SRM 506(2-1000pt)

DIV2 1000pt

题意：一个由n*m的网格组成的棋盘，有四种点，'.'表示空点，'#'表示是墙不能走，'$'表示起点(同样是空点)，'1'~'9'表示该点有复活时间为t的怪兽。每次，可以从一个点走到其上下左右的四个点，只要他们在棋盘上且不是墙，这样记为走了一步。如果走到的点有怪兽i，则杀死它，在杀死该怪兽以后，如果人又走了ti步(ti为该怪兽的复活时间)则该怪兽会复活，如果第ti步恰好走回到含有怪兽i的该点，则怪兽i会被再次杀死。问最少要多少步，才能使得整个棋盘上所有怪物同时处于死亡状态。如果不行，输出-1。

　　　n, m <= 50

解法：1、因为复活时间为1-9，所有最多有9个怪物。

　　　2、如果从这些已知的某个怪物出发，则最多有9!中可能的路径。

　　　所以得到解法，首先用BFS预处理出点'$'到所有怪物的最短距离，再预处理出每个怪物到其他怪物的最短距离，这一步时间复杂度最多O(10×50×50)。然后枚举出发的怪兽，求出从该怪兽出发，到使得所有怪物同时死亡所需要的最短时间，该时间加上'$'到出发怪兽的距离即为所求最短距离。　　

　　　为了方便编码时处理怪兽复活问题，所以枚举出发怪兽的时候，可以写成枚举在哪个怪兽那里结束，然后倒推。

tag:BFS, DFS

 // BEGIN CUT HERE
 /*
  * Author:  plum rain
  * score :
  */
 /*

  */
 // END CUT HERE
 #line 11 "SlimeXResidentSlime.cpp"
 #include <sstream>
 #include <stdexcept>
 #include <functional>
 #include <iomanip>
 #include <numeric>
 #include <fstream>
 #include <cctype>
 #include <iostream>
 #include <cstdio>
 #include <vector>
 #include <cstring>
 #include <cmath>
 #include <algorithm>
 #include <cstdlib>
 #include <set>
 #include <queue>
 #include <bitset>
 #include <list>
 #include <string>
 #include <utility>
 #include <map>
 #include <ctime>
 #include <stack>

 using namespace std;

 #define CLR(x) memset(x, 0, sizeof(x))
 #define CLR1(x) memset(x, -1, sizeof(x))
 #define PB push_back
 #define MP make_pair
 #define SZ(v) ((int)(v).size())
 #define zero(x) (((x)>0?(x):-(x))<eps)
 #define out(x) cout<<#x<<":"<<(x)<<endl
 #define tst(a) cout<<#a<<endl
 #define CINBEQUICKER std::ios::sync_with_stdio(false)

 typedef vector<int> VI;
 typedef vector<string> VS;
 typedef vector<double> VD;
 typedef long long int64;
 typedef pair<int, int> pii;

 const double eps = 1e-;
 const double PI = atan(1.0)*;
 const int maxint = ;

 struct bfs_nod{
     int x, y, d;
 };

 struct Nod{
     Nod(int xx, int yy, int cc){
         x = xx; y = yy; c = cc;
     }
     int x, y, c;
 };

 int dir[][] = {{-, }, {, }, {, -}, {, }};

 pii stt;
 int ans, n, m, nod_sz;
 map<pii, int> mp;
 bool v[][];
 bool vis[];
 int d[][];
 vector<Nod> nod;
 VS A;
 bfs_nod an[];

 bool cmp(Nod a, Nod b)
 {
     return a.c < b.c;
 }

 bool ok(int x, int y)
 {
     if (x <  || y < ) return ;
     if (x >= n || y >= m) return ;
     return A[x][y] != '#';
 }

 void BFS (int x, int y, int pos)
 {
     CLR (v);
     v[x][y] = ;

     int l = , r = ;
     bfs_nod tmp; tmp.d = ;
     for (int i = ; i < ; ++ i)
         if (ok(x+dir[i][], y+dir[i][])){
             int tx = x + dir[i][], ty = y + dir[i][];
             if (v[tx][ty]) continue;
             tmp.x = tx; tmp.y = ty;
             v[tx][ty] = ;
             an[r++] = tmp;
         }

     while (l < r){
         tmp = an[l++];
         if (mp.count(MP(tmp.x, tmp.y))){
             int num = mp[MP(tmp.x, tmp.y)];
             d[num][pos] = d[pos][num] = tmp.d;
         }

