HDOJ 1044

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1044

        题意有点类似于红白机上玩过的吃豆子游戏，呵呵。在规定的时间内逃出迷宫，并带走丢在路上的宝石们，价值尽可能的大。

       最直接的想法是以宝石为结点，DFS暴力搜索，这样首先需要求俩宝石的最短路径，用A*算法。

       然后就TLE了……

       然后剪枝吧，比如从A点出发，如d(AC) == d(AB) + d(BC)，那么C点是已经搜索过，continue。并且用了贪心策略，按离当前点的距离远近排序待搜索的结点。

       然后继续TLE……

       然后反省，是不是我对自己写的A*算法太自信了，应该记录结点间的距离供以后查找。亦或是不是我的整个思路就是错的……

       开始不自信了，看解题报告……

       原来如此，思路没错，确实应该先纪录结点间的距离。

       再次submit，然后WA……

       又开始不自信了，难道把A*还是DFS写错了？正当我准备用debug必杀技——print大法时，浏览了一下代码，终于发现问题所在了——const int INF = 1000000，这个INF是用来表示结点间不可达的情况，随手写了个100W，想想应该够大了吧，毕竟迷宫才50*50——再看题目，时间的范围正是100W……一怒之下后面加了俩0，AC了。

       早知要纪录所有结点间距离，也不用A*了，BFS更快。

       以下代码（因为用了A*，有点长）：

#include <cstdio> #include <cstring> #include <cmath> #include <map> #include <vector> using namespace std; const int INF = 100000000; const int WALK[4][2] = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}}; struct Location { int x_, y_; }; bool IsLocationEqual(const Location &a, const Location &b) { return a.x_ == b.x_ && a.y_ == b.y_; } struct Point { int g_; int h_; int f_; }; struct Compare { bool operator ()(const Location &a, const Location &b) { return (a.x_ > b.x_) || (a.x_ >= b.x_ && a.y_ > b.y_); } }; typedef map<Location, Point, Compare> PointMap; struct Jewel { int value_; Location loc_; }; struct Maze { char grids_[50][51]; int time_; Location start_loc_, goal_loc_; int jewels_dis_[12][12]; int cur_index_; Jewel jewels_[12]; int jewels_count_; bool exists_[10]; int wid_, len_; int max_value_; char Grid(const Location &loc) { return grids_[loc.y_][loc.x_]; } int GoalIndex() { return jewels_count_ + 1; } int StartIndex() { return jewels_count_; } int ThoughtDis(const Location &a, const Location &b) { return fabs(a.x_ - b.x_) + fabs(a.y_ - b.y_); } void GetMinFPoint(const PointMap &point_map, Location *p_loc, Point *p_point) { Point min_point; min_point.f_ = INF; Location min_loc; PointMap &temp = const_cast<PointMap &>(point_map); PointMap::iterator it; for (it=temp.begin(); it!=temp.end(); ++it) { if (it->second.f_ < min_point.f_) { min_point = it->second; min_loc = it->first; } } *p_loc = min_loc; *p_point = min_point; } Location NextLocation(const Location &src, const int &index) { Location r; r.x_ = src.x_ + WALK[index][0]; r.y_ = src.y_ + WALK[index][1]; return r; } bool IsLocationLegal(const Location &loc) { return loc.x_ >= 0 && loc.x_ < wid_ && loc.y_ >= 0 && loc.y_ < len_; } bool CanMove(const Location &loc) { return Grid(loc) != '*'; } void RemoveFromTable(PointMap *p_table, const PointMap::iterator &it) { if (it != p_table->end()) p_table->erase(it->first); } int MinDis(const Location &start, const Location &goal) { PointMap open_table, close_table; Point start_point; start_point.g_ = 0; start_point.f_ = start_point.h_ = ThoughtDis(start, goal); open_table[start] = start_point; while (!open_table.empty()) { Point wait_point; Location wait_loc; GetMinFPoint(open_table, &wait_loc, &wait_point); if (IsLocationEqual(wait_loc, goal)) return wait_point.g_; open_table.erase(wait_loc); close_table[wait_loc] = wait_point; for (int i=0; i<4; ++i) { Location next = NextLocation(wait_loc, i); if (!IsLocationLegal(next) || !CanMove(next)) continue; Point next_point; next_point.g_ = wait_point.g_ + 1; next_point.h_ = ThoughtDis(next, goal); next_point.f_ = next_point.g_ + next_point.h_; PointMap::iterator open_it = open_table.find(next); if (open_it != open_table.end() && open_it->second.f_ <= next_point.f_) continue; PointMap::iterator close_it = close_table.find(next); if (close_it != close_table.end() && close_it->second.f_ <= next_point.f_) continue; RemoveFromTable(&open_table, open_it); RemoveFromTable(&close_table, close_it); open_table[next] = next_point; } } return INF; } void GenerateAllDis() { for (int i=0; i<12; ++i) { memset(jewels_dis_[i], -1, 12 * sizeof(jewels_dis_[i][0])); } for (int i=0; i<jewels_count_+1; ++i) { for (int j=i+1; j<jewels_count_+2; ++j) { int t = MinDis(jewels_[i].loc_, jewels_[j].loc_); jewels_dis_[i][j] = jewels_dis_[j][i] = t; } } } void GetWaitingIndexes(vector<int> *p_jewel_indexes) { for (int i=0; i<jewels_count_; ++i) { if (exists_[i]) p_jewel_indexes->push_back(i); } } void Sort(vector<int> *p_jewel_indexes) { int size = p_jewel_indexes->size(); for (int i=size-1; i>0; --i) { for (int j=0; j<i; ++j) { if (jewels_[(*p_jewel_indexes)[j]].value_ < jewels_[(*p_jewel_indexes)[j+1]].value_) { int t = (*p_jewel_indexes)[j]; (*p_jewel_indexes)[j] = (*p_jewel_indexes)[j+1]; (*p_jewel_indexes)[j+1] = t; } } } for (int i=size-1; i>0; --i) { for (int j=0; j<i; ++j) { if (jewels_dis_[cur_index_][(*p_jewel_indexes)[j]] > jewels_dis_[cur_index_][(*p_jewel_indexes)[j+1]]) { int t = (*p_jewel_indexes)[j]; (*p_jewel_indexes)[j] = (*p_jewel_indexes)[j+1]; (*p_jewel_indexes)[j+1] = t; } } } } bool JewelReached(const int &index, vector<int> &searched_jewels) { vector<int>::iterator it; for (it=searched_jewels.begin(); it<searched_jewels.end(); ++it) { if (jewels_dis_[cur_index_][index] == jewels_dis_[cur_index_][*it] + jewels_dis_[*it][index]) return true; } return false; } void SearchNode(const int &max_value, const int &value_sum) { const int &goal_dis = jewels_dis_[cur_index_][GoalIndex()]; if (time_ < goal_dis) return; int store = cur_index_; vector<int> waiting_jewels; waiting_jewels.reserve(10); vector<int> searched_jewels; searched_jewels.reserve(10); GetWaitingIndexes(&waiting_jewels); Sort(&waiting_jewels); vector<int>::iterator it = waiting_jewels.begin(); for (it=waiting_jewels.begin(); it<waiting_jewels.end(); ++it) { if (time_ < jewels_dis_[store][*it]) continue; if (JewelReached(*it, searched_jewels)) continue; time_ -= jewels_dis_[*it][store]; cur_index_ = *it; exists_[*it] = false; int temp = value_sum + jewels_[*it].value_; SearchNode(max_value, temp); if (max_value_ == max_value) return; time_ += jewels_dis_[*it][store]; exists_[*it] = true; cur_index_ = store; searched_jewels.push_back(*it); } if (value_sum > max_value_) max_value_ = value_sum; } void Search() { cur_index_ = StartIndex(); memset(exists_, true, 10 * sizeof(exists_[0])); max_value_ = -1; jewels_[StartIndex()].loc_ = start_loc_; jewels_[GoalIndex()].loc_ = goal_loc_; int max_value = 0; for (int i=0; i<jewels_count_; ++i) { max_value += jewels_[i].value_; } GenerateAllDis(); SearchNode(max_value, 0); } }; int main() { int case_time; scanf("%d", &case_time); for (int i=1; i<=case_time; ++i) { Maze maze; scanf("%d%d%d%d", &maze.wid_, &maze.len_, &maze.time_, &maze.jewels_count_); for (int j=0; j<maze.jewels_count_; ++j) { scanf("%d", &maze.jewels_[j].value_); } getchar(); for (int j=0; j<maze.len_; ++j) { for (int k=0; k<maze.wid_; ++k) { char c = getchar(); maze.grids_[j][k] = c; if (c >= 'A' && c <= 'J') { Location *p_loc = &maze.jewels_[c-'A'].loc_; p_loc->x_ = k; p_loc->y_ = j; } else if (c == '@') { maze.start_loc_.x_ = k; maze.start_loc_.y_ = j; } else if (c == '<') { maze.goal_loc_.x_ = k; maze.goal_loc_.y_ = j; } } getchar(); } maze.Search(); printf("Case %d:\n", i); if (maze.max_value_ >= 0) { printf("The best score is %d.\n", maze.max_value_); } else { printf("Impossible\n"); } if (i < case_time) printf("\n"); } return 0; }