LCA+RMQ。挺不错的一道题目。
思路是如何通过LCA维护费用。当加入新的点u是，费用增量为
dis[u]-dis[lca(u, lower_u)] - dis[lca(u, greater_u)] + dis[lca(lower_u, greater_u)]。
若beg[u]大于当前最大值或小于最小值，lower_u=min of current, greater_u = max of current。
1 /* 5296 */
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, w, nxt;
45 } edge_t;
46
47 const int maxn = 1e5+5;
48 const int maxv = maxn;
49 const int maxe = maxv * 2;
50 int head[maxv];
51 edge_t E[maxe];
52 int dis[maxn], deep[maxn];
53 bool visit[maxn];
54 int beg[maxn];
55 int V[maxn<<1], D[maxn<<1];
56 int dp[18][maxn<<1];
57 int l, top;
58 sti st;
59 sti::iterator iter;
60
61 void init() {
62 st.clr();
63 memset(visit, false, sizeof(visit));
64 memset(head, -1, sizeof(head));
65 l = top = 0;
66 }
67
68 void addEdge(int u, int v, int w) {
69 E[l].v = v;
70 E[l].w = w;
71 E[l].nxt = head[u];
72 head[u] = l++;
73
74 E[l].v = u;
75 E[l].w = w;
76 E[l].nxt = head[v];
77 head[v] = l++;
78 }
79
80 void dfs(int u, int fa, int d, int w) {
81 dis[u] = w;
82 V[++top] = u;
83 D[top] = d;
84 beg[u] = top;
85
86 int v, k;
87
88 for (k=head[u]; k!=-1; k=E[k].nxt) {
89 v = E[k].v;
90 if (v == fa)
91 continue;
92 dfs(v, u, d+1, w+E[k].w);
93 V[++top] = u;
94 D[top] = d;
95 }
96 }
97
98 void init_RMQ(int n) {
99 int i, j;
100
101 for (i=1; i<=n; ++i)
102 dp[0][i] = i;
103 for (j=1; (1<<j)<=n; ++j)
104 for (i=1; i+(1<<j)-1<=n; ++i)
105 if (D[dp[j-1][i]] < D[dp[j-1][i+(1<<(j-1))]])
106 dp[j][i] = dp[j-1][i];
107 else
108 dp[j][i] = dp[j-1][i+(1<<(j-1))];
109 }
110
111 int RMQ(int l, int r) {
112 if (l > r)
113 swap(l, r);
114
115 int k = 0;
116
117 while (1<<(k+1) <= r-l+1)
118 ++k;
119
120 if (D[dp[k][l]] < D[dp[k][r-(1<<k)+1]])
121 return V[dp[k][l]];
122 else
123 return V[dp[k][r-(1<<k)+1]];
124 }
125
126 int calc(int u) {
127 if (st.empty())
128 return 0;
129
130 int x, y;
131
132 iter = st.upper_bound(beg[u]);
133 if (iter == st.end() || iter==st.begin()) {
134 y = *st.rbegin();
135 x = *st.begin();
136 } else {
137 y = *iter;
138 --iter;
139 x = *iter;
140 }
141
142 int ret = 0;
143
144 ret = dis[u] - dis[RMQ(x, beg[u])] - dis[RMQ(beg[u], y)] + dis[RMQ(x, y)];
145 return ret;
146 }
147
148 int main() {
149 ios::sync_with_stdio(false);
150 #ifndef ONLINE_JUDGE
151 freopen("data.in", "r", stdin);
152 freopen("data.out", "w", stdout);
153 #endif
154
155 int t;
156 int n, q;
157 int u, v, w;
158 int op;
159 int ans;
160
161 scanf("%d", &t);
162 rep(tt, 1, t+1) {
163 scanf("%d %d", &n, &q);
164 init();
165 rep(i, 1, n) {
166 scanf("%d %d %d", &u, &v, &w);
167 addEdge(u, v, w);
168 }
169 dfs(1, 0, 0, 0);
170 init_RMQ(top);
171 printf("Case #%d:\n", tt);
172 ans = 0;
173 while (q--) {
174 scanf("%d %d", &op, &u);
175 if (op == 1) {
176 if (!visit[u]) {
177 visit[u] = true;
178 ans += calc(u);
179 st.insert(beg[u]);
180 }
181 } else {
182 if (visit[u]) {
183 visit[u] = false;
184 st.erase(beg[u]);
185 ans -= calc(u);
186 }
187 }
188 printf("%d\n", ans);
189 }
190 }
191
192 #ifndef ONLINE_JUDGE
193 printf("time = %d.\n", (int)clock());
194 #endif
195
196 return 0;
197 }
数据发生器。
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 = 10**3
10 fout.write("%d\n" % (t))
11 for tt in xrange(t):
12 n = randint(20, 30)
13 q = randint(20, 30)
14 fout.write("%d %d\n" % (n, q))
15 ust = [1]
16 vst = range(1, n+1)
17 ust.append(1)
18 vst.remove(1)
19 un = 1
20 vn = n - 1
21 for i in xrange(1, n):
22 uidx = randint(0, un-1)
23 u = ust[uidx]
24 vidx = randint(0, vn-1)
25 v = vst[vidx]
26 ust.append(v)
27 vst.remove(v)
28 un += 1
29 vn -= 1
30 w = randint(1, 100)
31 fout.write("%d %d %d\n" % (u, v, w))
32 L = []
33 for i in xrange(q):
34 op = randint(1, 2)
35 x = randint(1, n)
36 fout.write("%d %d\n" % (op, x))
37
38
39
40 def MovDataIn():
41 desFileName = "F:\eclipse_prj\workspace\hdoj\data.in"
42 shutil.copyfile("data.in", desFileName)
43
44
45 if __name__ == "__main__":
46 GenDataIn()
47 MovDataIn()
时间： 2024-10-19 05:28:15