线段树合并
BZOJ4756 Promotion Counting
裸的线段树板子，一边dfs一边合并，然后找第比自己小的即可
BZOJ4399: 魔法少女LJJ
首先这题可坑了，数据范围\(c\)<=7
若\(c=1\)，之后一个正整数\(x\)，表示新建一个权值为\(x\)的节点，并且节点编号为\(n+1\)（当前有\(n\)个节点）。
若\(c=2\)，之后两个正整数\(a\)，\(b\)，表示在\(a\)，\(b\)之间连接一条边。
若\(c=3\)，之后两个正整数\(a\)，\(x\)，表示\(a\)联通快内原本权值小于\(x\)的节点全部变成\(x\)。
若\(c=4\)，之后两个正整数\(a\)，\(x\)，表示\(a\)联通快内原本权值大于\(x\)的节点全部变成\(x\)。
若\(c=5\)，之后两个正整数\(a\)，\(k\)，表示询问\(a\)所属于的联通块内的第\(k\)小的权值是多少。
若\(c=6\)，之后两个正整数\(a\)，\(b\)，表示询问\(a\)所属联通快内所有节点权值之积与\(b\)所属联通快内所有节点权值之积的大小， 若\(a\)所属联通快内所有节点权值之积大于b所属联通快内所有节点权值之积，输出\(1\)，否则为\(0\)。
若\(c=7\)，之后一个正整数a，表示询问a所在联通块大小
并查集套线段树裸题
1:直接新建一颗线段树即可
2:线段树合并，因为只考虑联通块，所以顺序无关
3,4:等价于删掉指定区间的点，推荐打 lazytag ,或者\(O(1)\)内存泄漏\(tree[fa].ch=0\)也行
5:权值线段树板子
6:小技巧：乘积显然会爆\(long long\)，因为只需要比较，所以取\(log\)即可
7:并查集直接维护
关于调了一下午:
一些ZZ错误
1.忘记\(pushdown\)
2.并查集\(fx = fy\)，联通块的点的根一定要用并查集的根!!!!!!!!!!!!!
3.\(pushdown\)没有清除\(lazy\)
4.\(erase\)没有判断是否节点为空,导致复杂度假掉，或者直接RE
1.学到的：删除操作可以打\(lazy\)
2.\(kth\)函数可以用循环
3.可以利用lazy和结束条件大力剪枝
4.其实没必要抄题解，可能就差一点点
5.erase函数可以记录一个删去了几个点, 省去query
6.想到高精度，可以想想能不能对数
9.其实没必要离散化，但是可以缩小常数，能离散化还是离散化了好
BZOJ4919 大根堆
这个题其实就是树上LIS
它的性质是多条链状的LIS，最后合并到一起
方法1：set平衡树维护Lis数组，网上题解好多都是这个，平衡树启发式合并，不细说
方法2：线段树合并模拟平衡树启发式合并，就是把 lower_bound(a.begin(), a.end(), key) 改成查找小于等于 \(key\) 的数字，然后直接插入即可
方法3：线段树优化dp
考虑\(O(n^2)\)的暴力dp
首先树形dp显然第一维要是点数，考虑第二维，因为对于一个点\(u\)我们要保证它的子结点都比\(u\)小,那么第二维就要考虑子树内最大值，dp实际含义就是点数
设\(f[i][j]\)为以\(i\)为子树，子树内最大值小于等于j时满足的点数
对于一个根，只有选或者不选两种情况，如果是选，就要满足\(j <= val[u]\), 如果不选
不难发现
先考虑不选择u的情况转移
\(f(i,j) = \sum_{v \in uson}f(v, j)\)
再转移选则u的情况
\(f(i,j) = max(f(i, j), f(i,val[u])+1)\)
暴力dp很容易写出来代码
$O(n^2)$
void dfs(int u, int fa){
for(int i = head[u]; i; i = e[i].nxt){
int v = e[i].to;
if(v == fa) continue;
dfs(v, u);
for(int j = 1; j <= n; ++j){
f[u][j] += f[v][j];
}
}
for(int i = n;i >= v[u]; --i){
f[u][i] = std::max(f[u][i], f[u][v[u]]+1);
}
}
然后我们考虑如何优化它,这个dp只有区间对一个值求max还有区间和相加操作
对于区间和相加，我们可以用线段树合并维护
对于求max，
由于线段树动态开点，所以lazytag很难维护，考虑懒惰标记永久化
还有一种方式，我们注意到\(f[i]\)数组是单调的，我们可以二分，寻找小于\(key\)的区间，将其统一修改成\(key\)，(像极了上面那道题)， 但复杂度是\(O(log^2)\)的
也可以线段树差分（不过我不会,以后更新）
PS：虽然后两种方法复杂度更优秀，但是第一种方法常数小，时间更优
LUOGU P4577 领导集团问题
这个题和上面基本一样，只不过严格大于子结点改成了不严格小于子结点
LUOGU P4556 雨天的尾巴
luogu 板子题
网上题解很详细了，直接线段树差分即可
LUOGU P4219 大融合
不难看出一条边经过简单路径的数量就是它他连接的两个联通块的点数乘积
用并查集维护联通块总点数和联通块根结点（一定要注意！！！一个联通块的合并顺序要一定！！！！并查集的根结点和线段树根结点要对应！！调了好久）
为了方便答案 = （总大小-一部分大小）×这一部分大小
其实就是子树大小
怎么方便的用线段树维护子树大小？
离线，dfs一遍，用dfs序建立线段树
加边操作合并线段树和并查集即可
LUOGU P2605 base 基站选址
大力dp+优化
这题重点在dp, 不在我们讨论范围内
不用线段树合并即可
LUOGU P5298 minimax
这题很妙，题解很多这里不细说
本题最有意思的技巧是在merge了两个子树，并且在merge时候update，而且打了区间lazytag
可以区间操作的原因是因为概率的线性性，区间的概率是单点的概率和
可以在merge时候区间操作也是很妙的，很难想到，由于题目中说任意两个点权值不同，不可能出现两个叶子重叠
大力分类：
1.两边结点都有值：大力递归push_up求概率
2.只有一边有值：通过公式区间更新
3.两边都没值:概率一定是0,因为已经push_down,return
而且:动态开点线段树区间操作时不能随便push_down, 否则会导致儿子过多，但是又不能直接忽略lazytag, 线段树没有儿子是说儿子和父亲的性质一样，不是说儿子节点为0
