結果
| 問題 | No.1776 Love Triangle 2 (Hard) |
| ユーザー |
👑  ygussany
|
| 提出日時 | 2021-11-24 13:15:17 |
| 言語 | C (gcc 13.3.0) |
| 結果 |
AC
|
| 実行時間 | 2,738 ms / 10,000 ms |
| コード長 | 7,608 bytes |
| コンパイル時間 | 721 ms |
| コンパイル使用メモリ | 37,264 KB |
| 実行使用メモリ | 6,944 KB |
| 最終ジャッジ日時 | 2024-07-06 21:15:53 |
| 合計ジャッジ時間 | 60,922 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 176 |
ソースコード
#include <stdio.h>
#define K_MAX 3
#define BIT_K_MAX 4
#define N_MAX 150
#define M_MAX 12000
const int bit[6] = {1, 2, 4, 8, 16, 32};
void chmin(int* a, int b)
{
if (*a > b) *a = b;
}
int lex_smaller(int a[], int b[])
{
int i;
for (i = 0; i <= a[0]; i++) {
if (a[i] < b[i]) return 1;
else if (a[i] > b[i]) return -1;
}
return 0;
}
void chlexmin(int a[], int b[])
{
int i;
if (lex_smaller(a, b) < 0) for (i = 0; i <= b[0]; i++) a[i] = b[i];
}
typedef struct Edge {
struct Edge *next;
int v, id;
unsigned int label;
} edge;
int complement_graph(int N, int M, int A[], int B[], edge* adj[], edge e[])
{
static char adj_mat[N_MAX + 1][N_MAX + 1];
static int i, u, w;
for (u = 1; u <= N; u++) for (w = u + 1; w <= N; w++) adj_mat[u][w] = 0;
for (i = 1; i <= M; i++) {
u = A[i];
w = B[i];
adj_mat[u][w] = 1;
}
for (u = 1; u <= N; u++) adj[u] = NULL;
for (u = 1, i = 0; u <= N; u++) {
for (w = u + 1; w <= N; w++) {
if (adj_mat[u][w] != 0) continue;
e[i].v = w;
e[i].id = i;
e[i].next = adj[u];
adj[u] = &(e[i++]);
e[i].v = u;
e[i].id = i;
e[i].next = adj[w];
adj[w] = &(e[i++]);
}
}
return i / 2;
}
#define MT_N 624
#define MT_M 397
#define MT_MATRIX_A 0x9908b0dfUL
#define MT_UPPER_MASK 0x80000000UL
#define MT_LOWER_MASK 0x7fffffffUL
static 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;
}
#define POWX 4 // 3 -> 2^8, 4 -> 2^16, 5 -> 2^32
const unsigned int powd[6] = {2, 4, 16, 256, 65536}, powe[6] = {1, 2, 4, 8, 16, 32};
// Multiplication on a finite field of size 2^32 with XOR addition
unsigned int nim_product(unsigned int A, unsigned int B)
{
if (A > B) return nim_product(B, A);
else if (A <= 1) return A * B;
static unsigned int memo[256][256] = {};
if (B < 256 && memo[A][B] != 0) return memo[A][B];
int i;
for (i = 0; i < POWX; i++) {
if (B == powd[i]) {
if (A == powd[i]) return (B >> 1) * 3;
else return A * B;
}
}
unsigned int a[2], b[2], ans[2][2];
for (i = POWX - 1; i >= 0; i--) if (B > powd[i]) break;
a[1] = A & (powd[i] - 1);
a[0] = (A ^ a[1]) >> powe[i];
b[1] = B & (powd[i] - 1);
b[0] = (B ^ b[1]) >> powe[i];
ans[0][0] = nim_product(a[0], b[0]);
ans[0][1] = nim_product(a[0], b[1]);
ans[1][0] = nim_product(a[1], b[0]);
ans[1][1] = nim_product(a[1], b[1]);
if (B < 256) {
memo[A][B] = (ans[0][0] ^ ans[0][1] ^ ans[1][0]) * powd[i] ^ nim_product(ans[0][0], powd[i] >> 1) ^ ans[1][1];
return memo[A][B];
} else return (ans[0][0] ^ ans[0][1] ^ ans[1][0]) * powd[i] ^ nim_product(ans[0][0], powd[i] >> 1) ^ ans[1][1];
}
// Computing the lexicographically-minimum shortest s-t path through K specified vertices in O(2^K L^2 M) time
int lexmin_shortest_path_through_specified_vertices(int N, edge* adj[], edge e[], int s, int t, int K, char flag[], int ans[], int rep)
{
static int i, k_done, u, w, n, v[N_MAX + 1];
for (u = 1, n = 0, k_done = 0; u <= N; u++) {
if (flag[u] > -2) v[++n] = u; // living vertices
else if (flag[u] < -2) k_done |= bit[-3 - flag[u]]; // dead terminals
