Tree chain split
For the operation of a chain composed of two nodes of the tree, a tree, we can split the chain to the tree into a plurality of sets (linear structure) of the chain, so that the tree structure is converted to a linear chain structure range operation.
- Find heavy son of each node (node that contains up to son)
- Heavy son priority order output dfs
For a split tree for the following
Find out the heavy son (red line)
Each node son recursive composition with its heavy chain (heavy leaf node has no son)
The split tree chain sequence is: \ (0,1,2,6,3,5,4 \)
To modify the weights now all points two points on the path, if two points on one strand, the sequence directly modify interval. Otherwise modified interval from the current point to the root of the chain, and then jump to the root of the chain's father recursive modify.
For example, now you want to modify \ (4-5 \) weights for all points
- 4 is a chain where the root 4, so that modifying 4-4, then skip the father 4 1
- 5 where the chain root 3, so that modification 3-5, then skip father 0 3
- 1,0 on the same chain, directly modify 1-0
So for the split interval change tree chain sequence (sequence subscript DFS) is: 7-7,5-6,1-2
BZOJ 1036
- Meaning of the questions: tree query interval maximum value, range and single-point modification
- Thinking (
Well directly copied code): First chain tree split by segment tree maintenance information and inquiry
#include<bits/stdc++.h>
#define ll long long
#define FOR(i,l,r) for(int i = l ; i <= r ;++i )
#define inf 0x3f3f3f3f
#define EPS (1e-9)
#define ALL(T) T.begin(),T.end()
#define lson(i) i<<1
#define rson(i) (i<<1|1)
using namespace std;
const int maxn =30010;
struct Edge{
int to,next;
}edge[maxn*2];
int head[maxn],tot; //前向星
int top[maxn]; // 所在重链的顶端节点
int fa[maxn]; // 父亲
int deep[maxn]; // 深度
int num[maxn]; // 子节点个数
int p[maxn]; // 在dfs序的位置
int fp[maxn]; // 位置节点号的反向映射
int son[maxn]; // 重儿子
int pos; // dfs序当前下标
// 加边
void addedge(int u,int v){
edge[tot].to = v;
edge[tot].next = head[u];
head[u] = tot++;
}
// 初始化
void init(){
memset(head,-1,sizeof(head));
memset(son,-1,sizeof(son));
tot = 0;
pos = 1;
}
//第一遍dfs 处理fa,num,deep,son
void dfs1(int u,int pre,int d){
deep[u] = d;
fa[u] = pre;
num[u] = 1;
for(int i=head[u];i!=-1;i=edge[i].next){
int v = edge[i].to;
if(v!=pre){ // 所指边不是父亲
dfs1(v,u,d+1);
num[u] += num[v]; // 更新父亲子节点数量
if(son[u] == -1 || num[v] > num[son[u]])
son[u] = v; // 更新父亲重儿子
}
}
}
// 第二遍dfs 处理 top,p,fp
void dfs2(int u,int sp){
top[u] = sp;
p[u] = pos++;
fp[p[u]] = u;
if(son[u]== -1) return ;
dfs2(son[u],sp); // 当前链继续走重儿子
for(int i=head[u];i!=-1;i=edge[i].next){
int v = edge[i].to;
if( v!= son[u] && v!=fa[u])
dfs2(v,v); // 以自己为链首的新链
}
}
// 原数组
int a[maxn];
struct node{
int l,r;
int sum,ma;
}seg[maxn*4];
// 线段树操作
void push_up(int p){
seg[p].sum = seg[lson(p)].sum + seg[rson(p)].sum;
seg[p].ma = max(seg[lson(p)].ma,seg[rson(p)].ma);
}
void build(int pp,int l,int r){
seg[pp].l = l;
seg[pp].r = r;
if(l==r){
// 这里要注意反向映射回原数组下标
seg[pp].ma = seg[pp].sum = a[fp[l]];
return;
}
int mid = (l+r)>>1;
build(lson(pp),l,mid);
build(rson(pp),mid+1,r);
push_up(pp);
}
void update(int p,int l,int r,int val){
if(seg[p].l >= l && seg[p].r <= r){
seg[p].sum = val;
seg[p].ma = val;
return;
}
int mid = (seg[p].r+seg[p].l)>>1;
if(l<=mid) update(lson(p),l,r,val);
if(r>mid) update(rson(p),l,r,val);
push_up(p);
}
int qmax(int p,int l,int r){
if(seg[p].l >= l && seg[p].r <= r){
return seg[p].ma;
}
int res = -inf;
int mid = (seg[p].r+seg[p].l)>>1;
if(l<=mid) res = max(res,qmax(lson(p),l,r));
if(r>mid) res = max(res,qmax(rson(p),l,r));
return res;
}
int qsum(int p,int l,int r){
if(seg[p].l >= l && seg[p].r <= r){
return seg[p].sum;
}
int res = 0;
int mid = (seg[p].r+seg[p].l)>>1;
if(l<=mid) res = res+qsum(lson(p),l,r);
if(r>mid) res = res+qsum(rson(p),l,r);
return res;
}
// 查询和
int fsum(int u,int v){
int res = 0;
int tu = top[u], tv = top[v];
while(tu != tv){
if(deep[tu]< deep[tv]){
swap(tu,tv);
swap(u,v);
}
res+= qsum(1,p[tu],p[u]);
u = fa[tu];
tu = top[u];
}
if(deep[u] > deep[v]) swap(u,v);
res += qsum(1,p[u],p[v]);
return res;
}
// 查询最大
int fmax(int u,int v){
int res = -1e9;
int tu = top[u], tv = top[v]; // u,v的链顶
while(tu != tv){ //不在同一条链
if(deep[tu]< deep[tv]){//先考虑较深节点
swap(tu,tv);
swap(u,v);
}
res=max(res,qmax(1,p[tu],p[u]));// 查询u节点到他的链顶
u = fa[tu]; // 跳到链顶的父节点
tu = top[u];// 更新链顶
}
if(deep[u] > deep[v]) swap(u,v);
res = max(res,qmax(1,p[u],p[v]));// 同一条链 直接区间查询
return res;
}
int n;
int main(){
scanf("%d",&n);
int fr,to;
init();
FOR(i,1,n-1){
scanf("%d%d",&fr,&to);
addedge(fr,to);
addedge(to,fr);
}
dfs1(1,0,0);
dfs2(1,1);
FOR(i,1,n) {
scanf("%d",&a[i]);
}
// FOR(i,1,n){
// printf("%d %d %d %d %d %d\n",top[i],fa[i],deep[i],num[i],p[i],son[i]);
// }cout << endl;
build(1,1,n);
// FOR(i,1,n){
// update(1,i,i,a[p[i]]);
// }
int q;
char op[10];
scanf("%d",&q);
FOR(i,1,q){
scanf("%s%d%d",op,&fr,&to);
if(op[0]=='C'){
update(1,p[fr],p[fr],to);
}else if(op[1]=='M'){
printf("%d\n",fmax(fr,to));
}else if(op[1]=='S'){
printf("%d\n",fsum(fr,to));
}
}
return 0;
}