一边Merge一边维护前缀后缀和也是非常妙的
附录：AC CODES
T1
#include<cstdio>
#include<algorithm>
#include<cassert>
using std::sort;
const int maxn = 1e6+10, maxtr = 32*maxn;
int ans[maxn];
int roots[maxn];
int a[maxn], b[maxn];
int n;
struct segment_tree{
int tot;
struct node{
int ls, rs, val;
node(){}
node(int a, int b, int c):ls(a), rs(b), val(c){}
}tree[maxtr];
segment_tree(){
tot = 0;
}
int newnode(){
return ++tot;
}
void push_up(int p){
tree[p].val = tree[tree[p].ls].val+tree[tree[p].rs].val;
}
void Modify(int& p, int l, int r, int s){
p = newnode();
// printf("M%d %d %d %d\n", p, l, r, s);
if(l == r && l == s)
return ++tree[p].val, void();
int mid = (l+r)>>1;
if(s <= mid)
Modify(tree[p].ls, l, mid, s);
if(s > mid)
Modify(tree[p].rs, mid+1, r, s);
push_up(p);
}
int Query(int p, int l, int r, int s, int t){
//s结点右边有多少
if(!p) {
return 0;
}
if(s <= l && r <= t){
return tree[p].val;
}
int mid = (l+r)>>1;
int ans = 0;
if(s <= mid)
ans = Query(tree[p].ls, l, mid, s, t);
if(t > mid)
ans += Query(tree[p].rs, mid+1, r, s, t);
return ans;
}
void merge(int &rt, int p, int l, int r){
if(!p) return;
if(!rt) return rt = p, void();
if(l == r){
return tree[rt].val += tree[p].val, void();
}
int mid = (l+r)>>1;
merge(tree[rt].ls, tree[p].ls, l, mid);
merge(tree[rt].rs, tree[p].rs, mid+1, r);
push_up(rt);
}
}segt;
struct Graph{
struct edge{
int to,nxt;
edge(){}
edge(int a, int b):to(a), nxt(b){}
}e[2*maxn];
int head[maxn];
void ins(int frm, int to){
static int i = 0;
++i;
e[i] = edge(to, head[frm]);
head[frm] = i;
}
void dfs(int u, int fa){
// printf("%d %d", u, fa);
for(int i = head[u]; i; i = e[i].nxt){
int v = e[i].to;
if(v == fa) continue;
dfs(v,u);
segt.merge(roots[u], roots[v], 1, n+1);
}
ans[u] = segt.Query(roots[u], 1, n+1, b[u]+1, n+1);
// printf("ans[%d] = %d\n",u,ans[u]);
}
}G;
int main(){
scanf("%d", &n);
for(int i = 1; i <= n; ++i){
scanf("%d", a+i);
}
for(int i = 2; i <= n; ++i){
int u;
scanf("%d", &u);
G.ins(i, u);
G.ins(u, i);
}
for(int i = 1; i <= n; ++i){
b[i] = a[i];
}
std::sort(a+1, a+1+n);
int len = std::unique(a+1, a+1+n)-a-1;
for(int i = 1; i <= n; ++i){
b[i] = std::lower_bound(a+1, a+1+len, b[i])-a;
}
for(int i = 1; i <= n; ++i){
segt.Modify(roots[i], 1, n+1, b[i]);
}
G.dfs(1, 1);
for(int i = 1; i <= n; ++i){
printf("%d\n", ans[i]);
}
return 0;
}
T2
#include<cstdio>
#include<stack>
#include<algorithm>
#include<cassert>
#include<cmath>
typedef long long ll;
const int maxn = 4e5+10, maxtr = 80*maxn, maxr = 1e9+10;
int tmp[maxn];
int roots[maxn];
int m, n;
int ranger;
struct input{
int opt,x,y;
input(){}
input(int a, int b, int c):opt(a), x(b), y(c){}
}inputs[maxn];
int Query(int x){
return std::lower_bound(tmp+1, tmp+1+tmp[0], x)-tmp;
}
int DeQuery(int x){
return tmp[x];
}
struct ret_t{
int cnt;
double lg;
ret_t():cnt(0),lg(0.0){}
ret_t(double a, int b):cnt(b),lg(a){}