         ++ tmp.d;
         for (int i = ; i < ; ++ i)
             if (ok(tmp.x+dir[i][], tmp.y+dir[i][])){
                 bfs_nod tmp2 = tmp;
                 int tx = tmp2.x + dir[i][], ty = tmp2.y + dir[i][];
                 if (v[tx][ty]) continue;
                 tmp2.x = tx; tmp2.y = ty;
                 v[tx][ty] = ;
                 an[r++] = tmp2;
             }
     }
 }

 void DFS (int p, int len, int num)
 {
     if (num == nod_sz){
         if (d[][p] > )
             ans = min(ans, len + d[][p]);
         return ;
     }

     vis[p] = ;
     for (int i = ; i < nod_sz; ++ i)
         if (!vis[i] && d[p][i] >  && len+d[p][i] < nod[i].c)
             DFS (i, len+d[p][i], num+);
     vis[p] = ;
 }

 class SlimeXResidentSlime
 {
     public:
         int exterminate(vector <string> AA){
             A = AA;
             n = A.size(); m = A[].size();
             nod.clear();
             for (int i = ; i < n; ++ i)
                 for (int j = ; j < m; ++ j){
                     if (A[i][j] == '.' || A[i][j] == '#') continue;
                     if (A[i][j] == '$'){
                         stt.first = i; stt.second = j;
                     }
                     else
                         nod.PB(Nod(i, j, A[i][j]-''));
                 }
             if (nod.size() > ) return -;
             sort (nod.begin(), nod.end(), cmp);

             nod_sz = nod.size();
             mp.clear();
             for (int i = ; i < nod_sz; ++ i)
                 mp[make_pair(nod[i].x, nod[i].y)] = i;
             mp[stt] = ;

             CLR1 (d);
             BFS (stt.first, stt.second, );
             for (int i = ; i < nod_sz; ++ i)
                 BFS (nod[i].x, nod[i].y, i);

             ans = maxint;
             for (int i = ; i < nod_sz; ++ i){
                 CLR (vis);
                 DFS (i, , );
             }
             if (ans == maxint) return -;
             return ans;
         }

