結果
| 問題 | No.1774 Love Triangle (Hard) |
| ユーザー |
👑  ygussany
|
| 提出日時 | 2021-10-03 21:05:13 |
| 言語 | C (gcc 13.3.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 9,577 bytes |
| コンパイル時間 | 953 ms |
| コンパイル使用メモリ | 41,600 KB |
| 実行使用メモリ | 6,948 KB |
| 最終ジャッジ日時 | 2024-07-26 20:58:12 |
| 合計ジャッジ時間 | 18,187 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 12 RE * 78 |
ソースコード
#include <stdio.h>#define DIM 200const int Mod[3] = {10007, 19997, 30011};int div_mod(int x, int y, int z){if (x % y == 0) return x / y;else return (div_mod((1 + x / y) * y - x, (z % y), y) * z + x) / y;}int rank_matrix(int d, int A[][DIM], int m){if (d <= 0) return 1;static int i, j, k, r, p[DIM], X[DIM][DIM], inv, tmp[DIM];for (i = 0; i < d; i++) p[i] = i;for (i = 0; i < d; i++) {for (j = 0; j < d; j++) {X[i][j] = A[i][j] % Mod[m];if (X[i][j] < 0) X[i][j] += Mod[m];}}for (i = 0, r = 0; i < d; i++) {for (j = r; j < d; j++) if (X[i][p[j]] != 0) break;if (j == d) continue;else if (j != r) {p[r] ^= p[j];p[j] ^= p[r];p[r] ^= p[j];}inv = div_mod(1, X[i][p[r]], Mod[m]);for (k = i; k < d; k++) tmp[k] = X[k][p[r]] * inv % Mod[m];for (j = r + 1; j < d; j++) {if (X[i][p[j]] != 0) {for (k = i + 1; k < d; k++) {X[k][p[j]] -= tmp[k] * X[i][p[j]] % Mod[m];if (X[k][p[j]] < 0) X[k][p[j]] += Mod[m];}X[i][p[j]] = 0;}}r++;}return r;}int inv_matrix(int d, int A[][DIM], int A_inv[][DIM], int m){static int i, j, k, p[DIM], X[DIM][DIM*2], inv;int dd = d * 2;for (i = 0; i < d; i++) p[i] = i;for (i = 0; i < d; i++) {for (j = 0; j < d; j++) {X[i][j] = A[i][j];X[i][j+d] = (j == i)? 1: 0;}}for (i = 0; i < d; i++) {for (k = i; k < d; k++) if (X[p[k]][i] != 0) break;if (k == d) return -1;else if (k != i) {p[i] ^= p[k];p[k] ^= p[i];p[i] ^= p[k];}inv = div_mod(1, X[p[i]][i], Mod[m]);for (j = i; j < dd; j++) X[p[i]][j] = X[p[i]][j] * inv % Mod[m];for (k = 0; k < d; k++) {if (k == i) continue;if (X[p[k]][i] != 0) {for (j = i + 1; j < dd; j++) {X[p[k]][j] -= X[p[k]][i] * X[p[i]][j] % Mod[m];if (X[p[k]][j] < 0) X[p[k]][j] += Mod[m];}X[p[k]][i] = 0;}}}for (i = 0; i < d; i++) for (j = 0; j < d; j++) A_inv[i][j] = X[p[i]][j+d];return 0;}// A = Bvoid copy_matrix(int d1, int d2, int A[][DIM], int B[][DIM]){int i, j;for (i = 0; i < d1; i++) for (j = 0; j < d2; j++) A[i][j] = B[i][j];}// A += cBvoid add_matrix(int d, int A[][DIM], int c, int B[][DIM], int m){int i, j;for (i = 0; i < d; i++) {for (j = 0; j < d; j++) {A[i][j] += B[i][j] * c % Mod[m];if (A[i][j] >= Mod[m]) A[i][j] -= Mod[m];}}}// A = A * Bvoid multiply_matrix_right(int d1, int d2, int d3, int A[][DIM], int B[][DIM], int m){static int i, j, k, C[DIM][DIM];for (i = 0; i < d1; i++) {for (j = 0; j < d3; j++) {for (k = 0, C[i][j] = 0; k < d2; k++) C[i][j] += A[i][k] * B[k][j] % Mod[m];C[i][j] %= Mod[m];}}for (i = 0; i < d1; i++) for (j = 0; j < d3; j++) A[i][j] = C[i][j];}// A = B * Avoid multiply_matrix_left(int d1, int d2, int d3, int B[][DIM], int A[][DIM], int