[HIHO1196]高斯消元·二（高斯消元、枚举自由变元）

1 #include <bits/stdc++.h>
2 using namespace std;
3
4 typedef pair<int, int> pii;
5 const int maxn = 230;
6 int equ, var;
7 int a[maxn][maxn];
8 int x[maxn];
9 int free_x[maxn];
10 int free_num;
11 int ret;
12
13 int gauss() {
14     int max_r, col, k;
15     free_num = 0;
16     for(k = 0, col = 0; k < equ && col < var; k++, col++) {
17         max_r = k;
18         for(int i = k + 1; i < equ; i++) {
19             if(abs(a[i][col]) > abs(a[max_r][col]))
20                 max_r = i;
21         }
22         if(a[max_r][col] == 0) {
23             k--;
24             free_x[free_num++] = col;
25             continue;
26         }
27         if(max_r != k) {
28             for(int j = col; j < var + 1; j++)
29                 swap(a[k][j], a[max_r][j]);
30         }
31         for(int i = k + 1; i < equ; i++) {
32             if(a[i][col] != 0) {
33                 for(int j = col; j < var + 1; j++) {
34                     a[i][j] ^= a[k][j];
35                 }
36             }
37         }
38     }
39     for(int i = k; i < equ; i++) {
40         if(a[i][col] != 0)
41             return -1;
42     }
43     if(k < var) return var - k;
44     for(int i = var - 1; i >= 0; i--) {
45         x[i] = a[i][var];
46         for(int j = i + 1; j < var; j++) {
47             x[i] ^= (a[i][j] & x[j]);
48         }
49     }
50     return 0;
51 }
52
53 char G[maxn][maxn];
54 int n, m;
55
56 int main() {
57     // freopen("in", "r", stdin);
58     m = 5, n = 6;
59     var = equ = 30;
60     ret = 0;
61     memset(a, 0, sizeof(a));
62     for(int i = 0; i < n; i++) scanf("%s", G[i]);
63     for(int i = 0; i < m; i++) {
64         for(int j = 0; j < n; j++) {
65             if(G[i][j] == '0') a[i*n+j][var] = 1;
66             else a[i*n+j][var] = 0;
67         }
68     }
69     for(int i = 0; i < 30; i++) {
70         a[i][i] = 1;
71         if(i % 6 != 0) a[i-1][i] = 1;
72         if(i % 6 != 5) a[i+1][i] = 1;
73         if(i > 5) a[i-6][i] = 1;
74         if(i < 24) a[i+6][i] = 1;
75     }
76     int v = gauss();
77     if(v == -1) ret = -1;
78     else if(v != 0) {
79         ret = maxn;
80         int tot = 1 << v;
81         for(int i = 0; i < tot; i++) {
82             int cnt = 0;
83             for(int j = 0; j < v; j++) {
84                 if(i&(1<<j)) {
85                     x[free_x[j]] = 1;
86                     cnt++;
87                 }
88                 else x[free_x[j]] = 0;
89             }
90             for(int j = var - v - 1; j >= 0; j--) {
91                 int idx;
92                 for(idx = j; idx < var; idx++) {
93                     if(a[j][idx]) break;
94                 }
95                 x[idx] = a[j][var];
96                 for(int l = idx + 1; l < var; l++) {
97                     if(a[j][l]) x[idx] ^= x[l];
98                 }
99                 cnt += x[idx];
100             }
101             ret = min(ret, cnt);
102         }
103     }
104     else for(int i = 0; i < var; i++) ret += x[i];
105     printf("%d\n", ret);
106     vector<pii> va;
107     for(int i = 0; i < 30; i++) {
108         if(x[i]) {
109             int pos = i + 1;
110             int r = 1, c = 0;
111             while(pos > 6) {
112                 pos -= 6;
113                 r++;
114             }
115             c += pos;
116             va.push_back(pii(r, c));
117         }
118     }
119     sort(va.begin(), va.end());
120     for(int i = 0; i < va.size(); i++) {
121         printf("%d %d\n", va[i].first, va[i].second);
122     }
123     return 0;
124 }