综合性很强的题目。
存在环，可以用tarjan处理，然后需要求LCA。并查集+RMQ可以搞。
非常不错的题目。
1 /* 4297 */
2 #include <iostream>
3 #include <sstream>
4 #include <string>
5 #include <map>
6 #include <queue>
7 #include <set>
8 #include <stack>
9 #include <vector>
10 #include <deque>
11 #include <algorithm>
12 #include <cstdio>
13 #include <cmath>
14 #include <ctime>
15 #include <cstring>
16 #include <climits>
17 #include <cctype>
18 #include <cassert>
19 #include <functional>
20 #include <iterator>
21 #include <iomanip>
22 using namespace std;
23 //#pragma comment(linker,"/STACK:102400000,1024000")
24
25 #define sti set<int>
26 #define stpii set<pair<int, int> >
27 #define mpii map<int,int>
28 #define vi vector<int>
29 #define pii pair<int,int>
30 #define vpii vector<pair<int,int> >
31 #define rep(i, a, n) for (int i=a;i<n;++i)
32 #define per(i, a, n) for (int i=n-1;i>=a;--i)
33 #define clr clear
34 #define pb push_back
35 #define mp make_pair
36 #define fir first
37 #define sec second
38 #define all(x) (x).begin(),(x).end()
39 #define SZ(x) ((int)(x).size())
40 #define lson l, mid, rt<<1
41 #define rson mid+1, r, rt<<1|1
42
43 typedef struct {
44 int v, nxt;
45 } edge_t;
46
47 const int maxn = 500005;
48 // input
49 int link[maxn], link2[maxn];
50
51 // tarjan
52 int low[maxn], pre[maxn], bn[maxn], C[maxn];
53 int S[maxn], top;
54 int dfs_clock, block;
55
56 // LCA
57 int head[maxn], l;
58 edge_t E[maxn<<1];
59 int deg[maxn], beg[maxn];
60 int deep[maxn], V[maxn<<1], D[maxn<<1];
61
62 // RMQ
63 int dp[maxn<<1][20];
64
65 int dis[maxn];
66 int fa[maxn];
67 int n;
68
69
70 int find(int x) {
71 if (x == fa[x])
72 return x;
73
74 int tmp = fa[x];
75 fa[x] = find(fa[x]);
76 dis[x] += dis[tmp];
77 return fa[x];
78 }
79
80 void tarjan(int u) {
81 S[top++] = u;
82 pre[u] = low[u] = ++dfs_clock;
83
84 int v = link[u];
85
86 if (!pre[v]) {
87 tarjan(v);
88 low[u] = min(low[u], low[v]);
89 } else if (!bn[v]) {
90 low[u] = min(low[u], pre[v]);
91 }
92
93 if (pre[u] == low[u]) {
94 ++block;
95 C[block] = 0;
96 do {
97 bn[S[--top]] = block;
98 ++C[block];
99 } while (S[top] != u);
100 }
101 }
102
103 void addEdge(int u, int v) {
104 E[l].v = v;
105 E[l].nxt = head[u];
106 head[u] = l++;
107 }
108
109 void dfs(int u, int d) {
110 deep[u] = d;
111 V[++top] = u;
112 D[top] = d;
113 beg[u] = top;
114
115 int v, k;
116
117 for (k=head[u]; k!=-1; k=E[k].nxt) {
118 v = E[k].v;
119 if (link2[v] == -1) {
120 link2[v] = link2[u];
121 }
122 dfs(v, d+1);
123 V[++top] = u;
124 D[top] = d;
125 }
126 }
127
128 void RMQ_init() {
129 int len = top;
130 int i, j, k;
131
132 for (i=1; i<=len; ++i)
133 dp[i][0] = i;
134 for (j=1; (1<<j)<=len; ++j) {
135 for (i=1; i+(1<<j)-1<=len; ++i) {
136 if (D[dp[i][j-1]] < D[dp[i+(1<<(j-1))][j-1]])
137 dp[i][j] = dp[i][j-1];
138 else
139 dp[i][j] = dp[i+(1<<(j-1))][j-1];
140 }
141 }
142 }
143
144 int RMQ(int l, int r) {
145 if (l > r)
146 swap(l, r);
147
148 int k = 0;
149
150 while ((1<<(k+1)) <= r-l+1)
151 ++k;
152
153 if (D[dp[l][k]] < D[dp[r-(1<<k)+1][k]])
154 return V[dp[l][k]];
155 else
156 return V[dp[r-(1<<k)+1][k]];
157 }
158
159 void init() {
160 dfs_clock = top = block = 0;
161 memset(pre, 0, sizeof(pre));
162 memset(bn, 0, sizeof(bn));
163
164 rep(i, 1, n+1) {
165 if (!pre[i])
166 tarjan(i);
167 }
168
169 l = 0;
170 memset(head, -1, sizeof(head));
171 memset(link2, -1, sizeof(link2));
172 memset(deg, 0, sizeof(deg));
173 memset(dis, 0, sizeof(dis));
174 rep(i, 1, n+1) {
175 int bv = bn[i];
