#714070 (C) No.1745 Selfish Spies 2 (à la Princess' Perfectionism)

提出ソース

結果

問題	No.1745 Selfish Spies 2 (à la Princess' Perfectionism)
ユーザー	👑 ygussany
提出日時	2021-11-07 19:44:20
言語	C (gcc 12.3.0)
結果	AC
実行時間	526 ms / 5,000 ms
コード長	6,276 bytes
コンパイル時間	543 ms
コンパイル使用メモリ	34,688 KB
実行使用メモリ	34,612 KB
最終ジャッジ日時	2024-10-01 10:39:50
合計ジャッジ時間	7,119 ms
ジャッジサーバーID （参考情報）	judge2 / judge3

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	5 ms 20,236 KB
testcase_01	AC	4 ms 16,268 KB
testcase_02	AC	4 ms 18,316 KB
testcase_03	AC	5 ms 20,100 KB
testcase_04	AC	4 ms 18,188 KB
testcase_05	AC	4 ms 18,176 KB
testcase_06	AC	4 ms 18,060 KB
testcase_07	AC	4 ms 18,304 KB
testcase_08	AC	4 ms 18,064 KB
testcase_09	AC	4 ms 18,308 KB
testcase_10	AC	4 ms 18,312 KB
testcase_11	AC	5 ms 20,232 KB
testcase_12	AC	4 ms 18,056 KB
testcase_13	AC	5 ms 18,188 KB
testcase_14	AC	4 ms 14,236 KB
testcase_15	AC	4 ms 18,316 KB
testcase_16	AC	4 ms 18,324 KB
testcase_17	AC	5 ms 18,332 KB
testcase_18	AC	4 ms 16,304 KB
testcase_19	AC	4 ms 18,184 KB
testcase_20	AC	5 ms 18,320 KB
testcase_21	AC	5 ms 18,180 KB
testcase_22	AC	4 ms 18,188 KB
testcase_23	AC	4 ms 18,056 KB
testcase_24	AC	12 ms 18,604 KB
testcase_25	AC	5 ms 18,076 KB
testcase_26	AC	4 ms 14,112 KB
testcase_27	AC	6 ms 18,224 KB
testcase_28	AC	69 ms 25,116 KB
testcase_29	AC	7 ms 18,356 KB
testcase_30	AC	6 ms 18,308 KB
testcase_31	AC	7 ms 20,280 KB
testcase_32	AC	6 ms 16,316 KB
testcase_33	AC	64 ms 28,540 KB
testcase_34	AC	59 ms 23,120 KB
testcase_35	AC	88 ms 21,508 KB
testcase_36	AC	87 ms 27,704 KB
testcase_37	AC	83 ms 23,532 KB
testcase_38	AC	61 ms 28,120 KB
testcase_39	AC	13 ms 20,508 KB
testcase_40	AC	25 ms 23,856 KB
testcase_41	AC	22 ms 22,716 KB
testcase_42	AC	51 ms 27,280 KB
testcase_43	AC	81 ms 28,912 KB
testcase_44	AC	106 ms 34,612 KB
testcase_45	AC	160 ms 29,604 KB
testcase_46	AC	180 ms 29,476 KB
testcase_47	AC	124 ms 29,372 KB
testcase_48	AC	127 ms 29,076 KB
testcase_49	AC	526 ms 30,748 KB
testcase_50	AC	468 ms 25,960 KB
testcase_51	AC	33 ms 18,780 KB
testcase_52	AC	21 ms 17,020 KB
testcase_53	AC	27 ms 22,792 KB
testcase_54	AC	189 ms 31,876 KB
testcase_55	AC	160 ms 24,316 KB
testcase_56	AC	232 ms 31,056 KB
testcase_57	AC	127 ms 29,380 KB
testcase_58	AC	123 ms 29,412 KB

