HDU3078 Network [2016年6月计划 树上问题05]
Network
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 1293 Accepted Submission(s): 575
ALPC company is now working on his own network system, which is
connecting all N ALPC department. To economize on spending, the backbone
network has only one router for each department, and N-1 optical fiber
in total to connect all routers.
The usual way to measure connecting
speed is lag, or network latency, referring the time taken for a sent
packet of data to be received at the other end.
Now the network is on
trial, and new photonic crystal fibers designed by ALPC42 is trying
out, the lag on fibers can be ignored. That means, lag happened when
message transport through the router. ALPC42 is trying to change routers
to make the network faster, now he want to know that, which router, in
any exactly time, between any pair of nodes, the K-th high latency is.
He needs your help.
Your
program is able to get the information of N routers and N-1 fiber
connections from input, and Q questions for two condition: 1. For some
reason, the latency of one router changed. 2. Querying the K-th longest
lag router between two routers.
For each data case, two integers N and Q for first line. 0<=N<=80000, 0<=Q<=30000.
Then n integers in second line refer to the latency of each router in the very beginning.
Then N-1 lines followed, contains two integers x and y for each, telling there is a fiber connect router x and router y.
Then
q lines followed to describe questions, three numbers k, a, b for each
line. If k=0, Telling the latency of router a, Ta changed to b; if
k>0, asking the latency of the k-th longest lag router between a and b
(include router a and b). 0<=b<100000000.
A blank line follows after each case.
each question k>0, print a line to answer the latency time. Once
there are less than k routers in the way, print "invalid request!"
instead.
5 1 2 3 4
3 1
2 1
4 3
5 3
2 4 5
0 1 2
2 2 3
2 1 4
3 3 5
2
2
invalid request!
#include <cstdio>
#include <cstring>
#include <iostream>
#include <cstdlib>
#include <algorithm>
inline void read(int &x){char ch = getchar();char c = ch;x = 0;while(ch < '0' || ch > '9')c = ch, ch = getchar();while(ch <= '9' && ch >= '0')x = x * 10 + ch - '0', ch = getchar();if(c == '-')x = -x;}
inline void swap(int &a, int &b){int tmp = a;a = b;b = tmp;} const int MAXN = 80000 + 10; struct Edge{int u,v,next;}edge[MAXN << 1];
int head[MAXN],cnt,n,m,w[MAXN],p[20][MAXN],deep[MAXN],fa[MAXN],num[MAXN],b[MAXN];
inline void insert(int a,int b){edge[++cnt] = Edge{a, b, head[a]},head[a] = cnt;} int llog2[MAXN],pow2[30]; void dfs(int u)
{
for(int pos = head[u];pos;pos = edge[pos].next)
{
int v = edge[pos].v;
if(b[v])continue;
b[v] = true,deep[v] = deep[u] + 1,p[0][v] = u,fa[v] = u,dfs(v);
}
} inline void yuchuli()
{
b[1] = true,deep[1] = 0,dfs(1);
register int i;
for(i = 1;i <= llog2[n];i ++)
for(int j = n;j >= 1;j --)
p[i][j] = p[i - 1][p[i - 1][j]];
} inline int lca(int va, int vb)
{
register int i;
if(deep[va] < deep[vb])swap(va, vb);
for(i = llog2[n];i >= 0;i --)
if(deep[va] - pow2[i] >= deep[vb])
va = p[i][va];
if(va == vb)return va;
for(i = llog2[n];i >= 0;i --)
if(p[i][va] != p[i][vb])
va = p[i][va],vb = p[i][vb];
return p[0][va];
} int ans[MAXN],rank; inline void work(int s, int t, int k)
{
int anc = lca(s, t);
int now = s;
register int i = 1;
num[i] = w[now];
while(now != anc)
num[++i] = w[(now = fa[now])];
now = t;
while(now != anc)
num[++i] = w[now], now = fa[now];
std::sort(num + 1, num + 1 + i);
if(i >= k)
ans[++rank] = num[i - k + 1];
else rank++;
} int main()
{
register int i,tmp1,tmp2,tmp3;
llog2[0] = -1,pow2[0] = 1;
for(int i = 1;i <= MAXN;i ++)llog2[i] = llog2[i >> 1] + 1;
for(int i = 1;i <= 25; i++)pow2[i] = (pow2[i - 1] << 1);
read(n),read(m);
for(i = 1;i <= n;i ++)read(w[i]);
for(i = 1;i < n;i ++)read(tmp1),read(tmp2),insert(tmp1, tmp2),insert(tmp2, tmp1);
yuchuli();
for(i = 1;i <= m;i ++)
{
read(tmp1),read(tmp2),read(tmp3);
if(tmp1)work(tmp2, tmp3, tmp1);
else w[tmp2] = tmp3;
}
for(int i = 1;i < rank;i ++)
if(ans[i])
printf("%d\n", ans[i]);
else
printf("invalid request!\n");
if(ans[rank])
printf("%d\n", ans[rank]);
else
printf("invalid request!\n");
return 0;
}
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