USACO All Latin Squares 解题报告

这道题就做到这儿吧。

running...
real 0m18.792s
user 0m18.564s
sys 0m0.149s
result:
12198297600

/* ID: thestor1 LANG: C++ TASK: latin */#include <iostream>#include <fstream>#include <cmath>#include <cstdio>#include <cstring>#include <climits>#include <cassert>#include <string>#include <vector>#include <list>#include <set>#include <map>#include <queue>#include <stack>#include <algorithm>#include <cassert>using namespace std;void DFS(int r, int c, const int N, unsigned long long int &cnt, vector<vector<bool> > &appearedrow, vector<vector<bool> > &appearedcol, vector<int> &sumrow);void printSquare(vector<vector<int> > &square){cout << "[debug]square:" << endl;for (int i = 0; i < square.size(); ++i){for (int j = 0; j < square[i].size(); ++j){cout << square[i][j];}cout << endl;}}void DFS(int r, int c, const int N, unsigned long long int &cnt, vector<vector<bool> > &appearedrow, vector<vector<bool> > &appearedcol, vector<int> &sumrow){// cout << "[debug][DFS]r: " << r << ", c: " << c << endl;// printSquare(square);if (r == N - 1){// cout << "[debug]" << cnt << endl;cnt++;return;}int num;if (c == N - 1){num = N * (N - 1) / 2 - sumrow[r];if (!appearedcol[num][c]){appearedcol[num][c] = true;DFS(r + 1, 1, N, cnt, appearedrow, appearedcol, sumrow);appearedcol[num][c] = false;// fill(r, c, num, N, cnt, appearedrow, appearedcol, sumrow);}}else{for (int num = 0; num < N; ++num){if (!appearedrow[num][r] && !appearedcol[num][c]){appearedrow[num][r] = true;appearedcol[num][c] = true;sumrow[r] += num;DFS(r, c + 1, N, cnt, appearedrow, appearedcol, sumrow);sumrow[r] -= num;appearedrow[num][r] = false;appearedcol[num][c] = false;}}}}int main(){ifstream fin("latin.in");int N;fin >> N;fin.close();if (N == 2){ofstream fout("latin.out");fout << 1 << endl;fout.close();return 0;}// if (N == 7)// {// ofstream fout("latin.out");// fout << 12198297600 << endl;// fout.close();// return 0;// }// vector<vector<int> > square(N, vector<int>(N, 0));vector<vector<bool> > appearedrow(N, vector<bool>(N, false));vector<vector<bool> > appearedcol(N, vector<bool>(N, false));vector<int> sumrow(N, 0);// vector<int> sumcol(N, 0);for (int i = 0; i < N; ++i){// square[0][i] = i;appearedrow[i][0] = true;appearedcol[i][i] = true;sumrow[0] += i;// sumcol[i] += i;}for (int i = 0; i < N; ++i){// square[i][0] = i;appearedrow[i][i] = true;appearedcol[i][0] = true;sumrow[i] += i;// sumcol[0] += i;}unsigned long long int cnt = 0;// square[1][1] = 0;appearedrow[0][1] = true;appearedcol[0][1] = true;sumrow[1] += 0;unsigned long long int cnt1 = 0;DFS(1, 2, N, cnt1, appearedrow, appearedcol, sumrow);cnt += cnt1;// square[1][1] = 2;appearedrow[0][1] = false;appearedcol[0][1] = false;appearedrow[2][1] = true;appearedcol[2][1] = true;sumrow[1] -= 0;sumrow[1] += 2;cnt1 = 0;DFS(1, 2, N, cnt1, appearedrow, appearedcol, sumrow);cnt += cnt1 * (N - 2);for (int i = N - 1; i > 1; --i){cnt *= i;}ofstream fout("latin.out");fout << cnt << endl;fout.close();return 0;  }