 // BEGIN CUT HERE
     public:
     //void run_test(int Case) { if ((Case == -1) || (Case == 0)) test_case_0(); if ((Case == -1) || (Case == 1)) test_case_1(); if ((Case == -1) || (Case == 2)) test_case_2(); if ((Case == -1) || (Case == 3)) test_case_3(); }
     void run_test(int Case) { if ((Case == -) || (Case == )) test_case_0();}
     private:
     template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
     void verify_case(int Case, const int &Expected, const int &Received) { cerr << "Test Case #" << Case << "..."; if (Expected == Received) cerr << "PASSED" << endl; else { cerr << "FAILED" << endl; cerr << "\tExpected: \"" << Expected << '\"' << endl; cerr << "\tReceived: \"" << Received << '\"' << endl; } }
     void test_case_0() { string Arr0[] =
 {".##.###..#....##.#.#......##...#.#....#####.#....#", "####..#####.####..#....###.#..######.##.#.#.##..##", ".##.#####.#.#####.#.###....#.##..##.##.#...######.", ".#.####.#..#.###.#.#....#.#.#.##.#.#..###..#.####.", "###.#.##....#..#..#.##..#####.####..##..#.#.#.#...", "....##.###...#####.#..#.######..####..#.##.#..###.", "######.##.#.##...#..#.#####..#..##.#.#.##.##.#....", "####.###..##.##.##..##..##.#####.#.####.#.##...###", "#.....#.###..#...#.###....#..#.#.#.##.#####.#....#", "###.###.##.#..#..###.###..##...#...#.##.#.####..#.", "..#....#..#..##.##...#....####.......#.####..#..##", ".#.....####.#.##.#.#.#..##.#.#.......####.$.###.##", "#####..#.#.##..#...##.#..##....#.##.##.#....##.###", "#.####...###.##.#..#.#....#.....#.#..###..#..##..#", ".#.##.#...########.#.......#..#..###.###.#.#.##.#.", ".##....#...##..##...#.#...#....##.##..#.....#.##..", "..##...###..#..#####..#.##..#.#.#..#.#....#.###.#.", ".####...##...#.##..#.#.#.#...###....######.....###", "#..##.###....#..###...####..#####.##.##.#.#..##...", "##...#..###..#.#.#.#.#...#.#.....###..#.#..#...###", "..#####.#.####..##.........##...###...#..###.#.###", "#.####.#..##....######..##.#.#...#..#..##..#.#...#", "...##.#..###....##.#.....#..#.#..#..##.#.....#...#", ".....#...#.#..###..##.##.....#.#..#.##.###.####.#.", ".#.#.#.#.####....#.##...#.###.###.#..#..#.###....#", ".#...#...#.....##.#..#.#...#.###..#...#.##.#..#.##", "#..##.#.##.##.####.##.##1.##...#.#...####..#.###.#", "#.##...###.##....####.##.###.##..##.#.#.#.#.#.....", ".......###...#.####....#..###..#.#.####...##.#####", "####..#..######........#..######.####.#...#.....##", "#######..#####...##..#.#...##..##..##.##.##.#...#.", "##..###.....#.#######..#.#...####....#.####.....##", "##.##...#.###.##.#.###...#....###....###..#####.#.", "#...#.###..#....#.###......#.#..##.#..##.....#.#.#", ".#.#.##..#..#..######.#.9...###.#.#..#.#####...#..", "#.##.#.###.####.###...#.#..####.....##.##.###...##", "#.....##.##....#######...#...#..#.##.#.#.##....###", "###.#.#.##.....#.#..###.#.#..#...##.##.###...##..#", "#.....##.#.#.####.#....##..##.#....##.##...#######", "..#...##..#.#####...#.#.##...##....#.#..#.#.#....#", "#.###...#####.##..##.##..##.###.####.#..#.#..#...#", "####.###...####.#..#..#....#.######.#.##.......#.#", "..#...#.....###....#####.##.##..#.#..#..##.##..#.#", ".###..##.#.#...###.#..#....##..#.#.#..#.#.##.#..##", ".####....#...##.##...###.##...########.#.....##.##", ".#.#######.###...#.....#.##..#.#..#####.#.##..##..", "#.##..#.##.##.####.#.#.#####...##.#.#.##.###...##.", ".###.#.#.#......####..##.##.#.#.#####.###.##...#..", ".#.#.#....#..#.#...#.#.....###...#...#.###......##", "#.##.###..###..#.#...#.######.#.##...##.#..#..####"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); int Arg1 = -; verify_case(, Arg1, exterminate(Arg0)); }
     void test_case_1() { string Arr0[] = {
 "$",
 "",
 ""}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); int Arg1 = -; verify_case(, Arg1, exterminate(Arg0)); }
     void test_case_2() { string Arr0[] = {
 "$124"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); int Arg1 = ; verify_case(, Arg1, exterminate(Arg0)); }
     void test_case_3() { string Arr0[] = {"$.#2"
 ,"#..1"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); int Arg1 = ; verify_case(, Arg1, exterminate(Arg0)); }

 // END CUT HERE

 };

 // BEGIN CUT HERE
 int main()
 {
     //freopen( "a.out" , "w" , stdout );
     SlimeXResidentSlime ___test;
     ___test.run_test(-);
        return ;
 }
 // END CUT HERE