【HDOJ】4601 Letter Tree

挺有意思的一道题，思路肯定是将图转化为Trie树，这样可以求得字典序。
然后，按照trie的层次求解。一直wa的原因在于将树转化为线性数据结构时要从原树遍历，从trie遍历就会wa。不同结点可能映射为trie上的同一结点，如
1->2 (a) 1->3(a) 2->4(b), 这是trie的结构是RT->a->b。然而，从结点3不能找到权重为b的路径。
用RMQ求满足边界的rank最大值，通过sa找到该最大值对应的trie上的根。从而求解。

 /* 4601 */
 #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
 // #define DEBUG 

 typedef struct {
     int u, v, w;
     int nxt;
 } edge_t;

 typedef struct ques_t {
     int u, m, id;

     ques_t() {}
     friend bool operator< (const ques_t& a, const ques_t& b) {
         if (a.m == b.m)
             return a.id < b.id;
         return a.m < b.m;
     }

 } ques_t;

 const int mod = 1e9+;
 const int maxn = 1e5+;
 const int maxv = maxn;
 const int maxe = maxv * ;
 int head[maxv], m;
 edge_t E[maxe];
 int nxt[maxn][], l;
 int Pos[maxv], Rank[maxv], sa[maxv];
 __int64 Base[maxn];
 __int64 Val[maxn];
 int deep[maxv];
 int fr[maxv], to[maxv];
 int dfs_clock;
 vi layer[maxn];
 int maxd;
 int n, qn, q;
 ques_t Qu[maxn];
 int ans[maxn];
 int dp[][maxn];
 int D[maxn];

 void Init() {
     Base[] = ;
     rep(i, , maxn)
         Base[i] = Base[i-] *  % mod;
 }

 void init() {
     memset(head, -, sizeof(head));
     m = ;
     memset(nxt[], , sizeof(nxt[]));
     l = ;
     dfs_clock = ;
     maxd = ;
     rep(i, , n+)
         layer[i].clr();
 }

 int newNode() {
     ++l;
     memset(nxt[l], , sizeof(nxt[l]));
     Val[l] = ;
     return l;
 }

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

     E[m].v = u;
     E[m].w = w;
     E[m].nxt = head[v];
     head[v] = m++;
 }

 void Build_Trie(int u, int fa, int rt) {
     int v, k, p;

     Pos[u] = rt;
     for (k=head[u]; k!=-; k=E[k].nxt) {
         v = E[k].v;
         if (v == fa)
             continue;

         int id = E[k].w;
         p = nxt[rt][id];
         if (!p)
             p = nxt[rt][id] = newNode();
         Build_Trie(v, u, p);
     }
 }

 void Mark_Rank(int rt, int d) {
     int p;

     Rank[rt] = ++dfs_clock;
     sa[dfs_clock] = rt;
     rep(i, , ) {
         p = nxt[rt][i];
         if (p) {
             Val[p] = (Val[rt]* + i) % mod;
             Mark_Rank(p, d+);
         }
     }
 }

 void calDepth(int u, int fa, int rt) {
     int v, k, p;

     D[++dfs_clock] = Rank[rt];
     fr[u] = dfs_clock + ;
     maxd = max(deep[u], maxd);
     layer[deep[u]].pb(dfs_clock);
     for (k=head[u]; k!=-; k=E[k].nxt) {
         v = E[k].v;
         if (v == fa)
             continue;
         deep[v] = deep[u] + ;
         p = nxt[rt][E[k].w];
         calDepth(v, u, p);
     }
     to[u] = dfs_clock;
 }

 void init_RMQ(int d, int n) {
     int i, j;

     for (i=; i<n; ++i)
         dp[][i] = D[layer[d][i]];
     for (j=; (<<j)<=n; ++j)
         for (i=; i+(<<j)-<n; ++i)
             dp[j][i] = max(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;

     return max(dp[k][l], dp[k][r-(<<k)+]);
 }

 int calc(int qid, int d) {
     int u = Qu[qid].u;
     int rt = Pos[u];
     int b = fr[u];
     int e = to[u];
     int l = lower_bound(all(layer[d]), b) - layer[d].begin();
     int r = upper_bound(all(layer[d]), e) - layer[d].begin();
     --r;

     if (l > r)
         return -;

     int mxrank = RMQ(l, r);
     int mxrt = sa[mxrank];
     int delta = d - deep[u];
     int ret = (Val[mxrt] - Val[rt] * Base[delta] % mod + mod) % mod;

     return ret;
 }

 void solve() {
     Build_Trie(, , );
     Mark_Rank(, );
     dfs_clock = ;
     deep[] = ;
     calDepth(, , );

     scanf("%d", &q);
     qn = ;
     rep(i, , q) {
         scanf("%d %d", &Qu[qn].u, &Qu[qn].m);
         int deepu = deep[Qu[qn].u];
         if (Qu[qn].m == ) {
             ans[i] = ;
         } else if (deepu+Qu[qn].m > maxd) {
             ans[i] = -;
         } else {
             Qu[qn].m += deepu;
             Qu[qn].id = i;
             ++qn;
         }
     }

     if (qn) {
         sort(Qu, Qu+qn);
         int j = ;
         rep(i, , maxd+) {
             if (i < Qu[j].m)
                 continue;
             int sz = SZ(layer[i]);
             init_RMQ(i, sz);
             while (j<=qn && Qu[j].m==i) {
                 int id = Qu[j].id;
                 ans[id] = calc(j, i);
                 ++j;
             }
             if (j == qn)
                 break;
         }
     }

     rep(i, , q) {
         if (ans[i] == -)
             puts("IMPOSSIBLE");
         else
             printf("%d\n", ans[i]);
     }
 }

 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;
     char ws[];

     Init();
     scanf("%d", &t);
     while (t--) {
         scanf("%d", &n);
         init();
         rep(i, , n) {
             scanf("%d %d %s", &u, &v, ws);
             addEdge(u, v, ws[]-'a');
         }
         solve();
     }

     #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
         lc = list(string.lowercase)
         fout.write("%d\n" % (t))
         for tt in xrange(t):
             n = randint(300, 500)
             fout.write("%d\n" % (n))
             ust = [1]
             vst = range(2, n+1)
             for i in xrange(1, n):
                 uid = randint(0, len(ust)-1)
                 vid = randint(0, len(vst)-1)
                 u = ust[uid]
                 v = vst[vid]
                 ust.append(v)
                 vst.remove(v)
                 idx = randint(0, 25)
                 c = lc[idx]
                 fout.write("%d %d %s\n" % (u, v, c))
             q = randint(400, 600)
             fout.write("%d\n" % (q))
             for i in xrange(q):
                 u = randint(1, n+1)
                 m = randint(0, 10)
                 fout.write("%d %d\n" % (u, m))

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

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