HDU 5274(LCA + 线段树）

Dylans loves tree

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)

Total Submission(s): 747    Accepted Submission(s): 144


Problem Description

Dylans is given a tree with N nodes.

All nodes have a value A[i].Nodes
on tree is numbered by 1∼N.

Then he is given Q questions
like that:

①0 x y：change
node x′s value
to y

②1 x y：For
all the value in the path from x to y,do
they all appear even times? 

For each ② question,it guarantees that there is at most one value that appears odd times on the path.

1≤N,Q≤100000,
the value A[i]∈N and A[i]≤100000

 

Input

In the first line there is a test number T.

(T≤3 and
there is at most one testcase that N>1000)

For each testcase:

In the first line there are two numbers N and Q.

Then in the next N−1 lines
there are pairs of (X,Y) that
stand for a road from x to y.

Then in the next line there are N numbers A1..AN stand
for value.

In the next Q lines
there are three numbers(opt,x,y).

 

Output

For each question ② in each testcase,if the value all appear even times output "-1",otherwise output the value that appears odd times.

 

Sample Input

1
3 2
1 2
2 3
1 1 1
1 1 2
1 1 3

 

Sample Output

-1
1

Hint
If you want to hack someone,N and Q in your testdata must smaller than 10000，and you shouldn't print any space in each end of the line.

 

Source

BestCoder Round #45

 

Recommend

hujie   |   We have carefully selected several similar problems for you:  5275 5272 5271 5270 5268 

先考虑无修改的情况，令Xor[i]表示i到根节点路径上的异或和，则任意节点的(u,v)的异或和可以转化为Xor[u]^Xor[v]^a[LCA(u,v)].考虑修改的情况，修改节点u，只会以u为根的子树的Xor值产生影响，因为一颗子树的dfs序是连续的我们很自然的想到用线段树去维护他，pSeg[u]表示u在dfs序中的位置，siz[u]表示以u为根的子树大小，则这课颗子树对应的区间就是[pSeg[u],pSeg[u]+siz[u]-1],修改的时候只需要将这段区间先异或上原来的值a[u],在异或上要变成的值y,然后修改a[u]
= y;两次异或可以一步到位。直接异或上a[u]^y就行。

#pragma comment(linker, "/STACK:102400000,102400000")
#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
typedef long long ll;
const ll mod = 1e9 + 7;
const int maxn = 1e5 + 10;
#define to first
#define next second
#define foreach(it,v) for(__typeof(v.begin()) it = v.begin(); it != v.end(); ++it)
int pos[maxn],d[20][maxn<<1],wid[maxn<<1],head[maxn];
int a[maxn],depth[maxn],sid,pSeg[maxn],siz[maxn],Xor[maxn];
typedef pair<int,int> Edge;
Edge edges[maxn<<1];
int tot = 0,e = 0;
void AddEdge(int u,int v)
{
edges[++e] = make_pair(v,head[u]);head[u] = e;
edges[++e] = make_pair(u,head[v]);head[v] = e;
}
void pre(int u,int fa,int dep = 0,int Xo = 0)
{
Xo ^= a[u];
Xor[++sid] = Xo;
pSeg[u] = sid;
siz[u] = 1;
d[0][++tot] = u;
if(!pos[u]) {
pos[u] = tot;
depth[u] = dep;
}
for(int i = head[u]; i ; i = edges[i].next) {
int v = edges[i].to;
if(v == fa) continue;
pre(v,u,dep+1,Xo);
siz[u] += siz[v];
d[0][++tot] = u;
}
}
void RMQ_init(int n)
{
for(int i = 1,w = 1; i <= n; i++) {
if((1<<w)<=i) w++;
wid[i] = w - 1;
}
for(int i = 1; (1<<i) <= n; i++) {
for(int j = 1; j + (1<<i) - 1 <= n; j++) {
d[i][j] = depth[d[i-1][j]] < depth[d[i-1][j+(1<<(i-1))]] ? d[i-1][j] : d[i-1][j+(1<<(i-1))];
}
}
}
int LCA(int u,int v)
{
u = pos[u];
v = pos[v];
if(u > v) swap(u,v);
int k = wid[v-u+1];
return depth[d[k][u]] < depth[d[k][v-(1<<k)+1]] ? d[k][u] : d[k][v-(1<<k)+1];
}
int seg[maxn<<2];
int ql,qr,x;
void push_down(int o)
{
seg[o<<1] ^= seg[o];
seg[o<<1|1] ^= seg[o];
seg[o] = 0;
}
void Modify(int o,int L,int R)
{
if(ql<=L&&qr>=R) {
seg[o] ^= x;
return ;
}
push_down(o);
int mid = (L+R)>>1;
if(ql<=mid) Modify(o<<1,L,mid);
if(qr>mid) Modify(o<<1|1,mid+1,R);
}
int Query(int o,int L,int R)
{
if(L == R) {
return Xor[L] ^ seg[o];
}
int mid = (L+R) >>1;
push_down(o);
if(x<=mid)return Query(o<<1,L,mid);
return Query(o<<1|1,mid+1,R);
}
int main(int argc, char const *argv[])
{
int T;scanf("%d",&T);
while(T--) {
int N,Q;scanf("%d%d",&N,&Q);
e = sid = tot = 0;
memset(head,0,sizeof(head[0])*(N+1));
for(int i = 1; i < N; i++) {
int u,v;scanf("%d%d",&u,&v);
AddEdge(u,v);
}
for(int i = 1; i <= N; i++) {
scanf("%d",a+i);
++a[i];
}
pre(1,-1);
RMQ_init(tot);
memset(seg,0,sizeof(seg[0])*(2*N+10));
while(Q--) {
scanf("%d%d%d",&x,&ql,&qr);
if(x==0) {
qr++;
int L = pSeg[ql], R = pSeg[ql] + siz[ql] - 1;
x = a[ql] ^ qr;
a[ql] = qr;
ql = L,qr = R;
Modify(1,1,N);
}else {
x = pSeg[ql];
int ans = Query(1,1,N);
x = pSeg[qr];
ans ^= Query(1,1,N);
ans ^= a[LCA(ql,qr)];
if(ans==0)puts("-1");
else printf("%d\n", ans-1);
}
}
}
return 0;
}