first) + abs(a[i].second - b[i].second); }
	return sum;
}
vector<vector<int>> Move(vector<vector<int>>p, int x, int y,int dir) {
	swap(p[x + dx[dir]][y + dy[dir]], p[x][y]); return p;
}
int BeemSearch(vector<vector<int>>Z) {
	vector<vector<int>>GOAL; int CNT = 0;
	for (int i = 0; i < 5; i++) { vector<int>GOAL2(5, -1); GOAL.push_back(GOAL2); }
	for (int i = 5; i < 20; i++) {
		if (OK[i / 5][i % 5] == 1) { CNT++; GOAL[i / 5][i % 5] = CNT; }
	}
	GOAL[0][2] = 0; GOAL[4][2] = 0;
	if (Z == GOAL)return 0;
	dp[0][0] = make_pair(score(Z), Z);
	for (int i = 0; i < MAX_N; i++) {
		int CNTS = 0;
		for (int j = 0; j < WIDTH; j++) {
			if (dp[i][j].second.size() == 0)continue;
			vector<vector<int>>D = dp[i][j].second;
			for (int k = 0; k < 25; k++) {
				if (D[k / 5][k % 5] != 0)continue;
				for (int l = 0; l < 4; l++) {
					int cx = (k / 5) + dx[l], cy = (k % 5) + dy[l];
					if (cx < 0 || cx >= 5 || cy < 0 || cy >= 5)continue;
					if (D[cx][cy] <= 0)continue;
					vector<vector<int>>D2 = Move(D, k / 5, k % 5, l);
					E[CNTS] = make_pair(score(D2), D2); CNTS++;
				}
			}
		}
		sort(E, E + CNTS); dp[i + 1][0] = E[0]; int CNT2 = 1;
		if (E[0].first == 0)return i + 1;
		for (int j = 1; j < CNTS; j++) {
			if (E[j - 1] != E[j]) { dp[i + 1][CNT2] = E[j]; CNT2++; }
			if (CNT2 == WIDTH)break;
		}
	}
	return -1;
}
int main() {
	while (true) {
		for (int i = 0; i < MAX_N + 2; i++) {
			for (int j = 0; j < WIDTH; j++) {
				vector<vector<int>>ZERO; dp[i][j] = make_pair(0, ZERO);
			}
		}
		for (int i = 0; i < WIDTH * 10; i++) { vector<vector<int>>ZERO; E[i] = make_pair(0, ZERO); }
		vector<vector<int>>C;
		for (int i = 0; i < 5; i++) { vector<int>C2(5, -1); C.push_back(C2); }
		cin >> C[0][2]; if (C[0][2] == -1)break;
		for (int i = 1; i < 4; i++)cin >> C[1][i];
		for (int i = 0; i < 5; i++)cin >> C[2][i];
		for (int i = 1; i < 4; i++)cin >> C[3][i]; cin >> C[4][2];
		int ret = BeemSearch(C);
		if (ret == -1)cout << "NA" << endl; else cout << ret << endl;
	}
	return 0;
}

C++: #include<bits/stdc++.h>
using namespace std;
  
typedef long long int64;
const int INF = 1 << 30;
  
vector< int > edge[13];
map< string, int > memo;
 
bool back(string str, int cnt){ //枝刈り大事だな
  int X[]={ 2, 1, 2, 3, 0, 1, 2, 3, 4, 1, 2, 3, 2};
  int Y[]={ 0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4};

  int diff = 0;
  for(int i = 0; i < 13; i++){
   
    if(str[i] != '0'){
      int pos = (str[i] > 'A' ? str[i] - 'A' : str[i] - '0');
      diff += abs( X[pos] - X[i]) + abs( Y[pos] - Y[i]);
    }
  }
  return diff + cnt > 20;
}
 
 
int bfs(string mas){
 
  queue< string > que;
  map< string , int > used;
  que.push( mas );
  memo[mas] = 0;
  while(!que.empty()){
 
    string p = que.front(); que.pop();
    if(back( p, memo[p])) break;
    if(p == "0123456789AB0") return memo[p];
 
    for(int i = 0; i < 13; i++){
      if(p[i] == '0') {
        for(int j = 0; j < edge[i].size(); j++){
          string next = p;
          swap( next[i], next[edge[i][j]]);
          if(memo.find(next) != memo.end()) continue;
          que.push( next );
          memo[next] = memo[p] + 1;
        }
      }
    }
  }
  return -1;
}
 
int main(){
  vector< int > mas(13);
 
  edge[0].push_back(2);
  edge[1].push_back(2); edge[1].push_back(4);
  edge[2].push_back(0); edge[2].push_back(1); edge[2].push_back(3); edge[2].push_back(6);
  edge[3].push_back(2); edge[3].push_back(7);
  edge[4].push_back(5);
  edge[5].push_back(1); edge[5].push_back(4); edge[5].push_back(6); edge[5].push_back(9);
  edge[6].push_back(2); edge[6].push_back(5); edge[6].push_back(7); edge[6].push_back(10);
  edge[7].push_back(3); edge[7].push_back(6); edge[7].push_back(8); edge[7].push_back(11);
  edge[8].push_back(7);
  edge[9].push_back(5); edge[9].push_back(10);
  edge[10].push_back(6); edge[10].push_back(9); edge[10].push_back(11); edge[10].push_back(12);
  edge[11].push_back(7); edge[11].push_back(10);
  edge[12].push_back(10);
 
  while(cin >> mas[0], mas[0] != -1){
    for(int i = 1; i < 13; i++){
      cin >> mas[i];
    }
 
    string start = "";
    for(int i = 0; i < 13; i++){
      if(mas[i] >= 10) start += (char)(mas[i] - 10 + 'A');
      else start += mas[i] + '0';
    }
    int ret = bfs(start);
    if(~ret) cout << ret << endl;
    else cout << "NA" << endl;
 
    memo.clear();
  }
}