[HIHO1196]高斯消元·二（高斯消元、枚举自由变元）

题目链接：http://hihocoder.com/problemset/problem/1196

 #include <bits/stdc++.h>
 using namespace std;

 typedef pair<int, int> pii;
 const int maxn = ;
 int equ, var;
 int a[maxn][maxn];
 int x[maxn];
 int free_x[maxn];
 int free_num;
 int ret;

 int gauss() {
     int max_r, col, k;
     free_num = ;
     for(k = , col = ; k < equ && col < var; k++, col++) {
         max_r = k;
         for(int i = k + ; i < equ; i++) {
             if(abs(a[i][col]) > abs(a[max_r][col]))
                 max_r = i;
         }
         if(a[max_r][col] == ) {
             k--;
             free_x[free_num++] = col;
             continue;
         }
         if(max_r != k) {
             for(int j = col; j < var + ; j++)
                 swap(a[k][j], a[max_r][j]);
         }
         for(int i = k + ; i < equ; i++) {
             if(a[i][col] != ) {
                 for(int j = col; j < var + ; j++) {
                     a[i][j] ^= a[k][j];
                 }
             }
         }
     }
     for(int i = k; i < equ; i++) {
         if(a[i][col] != )
             return -;
     }
     if(k < var) return var - k;
     for(int i = var - ; i >= ; i--) {
         x[i] = a[i][var];
         for(int j = i + ; j < var; j++) {
             x[i] ^= (a[i][j] & x[j]);
         }
     }
     return ;
 }

 char G[maxn][maxn];
 int n, m;

 int main() {
     // freopen("in", "r", stdin);
     m = , n = ;
     var = equ = ;
     ret = ;
     memset(a, , sizeof(a));
     for(int i = ; i < n; i++) scanf("%s", G[i]);
     for(int i = ; i < m; i++) {
         for(int j = ; j < n; j++) {
             if(G[i][j] == '') a[i*n+j][var] = ;
             else a[i*n+j][var] = ;
         }
     }
     for(int i = ; i < ; i++) {
         a[i][i] = ;
         if(i %  != ) a[i-][i] = ;
         if(i %  != ) a[i+][i] = ;
         if(i > ) a[i-][i] = ;
         if(i < ) a[i+][i] = ;
     }
     int v = gauss();
     if(v == -) ret = -;
     else if(v != ) {
         ret = maxn;
         int tot =  << v;
         for(int i = ; i < tot; i++) {
             int cnt = ;
             for(int j = ; j < v; j++) {
                 if(i&(<<j)) {
                     x[free_x[j]] = ;
                     cnt++;
                 }
                 else x[free_x[j]] = ;
             }
             for(int j = var - v - ; j >= ; j--) {
                 int idx;
                 for(idx = j; idx < var; idx++) {
                     if(a[j][idx]) break;
                 }
                 x[idx] = a[j][var];
                 for(int l = idx + ; l < var; l++) {
                     if(a[j][l]) x[idx] ^= x[l];
                 }
                 cnt += x[idx];
             }
             ret = min(ret, cnt);
         }
     }
     else for(int i = ; i < var; i++) ret += x[i];
     printf("%d\n", ret);
     vector<pii> va;
     for(int i = ; i < ; i++) {
         if(x[i]) {
             int pos = i + ;
             int r = , c = ;
             while(pos > ) {
                 pos -= ;
                 r++;
             }
             c += pos;
             va.push_back(pii(r, c));
         }
     }
     sort(va.begin(), va.end());
     for(int i = ; i < va.size(); i++) {
         printf("%d %d\n", va[i].first, va[i].second);
     }
     return ;
 }