HDU 3966 Aragorn's Story
先把树剖成链，然后用树状数组维护：
讲真，研究了好久，还是没明白 树状数组这样实现"区间更新+单点查询"的原理... 神奇...
#include <stdio.h>
#include <string.h>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <math.h>
#include <stdlib.h>
#include <time.h>
using namespace std;
const int MAXN = ; struct Edge
{
int to,next;
}edge[MAXN*]; int head[MAXN],tot;
int top[MAXN];
int fa[MAXN];
int deep[MAXN];
int num[MAXN];
int p[MAXN];
int fp[MAXN];
int son[MAXN];
int pos; void init()
{
tot = ;
memset(head,-,sizeof(head));
pos = ;//使用树状数组，编号从头1开始
memset(son,-,sizeof(son));
} void addedge(int u,int v)
{
edge[tot].to = v; edge[tot].next = head[u]; head[u] = tot++;
} void dfs1(int u,int pre,int d)
{
deep[u] = d;
fa[u] = pre;
num[u] = ;
for(int i = head[u];i != -; i = edge[i].next)
{
int v = edge[i].to;
if(v != pre)
{
dfs1(v,u,d+);
num[u] += num[v];
if(son[u] == - || num[v] > num[son[u]])
son[u] = v;
}
}
} void getpos(int u,int sp)
{
top[u] = sp;
p[u] = pos++;
fp[p[u]] = u;
if(son[u] == -) return;
getpos(son[u],sp);
for(int i = head[u];i != -;i = edge[i].next)
{
int v = edge[i].to;
if( v != son[u] && v != fa[u])
getpos(v,v);
}
} //树状数组
int lowbit(int x)
{
return x&(-x);
} int c[MAXN];
int n; int sum(int i)
{
int s = ;
while(i > )
{
s += c[i];
i -= lowbit(i);
}
return s;
} void add(int i,int val)
{
while(i <= n)
{
c[i] += val;
i += lowbit(i);
}
} void Change(int u,int v,int val)//u->v的路径上点的值改变val
{
int f1 = top[u], f2 = top[v];
int tmp = ;
while(f1 != f2)
{
if(deep[f1] < deep[f2])
{
swap(f1,f2);
swap(u,v);
}
add(p[f1],val);
add(p[u]+,-val);
u = fa[f1];
f1 = top[u];
}
if(deep[u] > deep[v]) swap(u,v);
add(p[u],val);
add(p[v]+,-val);
} int a[MAXN]; int main()
{
int M,P;
while(scanf("%d%d%d",&n,&M,&P) == )
{
int u,v;
int C1,C2,K;
char op[];
init();
for(int i = ;i <= n;i++)
{
scanf("%d",&a[i]);
}
while(M--)
{
scanf("%d%d",&u,&v);
addedge(u,v);
addedge(v,u);
}
dfs1(,,);
getpos(,);
memset(c,,sizeof(c)); for(int i = ;i <= n;i++)
{
add(p[i],a[i]);
add(p[i]+,-a[i]);
}
while(P--)
{
scanf("%s",op);
if(op[] == 'Q')
{
scanf("%d",&u);
printf("%d\n",sum(p[u]));
}
else
{
scanf("%d%d%d",&C1,&C2,&K);
if(op[] == 'D')
K = -K;
Change(C1,C2,K);
}
}
}
return ;
}
或者用线段树维护：
要注意，点权的时候，update函数里是不能 if (u == v) return;的。T_T
// HDU 3966 #include <stdio.h>
#include <string.h>
#include <iostream>
#define maxn 50010
#include <vector>
using namespace std; int a[maxn];
vector<int> edge[maxn]; int pos;
int top[maxn];
int fa[maxn];
int deep[maxn]; int num[maxn];
int p[maxn];
int fp[maxn];
int son[maxn]; //树链剖分
void dfs1(int u, int pre, int d) { // fa num deep
deep[u] = d;
fa[u] = pre;
num[u] = ;
for (int i=; i<edge[u].size(); ++i) {
