#720506 (C) No.1775 Love Triangle 2

提出ソース

結果

問題	No.1775 Love Triangle 2
ユーザー	👑 ygussany
提出日時	2021-11-28 14:48:55
言語	C (gcc 12.3.0)
結果	AC
実行時間	307 ms / 8,000 ms
コード長	5,891 bytes
コンパイル時間	398 ms
コンパイル使用メモリ	34,160 KB
実行使用メモリ	4,380 KB
最終ジャッジ日時	2023-09-16 22:26:07
合計ジャッジ時間	5,072 ms
ジャッジサーバーID （参考情報）	judge11 / judge13

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	1 ms 4,380 KB
testcase_01	AC	1 ms 4,380 KB
testcase_02	AC	1 ms 4,376 KB
testcase_03	AC	1 ms 4,376 KB
testcase_04	AC	307 ms 4,380 KB
testcase_05	AC	303 ms 4,380 KB
testcase_06	AC	241 ms 4,376 KB
testcase_07	AC	102 ms 4,376 KB
testcase_08	AC	287 ms 4,376 KB
testcase_09	AC	4 ms 4,376 KB
testcase_10	AC	4 ms 4,376 KB
testcase_11	AC	4 ms 4,380 KB
testcase_12	AC	4 ms 4,376 KB
testcase_13	AC	5 ms 4,380 KB
testcase_14	AC	5 ms 4,380 KB
testcase_15	AC	6 ms 4,376 KB
testcase_16	AC	6 ms 4,376 KB
testcase_17	AC	7 ms 4,376 KB
testcase_18	AC	12 ms 4,376 KB
testcase_19	AC	4 ms 4,380 KB
testcase_20	AC	4 ms 4,376 KB
testcase_21	AC	4 ms 4,376 KB
testcase_22	AC	5 ms 4,376 KB
testcase_23	AC	4 ms 4,380 KB
testcase_24	AC	3 ms 4,376 KB
testcase_25	AC	5 ms 4,376 KB
testcase_26	AC	4 ms 4,376 KB
testcase_27	AC	4 ms 4,380 KB
testcase_28	AC	5 ms 4,380 KB
testcase_29	AC	13 ms 4,380 KB
testcase_30	AC	21 ms 4,376 KB
testcase_31	AC	33 ms 4,376 KB
testcase_32	AC	35 ms 4,380 KB
testcase_33	AC	32 ms 4,376 KB
testcase_34	AC	31 ms 4,376 KB
testcase_35	AC	26 ms 4,376 KB
testcase_36	AC	19 ms 4,376 KB
testcase_37	AC	12 ms 4,380 KB
testcase_38	AC	4 ms 4,376 KB
testcase_39	AC	17 ms 4,376 KB
testcase_40	AC	28 ms 4,376 KB
testcase_41	AC	31 ms 4,380 KB
testcase_42	AC	25 ms 4,380 KB
testcase_43	AC	18 ms 4,380 KB
testcase_44	AC	14 ms 4,380 KB
testcase_45	AC	29 ms 4,380 KB
testcase_46	AC	12 ms 4,376 KB
testcase_47	AC	4 ms 4,376 KB
testcase_48	AC	7 ms 4,376 KB
testcase_49	AC	12 ms 4,380 KB
testcase_50	AC	20 ms 4,376 KB
testcase_51	AC	34 ms 4,376 KB
testcase_52	AC	44 ms 4,376 KB
testcase_53	AC	36 ms 4,376 KB
testcase_54	AC	36 ms 4,376 KB
testcase_55	AC	33 ms 4,376 KB
testcase_56	AC	21 ms 4,376 KB
testcase_57	AC	14 ms 4,376 KB
testcase_58	AC	9 ms 4,380 KB
testcase_59	AC	18 ms 4,376 KB
testcase_60	AC	22 ms 4,380 KB
testcase_61	AC	26 ms 4,380 KB
testcase_62	AC	14 ms 4,380 KB
testcase_63	AC	14 ms 4,380 KB
testcase_64	AC	13 ms 4,376 KB
testcase_65	AC	6 ms 4,376 KB
testcase_66	AC	6 ms 4,376 KB
testcase_67	AC	5 ms 4,376 KB
testcase_68	AC	4 ms 4,380 KB
testcase_69	AC	4 ms 4,380 KB
testcase_70	AC	7 ms 4,380 KB
testcase_71	AC	7 ms 4,376 KB
testcase_72	AC	9 ms 4,376 KB
testcase_73	AC	9 ms 4,376 KB
testcase_74	AC	8 ms 4,376 KB
testcase_75	AC	8 ms 4,376 KB
testcase_76	AC	7 ms 4,376 KB
testcase_77	AC	8 ms 4,380 KB
testcase_78	AC	8 ms 4,376 KB
testcase_79	AC	6 ms 4,376 KB
testcase_80	AC	6 ms 4,376 KB
testcase_81	AC	7 ms 4,380 KB
testcase_82	AC	7 ms 4,380 KB
testcase_83	AC	8 ms 4,376 KB
testcase_84	AC	7 ms 4,380 KB
testcase_85	AC	8 ms 4,380 KB
testcase_86	AC	6 ms 4,376 KB
testcase_87	AC	8 ms 4,380 KB
testcase_88	AC	10 ms 4,376 KB
testcase_89	AC	5 ms 4,376 KB