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ソースコード

raw source code

#include <stdio.h>
#include <stdlib.h>

#define N_MAX 100000
#define M_MAX 100000
#define L_MAX 200000

typedef struct Edge {
	struct Edge *next;
	int v;
} edge;



int DFS_bipartite_matching(edge* aux[], int par[], int u)
{
	int w;
	for (; aux[u] != NULL; aux[u] = aux[u]->next) {
		w = aux[u]->v;
		if (par[w] == 0) { // w is a sink
			par[w] = u;
			return w;
		} else if (par[w] > 0) continue; // w is already checked
		par[w] = u;
		w = DFS_bipartite_matching(aux, par, w);
		if (w > 0) return w;
	}
	return 0;
}

int bipartite_matching_augmentation(int N, char color[], edge* adj[], int mate[])
{
	static int i, u, w, depth[N_MAX + M_MAX + 1], par[N_MAX + M_MAX + 1], q[N_MAX + M_MAX + 1], head, tail;
	static edge *aux[N_MAX + M_MAX + 1], f[L_MAX * 2], *p;
	for (u = 1, tail = 0, par[0] = 0; u <= N; u++) {
		if (mate[u] == 0) { // u is a source of sink
			if (color[u] == 0) { // u is a source
				depth[u] = 0;
				q[tail++] = u;
			} else depth[u] = N;
			par[u] = 0;
		} else {
			depth[u] = N;
			par[u] = -1;
		}
	}
	
	// BFS for constructing the layered network
	for (head = 0, i = 0; head < tail; head++) {
		u = q[head];
		aux[u] = NULL;
		if (color[u] == 0) {
			for (p = adj[u]; p != NULL; p = p->next) {
				w = p->v;
				if (mate[u] == w) continue; // No arc in this direction
				if (depth[w] == N) { // w has been found for the first time
					depth[w] = depth[u] + 1;
					q[tail++] = w;
				}
				if (depth[w] == depth[u] + 1) { // Add the arc uw
					f[i].v = w;
					f[i].next = aux[u];
					aux[u] = &(f[i++]);
				}
			}
		} else if (mate[u] != 0) {
			w = mate[u];
			if (depth[w] == N) { // w has been found for the first time
				depth[w] = depth[u] + 1;
				q[tail++] = w;
			}
			if (depth[w] == depth[u] + 1) { // Add the arc uw
				f[i].v = w;
				f[i].next = aux[u];
				aux[u] = &(f[i++]);
			}
		}
	}

	// DFS for finding disjoint augmenting paths
	for (u = 1, tail = 0; u <= N; u++) {
		if (depth[u] != 0) continue;
		w = DFS_bipartite_matching(aux, par, u);
		if (w > 0) q[tail++] = w; // An augmenting path from u to w has been found
	}
	
	// Augmentation
	for (head = 0; head < tail; head++) {
		for (w = q[head], u = par[w]; u > 0; w = par[u], u = par[w]) {
			mate[u] = w;
			mate[w] = u;
		}
	}
	return tail;
}

int bipartite_matching(int N, char color[], edge* adj[], int mate[])
{
	int i, u, dif, ans = 0;
	edge *p;
	for (u = 1; u <= N; u++) mate[u] = 0; // Initialization
	do { // Augmentation
		dif = bipartite_matching_augmentation(N, color, adj, mate);
		ans += dif;
	} while (dif != 0);
	return ans;
}



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

int DFS_SCC(edge* adj[], int label[], int ord[], int low[], int s[], int* head, int u)
{
	s[(*head)++] = u; // Add u to the stack (which maintains the vertices already found but not determined)
	ord[u] = ord[0]++;
	low[u] = ord[u];
	
	int w;
	edge *p;
	for (p = adj[u]; p != NULL; p = p->next) {
		w = p->v;
		if (ord[w] == 0) chmin(&(low[u]), DFS_SCC(adj, label, ord, low, s, head, w)); // w has been found
		else if (ord[w] <= N_MAX + M_MAX) chmin(&(low[u]), ord[w]); // w is already found but not determined
	}
	
	if (low[u] == ord[u]) { // A new SCC containing u has been determined
		while (s[--(*head)] != u) {
			label[s[*head]] = label[0];
			ord[s[*head]] = N_MAX + M_MAX + 1;
		}
		label[u] = label[0]++;
		ord[u] = N_MAX + M_MAX + 1;
	}
	return low[u];
}

int SCC(int N, edge* adj[], int label[])
{
	int u, w, head;
	static int ord[N_MAX + M_MAX + 1], low[N_MAX + M_MAX + 1], s[N_MAX + M_MAX + 1];
	for (u = 1; u <= N; u++) {
		label[u] = 0;
		ord[u] = 0;
	}
	for (u = 1, label[0] = 1, ord[0] = 1; u <= N; u++) {
		if (ord[u] != 0) continue;
		head = 0;
		DFS_SCC(adj, label, ord, low, s, &head, u);
	}
	return label[0] - 1;
}