int v = edge[u][i];
if (v != pre) {
dfs1(v, u, d+);
num[u] += num[v];
if (son[u] == - || num[v] > num[son[u]]) {
son[u] = v;
}
}
}
} void dfs2(int u, int sp) {
top[u] = sp;
p[u] = pos++;
fp[p[u]] = u;
if (son[u] == -) return;
dfs2(son[u], sp);
for (int i=; i<edge[u].size(); ++i) {
int v = edge[u][i];
if (v != son[u] && v != fa[u])
dfs2(v, v);
}
} //线段树
struct Node {
int l, r;
int val;
int mark;
}segTree[maxn*]; void build(int rt, int l, int r) {
segTree[rt].l = l;
segTree[rt].r = r;
segTree[rt].mark = ;
segTree[rt].val = ;
if (l == r) {
segTree[rt].val = a[fp[l] - ];
return;
}
int mid = (l + r) / ;
build(rt<<, l, mid);
build((rt<<)|, mid+, r);
} void push_down(int rt) {
if (segTree[rt].mark != ) {
segTree[rt].val += segTree[rt].mark;
if (segTree[rt].l != segTree[rt].r) {
segTree[rt<<].mark += segTree[rt].mark;
segTree[(rt<<)|].mark += segTree[rt].mark;
}
segTree[rt].mark = ;
}
} void update_seg(int rt, int l, int r, int val) { // 把线段树的[l, r] 区间的值+val
push_down(rt);
if (segTree[rt].l >= l && segTree[rt].r <= r) {
segTree[rt].mark += val;
push_down(rt);
return;
}
int mid = (segTree[rt].l + segTree[rt].r) / ;
if (r <= mid) update_seg(rt<<, l, r, val);
else if (l > mid) update_seg((rt<<)|, l, r, val);
else {
update_seg(rt<<, l, mid, val);
update_seg((rt<<)|, mid+, r, val);
}
} void update(int u, int v, int w) { // u 到 v结点的路上的值增加 val
int f1 = top[u];
int f2 = top[v];
while(f1 != f2) {
if (deep[f1] < deep[f2]) {
swap(f1, f2);
swap(u, v);
}
update_seg(, p[f1], p[u], w);
u = fa[f1], f1 = top[u];
}
// if (u == v) return;
if (deep[u] > deep[v]) swap(u, v);
update_seg(, p[u], p[v], w);
} int query_seg(int rt, int los) { //查询线段树 los处的值
push_down(rt);
if (segTree[rt].l == segTree[rt].r && segTree[rt].r == los) {
return segTree[rt].val;
}
int mid = (segTree[rt].l + segTree[rt].r) / ;
if (los <= mid) return query_seg(rt<<, los);
else if (los > mid) return query_seg((rt<<)|, los);
} int query(int u) { // 询问u点处的值
return query_seg(, p[u]);
} int n; void init() {
pos = ;
memset(son, -, sizeof(son));
for (int i=; i<=n; ++i) {
edge[i].clear();
}
} int main() {
// freopen("in.cpp", "r", stdin);
int m, pp;
while(~scanf("%d%d%d", &n, &m, &pp)) {
init();
for (int i=; i<n; ++i) {
scanf("%d", &a[i]);
}
for (int i=; i<m; ++i) {
int a, b;
scanf("%d%d", &a, &b);
edge[a].push_back(b);
edge[b].push_back(a);
} dfs1(, , );
dfs2(, );
build(, , pos-); for (int i=; i<pp; ++i) {
char op[];
int u, v, w;
scanf("%s", op);
if (op[] == 'I' || op[] == 'D') {
scanf("%d%d%d", &u, &v, &w);
if (op[] == 'D') w = -w;
update(u, v, w);
}else {
scanf("%d", &u);
int ans = query(u);
printf("%d\n", ans);
}
}
}
return ;
}