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。

 /* 5296 */
#include <iostream>
#include <sstream>
#include <string>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <vector>
#include <deque>
#include <algorithm>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <cstring>
#include <climits>
#include <cctype>
#include <cassert>
#include <functional>
#include <iterator>
#include <iomanip>
using namespace std;
//#pragma comment(linker,"/STACK:102400000,1024000") #define sti set<int>
#define stpii set<pair<int, int> >
#define mpii map<int,int>
#define vi vector<int>
#define pii pair<int,int>
#define vpii vector<pair<int,int> >
#define rep(i, a, n) for (int i=a;i<n;++i)
#define per(i, a, n) for (int i=n-1;i>=a;--i)
#define clr clear
#define pb push_back
#define mp make_pair
#define fir first
#define sec second
#define all(x) (x).begin(),(x).end()
#define SZ(x) ((int)(x).size())
#define lson l, mid, rt<<1
#define rson mid+1, r, rt<<1|1 typedef struct {
int v, w, nxt;
} edge_t; const int maxn = 1e5+;
const int maxv = maxn;
const int maxe = maxv * ;
int head[maxv];
edge_t E[maxe];
int dis[maxn], deep[maxn];
bool visit[maxn];
int beg[maxn];
int V[maxn<<], D[maxn<<];
int dp[][maxn<<];
int l, top;
sti st;
sti::iterator iter; void init() {
st.clr();
memset(visit, false, sizeof(visit));
memset(head, -, sizeof(head));
l = top = ;
} void addEdge(int u, int v, int w) {
E[l].v = v;
E[l].w = w;
E[l].nxt = head[u];
head[u] = l++; E[l].v = u;
E[l].w = w;
E[l].nxt = head[v];
head[v] = l++;
} void dfs(int u, int fa, int d, int w) {
dis[u] = w;
V[++top] = u;
D[top] = d;
beg[u] = top; int v, k; for (k=head[u]; k!=-; k=E[k].nxt) {
v = E[k].v;
if (v == fa)
continue;
dfs(v, u, d+, w+E[k].w);
V[++top] = u;
D[top] = d;
}
} void init_RMQ(int n) {
int i, j; for (i=; i<=n; ++i)
dp[][i] = i;
for (j=; (<<j)<=n; ++j)
for (i=; i+(<<j)-<=n; ++i)
if (D[dp[j-][i]] < D[dp[j-][i+(<<(j-))]])
dp[j][i] = dp[j-][i];
else
dp[j][i] = dp[j-][i+(<<(j-))];
} int RMQ(int l, int r) {
if (l > r)
swap(l, r); int k = ; while (<<(k+) <= r-l+)
++k; if (D[dp[k][l]] < D[dp[k][r-(<<k)+]])
return V[dp[k][l]];
else
return V[dp[k][r-(<<k)+]];
} int calc(int u) {
if (st.empty())
return ; int x, y; iter = st.upper_bound(beg[u]);
if (iter == st.end() || iter==st.begin()) {
y = *st.rbegin();
x = *st.begin();
} else {
y = *iter;
--iter;
x = *iter;
} int ret = ; ret = dis[u] - dis[RMQ(x, beg[u])] - dis[RMQ(beg[u], y)] + dis[RMQ(x, y)];
return ret;
} int main() {
ios::sync_with_stdio(false);
#ifndef ONLINE_JUDGE
freopen("data.in", "r", stdin);
freopen("data.out", "w", stdout);
#endif int t;
int n, q;
int u, v, w;
int op;
int ans; scanf("%d", &t);
rep(tt, , t+) {
scanf("%d %d", &n, &q);
init();
rep(i, , n) {
scanf("%d %d %d", &u, &v, &w);
addEdge(u, v, w);
}
dfs(, , , );
init_RMQ(top);
printf("Case #%d:\n", tt);
ans = ;
while (q--) {
scanf("%d %d", &op, &u);
if (op == ) {
if (!visit[u]) {
visit[u] = true;
ans += calc(u);
st.insert(beg[u]);
}
} else {
if (visit[u]) {
visit[u] = false;
st.erase(beg[u]);
ans -= calc(u);
}
}
printf("%d\n", ans);
}
} #ifndef ONLINE_JUDGE
printf("time = %d.\n", (int)clock());
#endif return ;
}

数据发生器。

 from random import randint, shuffle
import shutil
import string def GenDataIn():
with open("data.in", "w") as fout:
t = 10
bound = 10**3
fout.write("%d\n" % (t))
for tt in xrange(t):
n = randint(20, 30)
q = randint(20, 30)
fout.write("%d %d\n" % (n, q))
ust = [1]
vst = range(1, n+1)
ust.append(1)
vst.remove(1)
un = 1
vn = n - 1
for i in xrange(1, n):
uidx = randint(0, un-1)
u = ust[uidx]
vidx = randint(0, vn-1)
v = vst[vidx]
ust.append(v)
vst.remove(v)
un += 1
vn -= 1
w = randint(1, 100)
fout.write("%d %d %d\n" % (u, v, w))
L = []
for i in xrange(q):
op = randint(1, 2)
x = randint(1, n)
fout.write("%d %d\n" % (op, x)) def MovDataIn():
desFileName = "F:\eclipse_prj\workspace\hdoj\data.in"
shutil.copyfile("data.in", desFileName) if __name__ == "__main__":
GenDataIn()
MovDataIn()

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