【HDOJ】4729 An Easy Problem for Elfness

其实是求树上的路径间的数据第K大的题目。
果断主席树 + LCA。
初始流量是这条路径上的最小值。
若a<=b，显然直接为s->t建立pipe可以使流量最优；
否则，对【0, 10**4】二分得到boundry，使得boundry * n_edge - sum_edge <= k/b， 或者建立s->t，然后不断extend s->t。

 /* 4729 */
 #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, c, nxt;
 } edge_t;

 const int maxn = 1e5+;
 const int m = ;
 const int maxm = maxn * ;
 int T[maxn];
 int lson[maxm], rson[maxm], c[maxm], sum[maxm];
 int head[maxn], l;
 edge_t E[maxn<<];
 int tot, n, q;
 int beg[maxn];
 int V[maxn<<], D[maxn<<], top;
 int dp[][maxn<<];

 void init() {
     memset(head, -, sizeof(head));
     l = top = ;
     tot = ;
 }

 int Build(int l, int r) {
     int rt = tot++;

     c[rt] = sum[rt] = ;
     if (l == r)
         return rt;

     int mid = (l + r) >> ;

     lson[rt] = Build(l, mid);
     rson[rt] = Build(mid+, r);

     return rt;
 }

 int Insert(int rt, int x, int val) {
     int nrt = tot++, ret = nrt;
     int l = , r = m - , mid;

     c[nrt] = c[rt] + ;
     sum[nrt] = sum[rt] + val;
     while (l < r) {
         mid = (l + r) >> ;
         if (x <= mid) {
             lson[nrt] = tot++;
             rson[nrt] = rson[rt];
             nrt = lson[nrt];
             rt = lson[rt];
             r = mid;
         } else {
             lson[nrt] = lson[rt];
             rson[nrt] = tot++;
             nrt = rson[nrt];
             rt = rson[rt];
             l = mid + ;
         }
         c[nrt] = c[rt] + ;
         sum[nrt] = sum[rt] + val;
     }

     return ret;
 }

 int Query_kth(int urt, int vrt, int frt, int k) {
     int l = , r = m - , mid;
     int tmp;

     while (l < r) {
         mid = (l + r) >> ;
         tmp = c[lson[urt]] + c[lson[vrt]] - (c[lson[frt]] << );
         if (tmp >= k) {
             urt = lson[urt];
             vrt = lson[vrt];
             frt = lson[frt];
             r = mid;
         } else {
             k -= tmp;
             urt = rson[urt];
             vrt = rson[vrt];
             frt = rson[frt];
             l = mid + ;
         }
     }

     return l;
 }

 int Query_Bound(int urt, int vrt, int frt, int delta) {
     int l = , r = m - , mid;
     int cc = , csum = ;
     int tc, tsum;
     int ans = , tmp;

     while (l < r) {
         mid = (l + r) >> ;
         tc = c[lson[urt]] + c[lson[vrt]] - (c[lson[frt]] << );
         tsum = sum[lson[urt]] + sum[lson[vrt]] - (sum[lson[frt]] << );
         tmp = mid*(tc+cc)-(tsum+csum);
         if (tmp <= delta)
             ans = max(ans, mid);
         if (mid*(tc+cc)-(tsum+csum) >= delta) {
             urt = lson[urt];
             vrt = lson[vrt];
             frt = lson[frt];
             r = mid;
         } else {
             urt = rson[urt];
             vrt = rson[vrt];
             frt = rson[frt];
             cc += tc;
             csum += tsum;
             l = mid + ;
         }
     }

     return ans;
 }

 void addEdge(int u, int v, int c) {
     E[l].v = v;
     E[l].c = c;
     E[l].nxt = head[u];
     head[u] = l++;

     E[l].v = u;
     E[l].c = c;
     E[l].nxt = head[v];
     head[v] = l++;
 }

 void dfs(int u, int fa, int dep) {
     int v, k;

     V[++top] = u;
     D[top] = dep;
     beg[u] = top;

     for (k=head[u]; k!=-; k=E[k].nxt) {
         v = E[k].v;
         if (v == fa)
             continue;
         T[v] = Insert(T[u], E[k].c, E[k].c);
         dfs(v, u, dep+);
         V[++top] = u;
         D[top] = dep;
     }
 }

 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)+]];
 }

 void solve() {
     T[] = Build(, m - );
     dfs(, , );
     Init_RMQ(top);

     int u, v, k, a, b;
     int lca;
     int ans, tmp, org;

     while (q--) {
         scanf("%d %d %d %d %d", &u, &v, &k, &a, &b);
         lca = RMQ(beg[u], beg[v]);
         org = Query_kth(T[u], T[v], T[lca], );
         #ifndef ONLINE_JUDGE
             // printf("f = %d\n", lca);
         #endif
         if (a <= b) {
             ans = org + k / a;
         } else {
             ans = org;
             if (k >= a)
                 ans +=  + (k-a)/b;
             tmp = Query_Bound(T[u], T[v], T[lca], k/b);
             #ifndef ONLINE_JUDGE
             // printf("org = %d, ans = %d, bound = %d\n", org, ans, tmp);
             #endif
             ans = max(ans, tmp);
         }
         printf("%d\n", ans);
     }
 }

 int main() {
     ios::sync_with_stdio(false);
     #ifndef ONLINE_JUDGE
         freopen("data.in", "r", stdin);
         freopen("data.out", "w", stdout);
     #endif

     int t;
     int u, v, c;

     scanf("%d", &t);
     rep(tt, , t+) {
         init();
         scanf("%d %d", &n, &q);
         rep(i, , n) {
             scanf("%d %d %d", &u, &v, &c);
             addEdge(u, v, c);
         }
         printf("Case #%d:\n", tt);
         solve();
     }

     #ifndef ONLINE_JUDGE
         printf("time = %d.\n", (int)clock());
     #endif

     return ;
 }

数据发生器。

 from copy import deepcopy
 from random import randint, shuffle
 import shutil
 import string

 def GenDataIn():
     with open("data.in", "w") as fout:
         t = 10
         bound = 10**4
         fout.write("%d\n" % (t))
         for tt in xrange(t):
             n = randint(100, 200)
             q = randint(100, 200)
             fout.write("%d %d\n" % (n, q))
             ust = [1]
             vst = range(2, n+1)
             for i in xrange(1, n):
                 idx = randint(0, len(ust)-1)
                 u = ust[idx]
                 idx = randint(0, len(vst)-1)
                 v = vst[idx]
                 ust.append(v)
                 vst.remove(v)
                 c = randint(0, bound-1)
                 fout.write("%d %d %d\n" % (u, v, c))
             for i in xrange(q):
                 u = randint(1, n)
                 while True:
                     v = randint(1, n)
                     if v!=u:
                         break
                 k = randint(0, bound)
                 a = randint(1, bound)
                 b = randint(1, bound)
                 fout.write("%d %d %d %d %d\n" % (u, v, k, a, b))

 def MovDataIn():
     desFileName = "F:\eclipse_prj\workspace\hdoj\data.in"
     shutil.copyfile("data.in", desFileName)

 if __name__ == "__main__":
     GenDataIn()
     MovDataIn()