#include #include #define N_MAX 100000 #define M_MAX 100000 #define L_MAX 200000 typedef struct Edge { struct Edge *next; int v, id; char flag; } edge; int bipartite_matching_augmentation_naive(int N, char color[], edge* adj[], int mate[]) { static int i, u, w, par[N_MAX + M_MAX + 1], q[N_MAX + M_MAX + 1], head, tail; edge *p; for (u = 1, tail = 0; u <= N; u++) { if (color[u] == 0 && mate[u] == 0) { par[u] = u; q[tail++] = u; } else par[u] = 0; } for (head = 0; head < tail; head++) { u = q[head]; if (color[u] == 0) { for (p = adj[u]; p != NULL; p = p->next) { if (p->flag == 0) continue; w = p->v; if (par[w] == 0) { par[w] = u; if (mate[w] == 0) break; q[tail++] = w; } } if (p != NULL) break; } else { par[mate[u]] = u; q[tail++] = mate[u]; } } if (head == tail) return 0; // Augmentation for (u = par[w]; u != w; w = par[u], u = par[w]) { mate[u] = w; mate[w] = u; } return 1; } 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; } // 2. Relatively naive solution (O(L^2) time) void rel_naive2(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].id = i * 2; e[i*2].flag = 1; e[i*2].next = adj[u]; adj[u] = &(e[i*2]); e[i*2+1].v = u; e[i*2+1].id = i * 2 + 1; e[i*2+1].flag = 1; e[i*2+1].next = adj[w]; adj[w] = &(e[i*2+1]); } int j = 0, x, mu = bipartite_matching(N + M, color, adj, mate); static int tmp_mate[N_MAX + M_MAX + 1]; for (i = 0; i < L; i++) { u = s[i+1]; w = t[i+1] + N; if (mate[u] == w || mate[u] == 0 || mate[w] == 0) { ans[i+1] = 1; continue; } for (x = 1; x <= N + M; x++) tmp_mate[x] = mate[x]; tmp_mate[tmp_mate[u]] = 0; tmp_mate[tmp_mate[w]] = 0; for (p = adj[u]; p != NULL; p = p->next) { p->flag = 0; e[p->id ^ 1].flag = 0; } for (p = adj[w]; p != NULL; p = p->next) { p->flag = 0; e[p->id ^ 1].flag = 0; } if (bipartite_matching_augmentation_naive(N + M, color, adj, tmp_mate) == 0) ans[i+1] = 0; else ans[i+1] = 1; for (p = adj[u]; p != NULL; p = p->next) { p->flag = 1; e[p->id ^ 1].flag = 1; } for (p = adj[w]; p != NULL; p = p->next) { p->flag = 1; e[p->id ^ 1].flag = 1; } } } 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])); rel_naive2(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; }