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ソースコード

raw source code

#include <stdio.h>

#define K_MAX 3
#define BIT_K_MAX 4 // 2^(K-1)
#define N_MAX 100
#define M_MAX 5000

const int bit[6] = {1, 2, 4, 8, 16, 32};

void chmin(int* a, int b)
{
	if (*a > b) *a = b;
}

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[5] = {2, 4, 16, 256, 65536}, powe[5] = {1, 2, 4, 8, 16};

// 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 length of a shortest cycle through K specified vertices in O(2^K LM) time
int shortest_cycle_through_specified_vertices(int N, edge* adj[], edge e[], int K, int T[])
{
	static char flag[N_MAX + 1];
	static int i, u, w, s;
	static edge *p;
	for (u = 1; u <= N; u++) flag[u] = -1; // nonterminals
	for (i = 0, s = T[K-1]; i < K; i++) flag[T[i]] = i; // terminals
	for (u = 1; u <= N; u++) {
		for (p = adj[u]; p != NULL; p = p->next) {
			w = p->v;
			if (w < u) continue;
			p->label = genrand() % (powd[POWX] - 1) + 1;
			if (u != s && w != s) e[p->id ^ 1].label = p->label; 
			else e[p->id ^ 1].label = genrand() % (powd[POWX] - 1) + 1; // around s
		}
	}
	
	static int k, l, cur, prev;
	static unsigned int dp[2][BIT_K_MAX][M_MAX * 2], tmp;
	for (k = 0; k < bit[K-1]; k++) {
		for (u = 1; u <= N; u++) {
			for (p = adj[u]; p != NULL; p = p->next) {
				dp[0][k][p->id] = 0;
				dp[1][k][p->id] = 0;
			}
		}
	}
	for (p = adj[s]; p != NULL; p = p->next) dp[0][0][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) tmp ^= dp[prev][bit[K-1] - 1][p->id ^ 1];
		if (tmp != 0) return l;
		else if (l == N) return N + 1;
		
		for (k = 0; k < bit[K-1]; k++) {
			for (u = 1; u <= N; u++) {
				i = flag[u];
				if (u == s || (i >= 0 && (k & bit[i]) != 0)) continue;
				for (p = adj[u], tmp = 0; p != NULL; p = p->next) tmp ^= dp[prev][k][p->id ^ 1];
				for (p = adj[u]; p != NULL; p = p->next) {
					if (i < 0) dp[cur][k][p->id] = nim_product(tmp, p->label);
					else dp[cur][k | bit[i]][p->id] = nim_product(tmp ^ dp[prev][k][p->id ^ 1], p->label);
					dp[prev][k][p->id ^ 1] = 0;
				}
			}
		}
	}
}

int solve(int N, int M, int X, int Y, int Z, int A[], int B[])
{
	static int K = 3, T[K_MAX], ans[2];
	static edge *adj[N_MAX + 1] = {}, e[M_MAX * 2];
	complement_graph(N, M, A, B, adj, e);
	T[0] = X;
	T[1] = Y;
	T[2] = Z;
	ans[0] = shortest_cycle_through_specified_vertices(N, adj, e, K, T);
	ans[1] = shortest_cycle_through_specified_vertices(N, adj, e, K, T);
	chmin(&(ans[0]), ans[1]);
	// ans[1] = shortest_cycle_through_specified_vertices(N, adj, e, K, T);
	// chmin(&(ans[0]), ans[1]);
	return (ans[0] <= N)? ans[0]: -1;
}



int main()
{
	static int i, N, M, X, Y, Z, A[M_MAX + 1], B[M_MAX + 1];
	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]));
	printf("%d\n", solve(N, M, X, Y, Z, A, B));
	fflush(stdout);
	return 0;
}

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結果

テストケース

ソースコード