176 int bu = bn[link[i]];
177 if (bu == bv) {
178 int fx = find(link[i]);
179 int fy = find(i);
180 if (fx != fy) {
181 fa[fy] = fx;
182 dis[fy] = dis[link[i]] + 1;
183 }
184 } else {
185 addEdge(bu, bv);
186 ++deg[bv];
187 if (C[bu] > 1) {
188 link2[bv] = link[i];
189 }
190 }
191 }
192
193 rep(i, 1, block+1) {
194 if (deg[i] == 0)
195 addEdge(0, i);
196 }
197
198
199 // init RMQ
200 top = 0;
201 dfs(0, 0);
202 RMQ_init();
203 }
204
205 void solve(int u, int v) {
206 if (u == v) {
207 puts("0 0");
208 return ;
209 }
210
211 int bu = bn[u];
212 int bv = bn[v];
213 int lca = RMQ(beg[bu], beg[bv]);
214
215
216 #ifndef ONLINE_JUDGE
217 printf("bu = %d, bv = %d, lca = %d\n", bu, bv, lca);
218 #endif
219
220 if (lca == 0) {
221 puts("-1 -1");
222 return ;
223 }
224
225 if (C[lca] == 1) {
226 printf("%d %d\n", deep[bu]-deep[lca], deep[bv]-deep[lca]);
227 return ;
228 }
229
230 int u2v, v2u;
231 int du, dv;
232
233 if (bu == bv) {
234 du = dv = 0;
235 find(u);
236 find(v);
237
238 if (dis[u] < dis[v]) {
239 u2v = C[bu] + dis[u] - dis[v];
240 v2u = dis[v] - dis[u];
241 } else {
242 u2v = dis[u] - dis[v];
243 v2u = C[bv] + dis[v] - dis[u];
244 }
245
246 } else {
247
248 du = deep[bu] - deep[lca];
249 dv = deep[bv] - deep[lca];
250
251 int uu = link2[bu]==-1 ? u:link2[bu];
252 int vv = link2[bv]==-1 ? v:link2[bv];
253
254 find(uu);
255 find(vv);
256
257 #ifndef ONLINE_JUDGE
258 // printf("uu=%d, duu=%d, vv=%d, dvv=%d\n", uu, dis[uu], vv, dis[vv]);
259 #endif
260 if (dis[uu] < dis[vv]) {
261 u2v = C[lca] + dis[uu] - dis[vv];
262 v2u = dis[vv] - dis[uu];
263 } else {
264 u2v = dis[uu] - dis[vv];
265 v2u = C[lca] + dis[vv] - dis[uu];
266 }
267 }
268
269 #ifndef ONLINE_JUDGE
270 printf("du=%d, dv=%d, u2v=%d, v2u=%d\n", du,dv,u2v,v2u);
271 #endif
272 if (max(u2v+du, dv) < max(v2u+dv, du)) {
273 printf("%d %d\n", u2v+du, dv);
274 } else if (max(u2v+du, dv) > max(v2u+dv, du)) {
275 printf("%d %d\n", du, v2u+dv);
276 } else {
277 if (min(u2v+du, dv) < min(v2u+dv, du)) {
278 printf("%d %d\n", u2v+du, dv);
279 } else if (min(u2v+du, dv) > min(v2u+dv, du)) {
280 printf("%d %d\n", du, v2u+dv);
281 } else {
282 printf("%d %d\n", max(u2v+du, dv), min(u2v+du, dv));
283 }
284 }
285 }
286
287 int main() {
288 ios::sync_with_stdio(false);
289 #ifndef ONLINE_JUDGE
290 freopen("data.in", "r", stdin);
291 freopen("data.out", "w", stdout);
292 #endif
293
294 int q;
295 int u, v;
296
297 while (scanf("%d %d", &n, &q)!=EOF) {
298 rep(i, 1, n+1) {
299 fa[i] = i;
300 scanf("%d", &link[i]);
301 }
302 init();
303 while (q--) {
304 scanf("%d %d", &u, &v);
305 solve(u, v);
306 }
307 }
308
309 #ifndef ONLINE_JUDGE
310 printf("time = %d.\n", (int)clock());
311 #endif
312
313 return 0;
314 }
数据生成器。
1 from random import randint, shuffle
2 import shutil
3 import string
4
5
6 def GenDataIn():
7 with open("data.in", "w") as fout:
8 t = 10
9 bound = 5*10**5
10 for tt in xrange(t):
11 n = randint(bound/10, bound)
12 q = randint(bound/10, bound)
13 fout.write("%d %d\n" % (n, q))
14 dataList = []
15 for i in xrange(n):
16 x = randint(1, n)
17 dataList.append(x)
18 fout.write(" ".join(map(str, dataList)) + "\n")
19 for i in xrange(q):
20 u = randint(1, n)
21 v = randint(1, n)
22 fout.write("%d %d\n" % (u, v))
23
24 def MovDataIn():
25 desFileName = "F:\eclipse_prj\workspace\hdoj\data.in"
26 shutil.copyfile("data.in", desFileName)
27
28
29 if __name__ == "__main__":
30 GenDataIn()
31 MovDataIn()
时间： 2024-10-15 22:24:26