}
static int h, j, k, l, l_ans, cur, prev;
static unsigned int dp[2][BIT_K_MAX][M_MAX * 2], tmp;
static edge *p;
for (j = 1, l_ans = n + 1; j <= rep; j++) {
for (i = 1; i <= n; i++) {
u = v[i];
for (p = adj[u]; p != NULL; p = p->next) {
w = p->v;
if (flag[w] > -2 && w < u) continue;
p->label = genrand() % (powd[POWX] - 1) + 1;
if (u != t && w != t) e[p->id ^ 1].label = p->label;
else e[p->id ^ 1].label = genrand() % (powd[POWX] - 1) + 1; // around t
}
}
for (k = 0; k < bit[K]; k++) {
if ((k & k_done) != k_done) continue;
for (i = 1; i <= n; i++) {
u = v[i];
for (p = adj[u]; p != NULL; p = p->next) {
dp[0][k][p->id] = 0;
dp[0][k][p->id ^ 1] = 0;
dp[1][k][p->id] = 0;
dp[1][k][p->id ^ 1] = 0;
}
}
for (p = adj[s]; p != NULL; p = p->next) {
dp[0][k][p->id ^ 1] = 0;
dp[1][k][p->id ^ 1] = 0;
}
}
for (p = adj[t]; p != NULL; p = p->next) dp[0][k_done][p->id] = p->label;
for (l = 1, cur = 1, prev = 0; l <= n; l++, cur ^= 1, prev ^= 1) {
for (p = adj[s], tmp = 0; p != NULL; p = p->next) if (flag[p->v] > -2) tmp ^= dp[prev][bit[K] - 1][p->id ^ 1];
if (tmp != 0 || l == n) break;
for (k = 0; k < bit[K]; k++) {
if ((k & k_done) != k_done) continue;
for (i = 1; i <= n; i++) {
u = v[i];
h = flag[u];
if (u == s || u == t || (h >= 0 && (k & bit[h]) != 0)) continue;
for (p = adj[u], tmp = 0; p != NULL; p = p->next) if (flag[p->v] > -2) tmp ^= dp[prev][k][p->id ^ 1];
for (p = adj[u]; p != NULL; p = p->next) {
if (h < 0) dp[cur][k][p->id] = nim_product(tmp, p->label);
else dp[cur][k | bit[h]][p->id] = nim_product(tmp ^ dp[prev][k][p->id ^ 1], p->label);
if (flag[p->v] > -2) dp[prev][k][p->id ^ 1] = 0;
}
}
}
}
if (tmp != 0) {
if (l < l_ans) {
for (p = adj[s], l_ans = l, ans[0] = N + 1; p != NULL; p = p->next) if (flag[p->v] > -2 && dp[prev][bit[K] - 1][p->id ^ 1] != 0) chmin(&(ans[0]), p->v);
} else if (l == l_ans) {
for (p = adj[s]; p != NULL; p = p->next) if (flag[p->v] > -2 && dp[prev][bit[K] - 1][p->id ^ 1] != 0) chmin(&(ans[0]), p->v);
}
}
}
if (l_ans > n) {
for (i = 0; i < n; i++) ans[i] = 0;
return n + 1;
} else if (l_ans == 1) {
ans[0] = s;
return 1;
} else {
if (flag[ans[0]] == -1) flag[ans[0]] = -2;
else flag[ans[0]] = -3 - flag[ans[0]];
return lexmin_shortest_path_through_specified_vertices(N, adj, e, ans[0], t, K, flag, &(ans[1]), rep) + 1;
}
}
void solve(int N, int M, int X, int Y, int Z, int A[], int B[], int ans[])
{
static int K = 2, T[K_MAX];
static edge *adj[N_MAX + 1] = {}, e[M_MAX * 2];
complement_graph(N, M, A, B, adj, e);
T[0] = Y;
T[1] = Z;
static char flag[N_MAX + 1];
static int i, u;
for (u = 1; u <= N; u++) flag[u] = -1; // nonterminals
for (i = 0; i < K; i++) flag[T[i]] = i; // terminals
ans[0] = lexmin_shortest_path_through_specified_vertices(N, adj, e, X, X, K, flag, &(ans[2]), 2);
if (ans[0] <= N) ans[1] = X;
}
void print_ans(int N, int ans[])
{
int i;
if (ans[0] > N) {
printf("-1\n");
return;
} else printf("%d\n", ans[0]);
for (i = 1; i <= ans[0]; i++) printf("%d ", ans[i]);
printf("%d\n", ans[1]);
}
int main()
{
int i, N, M, X, Y, Z, A[M_MAX + 1], B[M_MAX + 1], ans[N_MAX + 2];
scanf("%d %d", &N, &M);
scanf("%d %d %d", &X, &Y, &Z);
for (i = 1; i <= M; i++) scanf("%d %d", &(A[i]), &(B[i]));
solve(N, M, X, Y, Z, A, B, ans);
print_ans(N, ans);
fflush(stdout);
return 0;
}