// 2. Solution example (O(sqrt{N + M} L) time)
void solve2(int N, int M, int L, int s[], int t[], char ans[])
{
	static char color[N_MAX + M_MAX + 1];
	static int i, u, w, mate[N_MAX + M_MAX + 1];
	static edge *adj[N_MAX + M_MAX + 1], e[L_MAX * 2 + 1], *p;
	for (u = 1; u <= N + M; u++) {
		adj[u] = NULL;
		color[u] = (u > N)? 1: 0;
	}
	for (i = 0; i < L; i++) {
		u = s[i+1];
		w = t[i+1] + N;
		e[i*2].v = w;
		e[i*2].next = adj[u];
		adj[u] = &(e[i*2]);
		e[i*2+1].v = u;
		e[i*2+1].next = adj[w];
		adj[w] = &(e[i*2+1]);
	}
	bipartite_matching(N + M, color, adj, mate);
	
	static int par[N_MAX + M_MAX + 1], q[N_MAX + M_MAX + 1], head, tail;
	for (u = 1; u <= N + M; u++) par[u] = 0;
	for (u = 1, tail = 0; u <= N; u++) {
		if (mate[u] == 0) {
			par[u] = u;
			q[tail++] = u;
		}
	}
	for (head = 0; head < tail; head++) {
		u = q[head];
		if (color[u] == 0) {
			for (p = adj[u]; p != NULL; p = p->next) {
				w = p->v;
				if (par[w] == 0) {
					par[w] = u;
					q[tail++] = w;
				}
			}
		} else {
			par[mate[u]] = u;
			q[tail++] = mate[u];
		}
	}
	for (u = N + 1, tail = 0; u <= N + M; u++) {
		if (mate[u] == 0) {
			par[u] = -u;
			q[tail++] = u;
		}
	}
	for (head = 0; head < tail; head++) {
		u = q[head];
		if (color[u] != 0) {
			for (p = adj[u]; p != NULL; p = p->next) {
				w = p->v;
				if (par[w] == 0) {
					par[w] = -u;
					q[tail++] = w;
				}
			}
		} else {
			par[mate[u]] = -u;
			q[tail++] = mate[u];
		}
	}
	
	int m = 0;
	static int label[N_MAX + M_MAX + 1];
	static edge *aux[N_MAX + M_MAX + 1], f[L_MAX + N_MAX + 1];
	for (u = 1; u <= N; u++) {
		aux[u] = NULL;
		if (par[u] != 0) continue;
		for (p = adj[u]; p != NULL; p = p->next) {
			w = p->v;
			if (par[w] != 0) continue;
			f[m].v = w;
			f[m].next = aux[u];
			aux[u] = &(f[m++]);
		}
	}
	for (u = N + 1; u <= N + M; u++) {
		aux[u] = NULL;
		if (par[u] != 0 || mate[u] == 0) continue;
		w = mate[u];
		f[m].v = w;
		f[m].next = aux[u];
		aux[u] = &(f[m++]);
	}
	SCC(N + M, aux, label);
	
	for (i = 1; i <= L; i++) {
		u = s[i];
		w = t[i] + N;
		if (par[u] > 0 && par[w] > 0) ans[i] = 1;
		else if (par[u] < 0 && par[w] < 0) ans[i] = 1;
		else if (label[u] == label[w]) ans[i] = 1;
		else ans[i] = 0;
	}
}



int main()
{
	char ans[L_MAX + 1];
	int i, N, M, L, s[L_MAX + 1], t[L_MAX + 1];
	scanf("%d %d %d", &N, &M, &L);
	for (i = 1; i <= L; i++) scanf("%d %d", &(s[i]), &(t[i]));
	solve2(N, M, L, s, t, ans);
	for (i = 1; i <= L; i++) {
		if (ans[i] == 0) printf("No\n");
		else printf("Yes\n");
	}
	fflush(stdout);
	return 0;
}

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結果

テストケース

ソースコード