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
1 // BEGIN CUT HERE 2 /* 3 * Author: plum rain 4 * score : 5 */ 6 /* 7 8 */ 9 // END CUT HERE 10 #line 11 "SlimeXResidentSlime.cpp" 11 #include <sstream> 12 #include <stdexcept> 13 #include <functional> 14 #include <iomanip> 15 #include <numeric> 16 #include <fstream> 17 #include <cctype> 18 #include <iostream> 19 #include <cstdio> 20 #include <vector> 21 #include <cstring> 22 #include <cmath> 23 #include <algorithm> 24 #include <cstdlib> 25 #include <set> 26 #include <queue> 27 #include <bitset> 28 #include <list> 29 #include <string> 30 #include <utility> 31 #include <map> 32 #include <ctime> 33 #include <stack> 34 35 using namespace std; 36 37 #define CLR(x) memset(x, 0, sizeof(x)) 38 #define CLR1(x) memset(x, -1, sizeof(x)) 39 #define PB push_back 40 #define MP make_pair 41 #define SZ(v) ((int)(v).size()) 42 #define zero(x) (((x)>0?(x):-(x))<eps) 43 #define out(x) cout<<#x<<":"<<(x)<<endl 44 #define tst(a) cout<<#a<<endl 45 #define CINBEQUICKER std::ios::sync_with_stdio(false) 46 47 typedef vector<int> VI; 48 typedef vector<string> VS; 49 typedef vector<double> VD; 50 typedef long long int64; 51 typedef pair<int, int> pii; 52 53 const double eps = 1e-8; 54 const double PI = atan(1.0)*4; 55 const int maxint = 2139062143; 56 57 struct bfs_nod{ 58 int x, y, d; 59 }; 60 61 struct Nod{ 62 Nod(int xx, int yy, int cc){ 63 x = xx; y = yy; c = cc; 64 } 65 int x, y, c; 66 }; 67 68 int dir[4][2] = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}}; 69 70 pii stt; 71 int ans, n, m, nod_sz; 72 map<pii, int> mp; 73 bool v[100][100]; 74 bool vis[100]; 75 int d[20][20]; 76 vector<Nod> nod; 77 VS A; 78 bfs_nod an[10000]; 79 80 bool cmp(Nod a, Nod b) 81 { 82 return a.c < b.c; 83 } 84 85 bool ok(int x, int y) 86 { 87 if (x < 0 || y < 0) return 0; 88 if (x >= n || y >= m) return 0; 89 return A[x][y] != '#'; 90 } 91 92 void BFS (int x, int y, int pos) 93 { 94 CLR (v); 95 v[x][y] = 1; 96 97 int l = 0, r = 0; 98 bfs_nod tmp; tmp.d = 1; 99 for (int i = 0; i < 4; ++ i) 100 if (ok(x+dir[i][0], y+dir[i][1])){ 101 int tx = x + dir[i][0], ty = y + dir[i][1]; 102 if (v[tx][ty]) continue; 103 tmp.x = tx; tmp.y = ty; 104 v[tx][ty] = 1; 105 an[r++] = tmp; 106 } 107 108 while (l < r){ 109 tmp = an[l++]; 110 if (mp.count(MP(tmp.x, tmp.y))){ 111 int num = mp[MP(tmp.x, tmp.y)]; 112 d[num][pos] = d[pos][num] = tmp.d; 113 } 114 115 ++ tmp.d; 116 for (int i = 0; i < 4; ++ i) 117 if (ok(tmp.x+dir[i][0], tmp.y+dir[i][1])){ 118 bfs_nod tmp2 = tmp; 119 int tx = tmp2.x + dir[i][0], ty = tmp2.y + dir[i][1]; 120 if (v[tx][ty]) continue; 121 tmp2.x = tx; tmp2.y = ty; 122 v[tx][ty] = 1; 123 an[r++] = tmp2; 124 } 125 } 126 } 127 128 void DFS (int p, int len, int num) 129 { 130 if (num == nod_sz){ 131 if (d[10][p] > 0) 132 ans = min(ans, len + d[10][p]); 133 return ; 134 } 135 136 vis[p] = 1; 137 for (int i = 0; i < nod_sz; ++ i) 138 if (!vis[i] && d[p][i] > 0 && len+d[p][i] < nod[i].c) 139 DFS (i, len+d[p][i], num+1); 140 vis[p] = 0; 141 } 142 143 class SlimeXResidentSlime 144 { 145 public: 146 int exterminate(vector <string> AA){ 147 A = AA; 148 n = A.size(); m = A[0].size(); 149 nod.clear(); 150 for (int i = 0; i < n; ++ i) 151 for (int j = 0; j < m; ++ j){ 152 if (A[i][j] == '.' || A[i][j] == '#') continue; 153 if (A[i][j] == '$'){ 154 stt.first = i; stt.second = j; 155 } 156 else 157 nod.PB(Nod(i, j, A[i][j]-'0')); 158 } 159 if (nod.size() > 9) return -1; 160 sort (nod.begin(), nod.end(), cmp); 161 162 nod_sz = nod.size(); 163 mp.clear(); 164 for (int i = 0; i < nod_sz; ++ i) 165 mp[make_pair(nod[i].x, nod[i].y)] = i; 166 mp[stt] = 10; 167 168 CLR1 (d); 169 BFS (stt.first, stt.second, 10); 170 for (int i = 0; i < nod_sz; ++ i) 171 BFS (nod[i].x, nod[i].y, i); 172 173 ans = maxint; 174 for (int i = 0; i < nod_sz; ++ i){ 175 CLR (vis); 176 DFS (i, 0, 1); 177 } 178 if (ans == maxint) return -1; 179 return ans; 180 } 181 182 // BEGIN CUT HERE 183 public: 184 //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(); } 185 void run_test(int Case) { if ((Case == -1) || (Case == 0)) test_case_0();} 186 private: 187 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(); } 188 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 << " Expected: "" << Expected << '"' << endl; cerr << " Received: "" << Received << '"' << endl; } } 189 void test_case_0() { string Arr0[] = 190 {".