m){static int i, j, k, C[DIM][DIM];for (i = 0; i < d1; i++) {for (j = 0; j < d3; j++) {for (k = 0, C[i][j] = 0; k < d2; k++) C[i][j] += B[i][k] * A[k][j] % Mod[m];C[i][j] %= Mod[m];}}for (i = 0; i < d1; i++) for (j = 0; j < d3; j++) A[i][j] = C[i][j];}int SMW_rank2_update_inv(int d, int A_inv[][DIM], int U[][DIM], int VT[][DIM], int m){static int I[DIM][DIM] = {{1, 0}, {0, 1}}, B[DIM][DIM], B_inv[DIM][DIM];int i, j;copy_matrix(d, d, B, A_inv);multiply_matrix_left(2, d, d, VT, B, m);multiply_matrix_right(2, d, 2, B, U, m);add_matrix(2, B, 1, I, m);if (inv_matrix(2, B, B_inv, m) != 0) return -1;multiply_matrix_left(d, d, 2, A_inv, U, m);multiply_matrix_right(2, d, d, VT, A_inv, m);multiply_matrix_left(d, 2, 2, U, B_inv, m);multiply_matrix_right(d, 2, d, B_inv, VT, m);add_matrix(d, A_inv, Mod[m] - 1, B_inv, m);return 0;}void wedge_prod_vector(int d, int b[], int c[], int A[][DIM], int m){int i, j;for (i = 0; i < d; i++) {for (j = 0; j < d; j++) {A[i][j] = (b[i] * c[j] - c[i] * b[j]) % Mod[m];if (A[i][j] >= Mod[m]) A[i][j] -= Mod[m];else if (A[i][j] < 0) A[i][j] += Mod[m];}}}#define MT_N 624#define MT_M 397#define MT_MATRIX_A 0x9908b0dfUL#define MT_UPPER_MASK 0x80000000UL#define MT_LOWER_MASK 0x7fffffffULstatic unsigned int mt[MT_N];static int mti = MT_N + 1;void init_genrand(unsigned int s){mt[0] = s & 0xffffffffUL;for (mti = 1; mti < MT_N; mti++) {mt[mti] = (1812433253UL * (mt[mti-1] ^ (mt[mti-1] >> 30)) + mti);mt[mti] &= 0xffffffffUL;}}unsigned int genrand(){unsigned int y;static unsigned int mag01[2] = {0x0UL, MT_MATRIX_A};if (mti >= MT_N) {int kk;if (mti == MT_N + 1) init_genrand(5489UL);for (kk = 0; kk < MT_N - MT_M; kk++) {y = (mt[kk] & MT_UPPER_MASK) | (mt[kk+1] & MT_LOWER_MASK);mt[kk] = mt[kk+MT_M] ^ (y >> 1) ^ mag01[y&0x1UL];}for (; kk < MT_N - 1; kk++) {y = (mt[kk] & MT_UPPER_MASK) | (mt[kk+1] & MT_LOWER_MASK);mt[kk] = mt[kk+(MT_M-MT_N)] ^ (y >> 1) ^ mag01[y&0x1UL];}y = (mt[MT_N-1] & MT_UPPER_MASK) | (mt[0] & MT_LOWER_MASK);mt[MT_N-1] = mt[MT_M-1] ^ (y >> 1) ^ mag01[y&0x1UL];mti = 0;}y = mt[mti++];y ^= (y >> 11);y ^= (y << 7) & 0x9d2c5680UL;y ^= (y << 15) & 0xefc60000UL;y ^= (y >> 18);return y;}void chmax(int* a, int b){if (*a < b) *a = b;}void naive(int N, int M, int u[], int v[], int w[]){int i, j, m, ans = 0, Y[3][DIM][DIM] = {}, r;for (i = 1; i <= M; i++) {for (m = 0; m < 3; m++) {r = genrand() % Mod[m];Y[m][u[i]][v[i]] += r;if (Y[m][u[i]][v[i]] >= Mod[m]) Y[m][u[i]][v[i]] -= Mod[m];Y[m][u[i]][w[i]] -= r;if (Y[m][u[i]][w[i]] < 0) Y[m][u[i]][w[i]] += Mod[m];Y[m][v[i]][u[i]] -= r;if (Y[m][v[i]][u[i]] < 0) Y[m][v[i]][u[i]] += Mod[m];Y[m][v[i]][w[i]] += r;if (Y[m][v[i]][w[i]] >= Mod[m]) Y[m][v[i]][w[i]] -= Mod[m];Y[m][w[i]][u[i]] += r;if (Y[m][w[i]][u[i]] >= Mod[m]) Y[m][w[i]][u[i]] -= Mod[m];Y[m][w[i]][v[i]] -= r;if (Y[m][w[i]][v[i]] < 0) Y[m][w[i]][v[i]] += Mod[m];chmax(&ans, rank_matrix(N, Y[m], m));}printf("%d\n", ans / 2);}}void solve(int