【HDOJ】5296 Annoying problem

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()