##.###..#....##.#.#......##...#.#....#####.#....#", "####..#####.####..#....###.#..######.##.#.#.##..##", ".##.#####.#.#####.#.###....#.##..##.##.#...######.", ".#.####.#..#.###.#.#....#.#.#.##.#.#..###..#.####.", "###.#.##....#..#..#.##..#####.####..##..#.#.#.#...", "....##.###...#####.#..#.######..####..#.##.#..###.", "######.##.#.##...#..#.#####..#..##.#.#.##.##.#....", "####.###..##.##.##..##..##.#####.#.####.#.##...###", "#.....#.###..#...#.###....#..#.#.#.##.#####.#....#", "###.###.##.#..#..###.###..##...#...#.##.#.####..#.", "..#....#..#..##.##...#....####.......#.####..#..##", ".#.....####.#.##.#.#.#..##.#.#.......####.$.###.##", "#####..#.#.##..#...##.#..##....#.##.##.#....##.###", "#.####...###.##.#..#.#....#.....#.#..###..#..##..#", ".#.##.#...########.#.......#..#..###.###.#.#.##.#.", ".##....#...##..##...#.#...#....##.##..#.....#.##..", "..##...###..#..#####..#.##..#.#.#..#.#....#.###.#.", ".####...##...#.##..#.#.#.#...###....######.....###", "#..##.###....#..###...####..#####.##.##.#.#..##...", "##...#..###..#.#.#.#.#...#.#.....###..#.#..#...###", "..#####.#.####..##.........##...###...#..###.#.###", "#.####.#..##....######..##.#.#...#..#..##..#.#...#", "...##.#..###....##.#.....#..#.#..#..##.#.....#...#", ".....#...#.#..###..##.##.....#.#..#.##.###.####.#.", ".#.#.#.#.####....#.##...#.###.###.#..#..#.###....#", ".#...#...#.....##.#..#.#...#.###..#...#.##.#..#.##", "#..##.#.##.##.####.##.##1.##...#.#...####..#.###.#", "#.##...###.##....####.##.###.##..##.#.#.#.#.#.....", ".......###...#.####....#..###..#.#.####...##.#####", "####..#..######........#..######.####.#...#.....##", "#######..#####...##..#.#...##..##..##.##.##.#...#.", "##..###.....#.#######..#.#...####....#.####.....##", "##.##...#.###.##.#.###...#....###....###..#####.#.", "#...#.###..#....#.###......#.#..##.#..##.....#.#.#", ".#.#.##..#..#..######.#.9...###.#.#..#.#####...#..", "#.##.#.###.####.###...#.#..####.....##.##.###...##", "#.....##.##....#######...#...#..#.##.#.#.##....###", "###.#.#.##.....#.#..###.#.#..#...##.##.###...##..#", "#.....##.#.#.####.#....##..##.#....##.##...#######", "..#...##..#.#####...#.#.##...##....#.#..#.#.#....#", "#.###...#####.##..##.##..##.###.####.#..#.#..#...#", "####.###...####.#..#..#....#.######.#.##.......#.#", "..#...#.....###....#####.##.##..#.#..#..##.##..#.#", ".###..##.#.#...###.#..#....##..#.#.#..#.#.##.#..##", ".####....#...##.##...###.##...########.#.....##.##", ".#.#######.###...#.....#.##..#.#..#####.#.##..##..", "#.##..#.##.##.####.#.#.#####...##.#.#.##.###...##.", ".###.#.#.#......####..##.##.#.#.#####.###.##...#..", ".#.#.#....#..#.#...#.#.....###...#...#.###......##", "#.##.###..###..#.#...#.######.#.##...##.#..#..####"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = -1; verify_case(0, Arg1, exterminate(Arg0)); } 191 void test_case_1() { string Arr0[] = { 192 "$", 193 "1", 194 "1"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = -1; verify_case(1, Arg1, exterminate(Arg0)); } 195 void test_case_2() { string Arr0[] = { 196 "$124"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 5; verify_case(2, Arg1, exterminate(Arg0)); } 197 void test_case_3() { string Arr0[] = {"$.#2" 198 ,"#..1"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 6; verify_case(3, Arg1, exterminate(Arg0)); } 199 200 // END CUT HERE 201 202 }; 203 204 // BEGIN CUT HERE 205 int main() 206 { 207 //freopen( "a.out" , "w" , stdout ); 208 SlimeXResidentSlime ___test; 209 ___test.run_test(-1); 210 return 0; 211 } 212 // END CUT HERE