friend ret_t operator +(const ret_t a, const ret_t b){
return ret_t(a.lg+b.lg, a.cnt+b.cnt);
}
};
struct segment_tree{
struct node{
int cnt;
double lg;
bool is_clear;
int ls, rs;
}tree[maxtr];
int tot;
segment_tree(){
tot = 0;
}
int newnode(){
return ++tot;
}
void update(int p, double lg, ll cnt){
tree[p].lg += lg;
tree[p].cnt += cnt;
}
void clear(int p){
tree[p].is_clear = true;
tree[p].lg = 0;
tree[p].cnt = 0;
}
void push_down(int rt){
if(tree[rt].is_clear){
clear(tree[rt].ls);
clear(tree[rt].rs);
tree[rt].is_clear = false;
}
}
void push_up(int rt){
int ls = tree[rt].ls, rs = tree[rt].rs;
tree[rt].lg = tree[ls].lg+tree[rs].lg;
tree[rt].cnt = tree[ls].cnt+tree[rs].cnt;
}
void modify(int &p, int l, int r, int s, double lg, ll cnt){
if(!p) p = newnode();
if(l == r){
return update(p, lg*cnt, cnt);
}
int mid = (l+r)>>1;
push_down(p);
if(s <= mid)
modify(tree[p].ls, l, mid, s, lg, cnt);
if(s > mid)
modify(tree[p].rs, mid+1, r ,s ,lg, cnt);
push_up(p);
}
void merge(int &rt, int p, int l, int r){
if(!p || tree[p].is_clear) return;
if(!rt || tree[p].is_clear) return rt = p, void();
if(l == r)
return update(rt, tree[p].lg, tree[p].cnt);
push_down(rt);
push_down(p);
int mid = (l+r)>>1;
merge(tree[rt].ls, tree[p].ls, l, mid);
merge(tree[rt].rs, tree[p].rs, mid+1, r);
push_up(rt);
}
ret_t query(int &rt, int l, int r, int s, int t){
if(s > t || !rt)
return ret_t();
if(s <= l && r <= t){
return ret_t(tree[rt].lg, tree[rt].cnt);
}
push_down(rt);
int mid = (l+r)>>1;
ret_t ret;
if(s <= mid)
ret = ret+query(tree[rt].ls, l, mid, s, t);
if(t > mid)
ret = ret+query(tree[rt].rs, mid+1, r, s, t);
return ret;
}
int erase(int &p, int l, int r, int s, int t){
int ret = 0;
if(s > t) return 0;
if(!p || tree[p].is_clear) return 0;
//删除[s, t]区间
if(s <= l && r <= t)
return ret = tree[p].cnt, clear(p), ret;
int mid = (l+r)>>1;
push_down(p);
if(s <= mid)
ret = erase(tree[p].ls, l, mid, s, t);
if(t > mid)
ret += erase(tree[p].rs, mid+1, r ,s ,t);
push_up(p);
return ret;
}
int kth(int p, int l, int r, int k){
int lsiz = tree[tree[p].ls].cnt;
if(l == r)
return l;
push_down(p);
int mid = (l+r)>>1;
if(k <= lsiz)
return kth(tree[p].ls, l, mid, k);
else
return kth(tree[p].rs, mid+1, r, k-lsiz);
}
}segt;
struct DFU{
int fa[maxn];
int siz[maxn];
void init(int len){
for(int i = 1; i <= len; ++i){
fa[i] = i;
siz[i] = 1;
}
}
int Find(int u){
return u == fa[u]? u : (fa[u] = Find(fa[u]));
}
void merge_s(int fu, int fv){//把fv挂在fu上(已经Find)
segt.merge(roots[fu], roots[fv], 1, ranger);
siz[fu] += siz[fv];
fa[fv] = fa[fu];
}
void merge(int u, int v){
int fu = Find(u), fv = Find(v);
if(fu == fv) return;
int su = siz[fu], sv = siz[fv];
if(su >= sv){
merge_s(fu, fv);
}else{
merge_s(fv, fu);
}
}
int getsiz(int u){
return siz[Find(u)];
}
}un;
void operation_3(int x, int val){
