高斯消元

Posted 2020-07-13 __AiR_H

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1 HDU 3364 Lanterns

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <cstdlib>
 5 #include <algorithm>
 6 #include <queue>
 7 #include <vector>
 8 #include <stack>
 9 #include <map>
10 #include <set>
11 #include <cmath>
12 #include <cctype>
13 #include <ctime>
14 #include <bitset>
15 
16 using namespace std;
17 
18 #define REP(i, n) for (int i = 0; i < (n); ++i)
19 #define eps 1e-9
20 
21 typedef long long ll;
22 typedef pair<int, int> pii;
23 
24 const int INF = 0x7fffffff;
25 const int maxn = 55;
26 struct Matrix { int det[maxn][maxn]; };
27 int T, n, m, q, Case = 0;
28 Matrix A, A_t;
29 
30 int solve(Matrix A, int m, int n) {
31     int i = 0, j = 0, k, r, u;
32     while (i < m && j < n) {
33         r = i;
34         for (k = i; k < m; ++k) {
35             if (A.det[k][j]) { r = k; break; }
36         }
37         if (!A.det[r][j]) { ++j; continue; }
38         if (r != i) {
39             for (int k = 0; k <= n; ++k) { swap(A.det[r][k], A.det[i][k]); }
40         }
41         for (u = i + 1; u < m; ++u) if (A.det[u][j]) {
42             for (k = i; k <= n; ++k) { A.det[u][k] ^= A.det[i][k]; }
43         }
44         ++i; ++j;
45     }
46     for (u = i; u < m; ++u) {
47         if (A.det[u][n]) { return -1; }
48     }
49     return i;
50 }
51 
52 int main() {
53 #ifdef __AiR_H
54     freopen("in.txt", "r", stdin);
55 //    freopen("out.txt", "w", stdout);
56 #endif // __AiR_H
57     scanf("%d", &T);
58     while (T--) {
59         scanf("%d %d", &n, &m); int k, x;
60         memset(A_t.det, 0, sizeof(A_t.det));
61         for (int i = 0; i < m; ++i) {
62             scanf("%d", &k);
63             for (int j = 0; j < k; ++j) {
64                 scanf("%d", &x); A_t.det[x - 1][i] = 1;
65             }
66         }
67         scanf("%d", &q); printf("Case %d:\n", ++Case);
68         while (q--) {
69             A = A_t;
70             for (int i = 0; i < n; ++i) { scanf("%d", &A.det[i][m]); }
71             int ans = solve(A, n, m); if (ans == -1) { printf("0\n"); continue; }
72             ans = m - ans; printf("%lld\n", 1ll << ans);
73         }
74     }
75     return 0;
76 }

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2 HDU 5833 Zhu and 772002

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <cstdlib>
 5 #include <algorithm>
 6 #include <queue>
 7 #include <vector>
 8 #include <stack>
 9 #include <map>
10 #include <set>
11 #include <cmath>
12 #include <cctype>
13 #include <ctime>
14 #include <bitset>
15 
16 using namespace std;
17 
18 #define REP(i, n) for (int i = 0; i < (n); ++i)
19 #define eps 1e-9
20 
21 typedef long long ll;
22 typedef pair<int, int> pii;
23 
24 const int INF = 0x7fffffff;
25 const int maxn = 2000 + 10;
26 const ll mod = 1e9 + 7;
27 int prime[maxn];
28 int prime_cnt = 0, T, n, Case = 0;
29 bool is_prime[maxn];
30 
31 struct Matrix { int det[maxn][maxn]; };
32 Matrix A;
33 
34 void init() {
35     memset(is_prime, true, sizeof(is_prime));
36     is_prime[0] = is_prime[1] = false;
37     for (int i = 2; i < maxn; ++i) {
38         if (is_prime[i]) { prime[prime_cnt++] = i; }
39         for (int j = 0; j < prime_cnt; ++j) {
40             if (i * prime[j] >= maxn) { break; }
41             is_prime[i * prime[j]] = false;
42             if (i % prime[j] == 0) { break; }
43         }
44     }
45 }
46 int solve(int m, int n) {
47     int i = 0, j = 0, k, r, u;
48     while (i < m && j < n) {  //当前正在处理第i个方程，第j个变量
49         r = i;
50         for (k = i; k < m; ++k) {
51             if (A.det[k][j]) { r = k; break; }
52         }
53         if (!A.det[r][j]) { ++j; continue; }
54         if (r != i) {
55             for (k = 0; k <= n; ++k) { swap(A.det[r][k], A.det[i][k]); }
56         }
57         for (u = i + 1; u < m; ++u) if (A.det[u][j]) {
58             for (k = i; k <= n; ++k) { A.det[u][k] ^= A.det[i][k]; }
59         }
60         ++i; ++j;
61     }
62     return i;
63 }
64 ll my_pow(ll x, ll y) {
65     ll ret = 1, t = x;
66     while (y) {
67         if (y & 1) { ret *= t; ret %= mod; }
68         y >>= 1; t *= t; t %= mod;
69     }
70     return ret;
71 }
72 
73 int main() {
74 #ifdef __AiR_H
75     freopen("in.txt", "r", stdin);
76 //    freopen("out.txt", "w", stdout);
77 #endif // __AiR_H
78     scanf("%d", &T); init();
79     while (T--) {
80         scanf("%d", &n); memset(A.det, 0, sizeof(A.det));
81         int maxp = 0; ll x;
82         for (int i = 0; i < n; ++i) {
83             scanf("%lld", &x);
84             for (int j = 0; j < prime_cnt; ++j) {
85                 while (x % prime[j] == 0) {
86                     maxp = max(maxp, j); x /= prime[j]; A.det[j][i] ^= 1;
87                 }
88             }
89         }
90         printf("Case #%d:\n", ++Case);
91         int ans = solve(maxp + 1, n); ans = n - ans;
92         ll ret = my_pow(2, ans); --ret;
93         if (ret < 0) { ret += mod; } printf("%lld\n", ret);
94     }
95     return 0;
96 }

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