N, int M, int u[], int v[], int w[]){int i, j, k, m, r, ans[601] = {}, x[601], Y[DIM][DIM], Y_inv[DIM][DIM], Z[DIM][DIM], b[DIM], c[DIM], U[DIM][DIM], VT[DIM][DIM];if (N % 2 != 0) N++;for (m = 0; m < 3; m++) {for (i = 0; i < N; i++) for (j = 0; j < N; j++) Y[i][j] = 0;for (i = 1; i <= M; i++) {r = genrand() % Mod[m];x[i] = r;Y[u[i]][v[i]] += r;if (Y[u[i]][v[i]] >= Mod[m]) Y[u[i]][v[i]] -= Mod[m];Y[u[i]][w[i]] -= r;if (Y[u[i]][w[i]] < 0) Y[u[i]][w[i]] += Mod[m];Y[v[i]][u[i]] -= r;if (Y[v[i]][u[i]] < 0) Y[v[i]][u[i]] += Mod[m];Y[v[i]][w[i]] += r;if (Y[v[i]][w[i]] >= Mod[m]) Y[v[i]][w[i]] -= Mod[m];Y[w[i]][u[i]] += r;if (Y[w[i]][u[i]] >= Mod[m]) Y[w[i]][u[i]] -= Mod[m];Y[w[i]][v[i]] -= r;if (Y[w[i]][v[i]] < 0) Y[w[i]][v[i]] += Mod[m];}r = rank_matrix(N, Y, m);chmax(&(ans[M]), r / 2);for (k = 0; k * 2 + r < N; k++) {for (j = 0; j < N; j++) {b[j] = genrand() % Mod[m];c[j] = genrand() % Mod[m];}wedge_prod_vector(N, b, c, Z, m);add_matrix(N, Y, genrand() % Mod[m], Z, m);}if (inv_matrix(N, Y, Y_inv, m) != 0) {m--;continue;}for (i = M, k = r / 2; i > 1; i--) {for (j = 0; j < N; j++) {U[j][0] = 0;U[j][1] = 0;VT[0][j] = 0;VT[1][j] = 0;}U[u[i]][0] = x[i];U[v[i]][0] = Mod[m] - x[i];U[u[i]][1] = x[i];U[w[i]][1] = Mod[m] - x[i];VT[0][u[i]] = Mod[m] - 1;VT[0][w[i]] = 1;VT[1][u[i]] = 1;VT[1][v[i]] = Mod[m] - 1;if (SMW_rank2_update_inv(N, Y_inv, U, VT, m) != 0) {chmax(&(ans[i-1]), ans[i] - 1);do {r = genrand() % Mod[m];for (j = 0; j < N; j++) {b[j] = genrand() % Mod[m];c[j] = genrand() % Mod[m];U[j][0] = b[j] * r % Mod[m];U[j][1] = c[j] * r % Mod[m];VT[0][j] = c[j];VT[1][j] = Mod[m] - b[j];}if (SMW_rank2_update_inv(N, Y_inv, U, VT, m) != 0) continue;for (j = 0; j < N; j++) {U[j][0] = 0;U[j][1] = 0;VT[0][j] = 0;VT[1][j] = 0;}U[u[i]][0] = x[i];U[v[i]][0] = Mod[m] - x[i];U[u[i]][1] = x[i];U[w[i]][1] = Mod[m] - x[i];VT[0][u[i]] = Mod[m] - 1;VT[0][w[i]] = 1;VT[1][u[i]] = 1;VT[1][v[i]] = Mod[m] - 1;if (SMW_rank2_update_inv(N, Y_inv, U, VT, m) == 0) break;for (j = 0; j < N; j++) {U[j][0] = b[j] * r % Mod[m];U[j][1] = c[j] * r % Mod[m];VT[0][j] = Mod[m] - c[j];VT[1][j] = b[j];}SMW_rank2_update_inv(N, Y_inv, U, VT, m);} while (1);wedge_prod_vector(N, b, c, Z, m);add_matrix(N, Y, r, Z, m);k--;}chmax(&(ans[i-1]), k);r = x[i];Y[u[i]][v[i]] -= r;if (Y[u[i]][v[i]] < 0) Y[u[i]][v[i]] += Mod[m];Y[u[i]][w[i]] += r;if (Y[u[i]][w[i]] >= Mod[m]) Y[u[i]][w[i]] -= Mod[m];Y[v[i]][u[i]] += r;if (Y[v[i]][u[i]] >= Mod[m]) Y[v[i]][u[i]] -= Mod[m];Y[v[i]][w[i]] -= r;if (Y[v[i]][w[i]] < 0) Y[v[i]][w[i]] += Mod[m];Y[w[i]][u[i]] -= r;if (Y[w[i]][u[i]] < 0) Y[w[i]][u[i]] += Mod[m];Y[w[i]][v[i]] += r;if (Y[w[i]][v[i]] >= Mod[m]) Y[w[i]][v[i]] -= Mod[m];}}for (i = 1; i <= M; i++) printf("%d\n", ans[i]);}int main(){init_genrand(46);int i, N, M, u[601], v[601], w[601];scanf("%d %d", &N, &M);for (i = 1; i <= M; i++) scanf("%d %d %d", &(u[i]), &(v[i]), &(w[i]));solve(N, M, u, v, w);fflush(stdout);return 0;}