Usaco Camelot solution report

This question is also a solution obtained by reading the online problem solving report...

First, Knight points connected to King do not need to be enumerated on the entire board. King moves up to two steps. This can pass all test points. As for why, I also found proof on the Internet, but I did not want to read it.

Secondly, Floyd is a very inefficient algorithm, because it determines the time complexity of N ^ 3 undoubtedly, and is suitable for intensive graphs (because the algorithm has nothing to do with the number of edges ), however, we generally encounter sparse graphs. Spfa and even BFS are better. Previously, the Johnson algorithm seems to be applicable to sparse graphs.

Again, the mark provided by usaco is not understood...

/*ID: thestor1LANG: C++TASK: camelot*/#include <iostream>#include <cmath>#include <cstdio>#include <cstring>#include <climits>#include <vector>#include <cassert>#include <string>#include <algorithm>#include <stack>#include <set>#include <queue>using namespace std;struct Position{int r, c;Position(){}Position(int r, int c){this->r = r;this->c = c;}Position(const Position& other):r(other.r), c(other.c){}Position& operator =(const Position& other){r=other.r;c=other.c;return *this;}};const int MAXR = 26;const int MAXC = 30;const int MAXN = MAXR * MAXC;int dis[MAXR][MAXC][MAXR][MAXC];const int directx[] = {-2, -1, 1, 2, 2, 1, -1, -2};const int directy[] = {1, 2, 2, 1, -1, -2, -2, -1};bool marked[MAXR][MAXC];int index(int r, int c, int C){return r * C + c;}bool isWithin(int r, int c, int R, int C){return r >= 0 && r < R && c >= 0 && c < C;}void spfa(const Position &s, const int R, const int C){if(marked[s.r][s.c]){return;}marked[s.r][s.c] = true;for(int i = 0; i < R; ++i){for(int j = 0; j < C; ++j){dis[s.r][s.c][i][j] = INT_MAX;}}dis[s.r][s.c][s.r][s.c] = 0;deque<Position> que;bool onQueue[MAXR][MAXC];memset(onQueue, false, MAXN * sizeof(bool));//int s = index(r, c, C);que.push_back(s);onQueue[s.r][s.c] = true;while(!que.empty()){/*if(que.size() == 51 && que.front().r == 24 && que.front().c == 18){fprintf(stdout, "debug\n");}fprintf(stdout, "que.size: %d\n", que.size());*/Position u = que.front();que.pop_front();//fprintf(stdout, "u: (%d, %d)\n", u.r, u.c);if(dis[s.r][s.c][u.r][u.c] == INT_MAX){continue;}onQueue[u.r][u.c] = false;for(int d = 0; d < 8; ++d){int vr = u.r + directx[d];int vc = u.c + directy[d];if(!isWithin(vr, vc, R, C)){continue;}Position v(vr, vc);//v.r = vr;//v.c = vc;if(dis[s.r][s.c][u.r][u.c] + 1 < dis[s.r][s.c][v.r][v.c]){dis[s.r][s.c][v.r][v.c] = dis[s.r][s.c][u.r][u.c] + 1;if(!onQueue[v.r][v.c]){if(que.empty() || dis[s.r][s.c][v.r][v.c] < dis[s.r][s.c][que.front().r][que.front().c]){que.push_front(v);}else{que.push_back(v);}onQueue[v.r][v.c] = true;}}}}}int main(){FILE *fin  = fopen ("camelot.in", "r");FILE *fout = fopen ("camelot.out", "w");//freopen("log.txt", "w", stdout);int R, C;fscanf(fin, "%d%d\n", &C, &R);//int N = R * C;memset(marked, false, R * C * sizeof(bool));Position king;char r;fscanf(fin, "%c", &r);king.r = r - 'A';int c;fscanf(fin, "%d\n", &c);king.c = c - 1;assert(king.r < R && king.c < C);//fprintf(stdout, "king: \n%d %d\n", king.r, king.c);vector<Position> knights;while(fscanf(fin, "%c", &r) > 0){if(r < 'A' || r > 'Z'){continue;}Position knight;knight.r = r - 'A';fscanf(fin, " %d", &c);knight.c = c - 1;knights.push_back(knight);}//for(int i = 0; i < knights.size(); ++i)//{//assert(knights[i].r < R && knights[i].c < C);//fprintf(stdout, "%c %d\n", knights[i].r + 'A', knights[i].c + 1);//}//fprintf(stdout, "number of knights: %d\n", knights.size());for(int i = 0; i < knights.size(); ++i){spfa(knights[i], R, C);/*for(int r = 0; r < R; ++r){for(int c = 0; c < C; ++c){fprintf(stdout, "%d\t", dis[knights[i].r][knights[i].c][r][c]);}fprintf(stdout, "\n");}*/}int minmoves = -1;for(int gr = 0; gr < R; ++gr)//gathering point{for(int gc = 0; gc < C; ++gc){int knightsdis = 0;for(int i = 0; i < knights.size(); ++i){knightsdis += dis[knights[i].r][knights[i].c][gr][gc];}int kingmove = 0;int pr, pc;int knightsmove = 0;for(int kingmover = -2; kingmover <= 2; ++kingmover){for(int kingmovec = -2; kingmovec <= 2; ++kingmovec){kingmove = max(abs(kingmover), abs(kingmovec));//if(!kingmover && !kingmovec)//{//kingmove = 0;//}//else//{//kingmove = 1;//}pr = king.r + kingmover;pc = king.c + kingmovec;if(!isWithin(pr, pc, R, C)){continue;}spfa(Position(pr, pc), R, C);for(int pk = 0; pk < knights.size(); ++pk) //pickup knight{if(dis[knights[pk].r][knights[pk].c][pr][pc] == INT_MAX || dis[pr][pc][gr][gc] == INT_MAX){continue;}knightsmove = knightsdis - dis[knights[pk].r][knights[pk].c][gr][gc] + dis[knights[pk].r][knights[pk].c][pr][pc] + dis[pr][pc][gr][gc];int moves = knightsmove + kingmove;if(minmoves < 0 || moves < minmoves){minmoves = moves;}}}}}}fprintf(fout, "%d\n", minmoves < 0 ? 0 : minmoves);return 0;}