int fx = un.Find(x), p = Query(val);
int mycnt = segt.erase(roots[fx], 1, ranger, 1, p-1);
segt.modify(roots[fx], 1, ranger, p, log(val), mycnt);
}
void operation_4(int x, int val){
int fx = un.Find(x), p = Query(val);
int mycnt = segt.erase(roots[fx], 1, ranger, p+1, ranger);
segt.modify(roots[fx], 1, ranger, p, log(val), mycnt);
}
int operation_5(int x, int k){
int fx = un.Find(x);
int res = segt.kth(roots[fx], 1, ranger, k);
return DeQuery(res);
}
int operation_6(int a, int b){
int fa = un.Find(a), fb = un.Find(b);
double x1 = segt.tree[roots[fa]].lg;
double x2 = segt.tree[roots[fb]].lg;
return x1 > x2;
}
int main(){
scanf("%d", &m);
for(int i = 1; i <= m; ++i){
int c,x,y = 0;
scanf("%d%d", &c, &x);
if(c != 1 && c !=7){
scanf("%d", &y);
}
if(c == 1){
tmp[++tmp[0]] = x;
++n;
}
if(c == 3 || c == 4){
tmp[++tmp[0]] = y;
}
inputs[i] = input(c, x, y);
}
un.init(n);
std::sort(tmp+1, tmp+1+tmp[0]);
tmp[0] = std::unique(tmp+1, tmp+1+tmp[0])-tmp-1;
ranger = tmp[0];
int ptscnt = 0;
for(int i = 1; i <= m; ++i){
int opt = inputs[i].opt;
int x = inputs[i].x, y = inputs[i].y;
switch(opt){
case 1:
++ptscnt;
segt.modify(roots[ptscnt], 1, ranger, Query(x), log(x), 1);
break;
case 2:
un.merge(x, y);
break;
case 3:{
operation_3(x, y);
break;
}
case 4:
operation_4(x, y);
break;
case 5:{
int res = operation_5(x, y);
printf("%d\n", res);
break;
}
case 6:{
int res = operation_6(x, y);
printf("%d\n", res);
break;
}
case 7:{
int ans = un.getsiz(x);
printf("%d\n", ans);
break;
}
}
}
return 0;
}
T3
#include<cstdio>
#include<algorithm>
#include<cstring>
const int maxn = 200000+10, maxtr = 32*maxn, maxm = 2*maxn;
int n;
int v[maxn], tmp[maxn];
int roots[maxn];
int len;
struct segment_tree{
struct node{
int ls, rs, val, lazy;
}tree[maxtr];
int tot;
segment_tree(){
tot = 0;
}
inline int newnode(){
return ++tot;
}
inline void update(int p, int val){
tree[p].val += val;
tree[p].lazy += val;
}
inline void push_down(int p){
int ls = tree[p].ls, rs = tree[p].rs;
if(ls)update(ls, tree[p].lazy);
if(rs)update(rs, tree[p].lazy);
tree[p].lazy = 0;
}
void merge(int &rt, int p, int l, int r, int ladd, int radd){
// printf("MERGE %d %d %d %d %d %d\n",rt, p, l, r, ladd, radd);
ladd = std::max(ladd, tree[rt].val), radd = std::max(radd, tree[p].val);
if(!rt || !p){
if(rt) update(rt, radd);//这里相当与单点merge的递归到了叶子，这里是递归到了区间，
if(p) update(p, ladd), rt = p;//加上另外的子树的影响
//不知道y这里有没有用
return;
}
push_down(rt);
push_down(p);
int mid = (l+r)>>1;
merge(tree[rt].ls, tree[p].ls, l, mid, ladd, radd);
merge(tree[rt].rs, tree[p].rs, mid+1, r, ladd, radd);
tree[rt].val = ladd+radd;
}
int query(int p, int l, int r, int s){//单点查询
if(!p) return 0;
if(l == r) return tree[p].val;
int mid = (l+r)>>1;
int ret = tree[p].val;//懒惰标记永久化
push_down(p);
if(s <= mid)
ret = std::max(ret, query(tree[p].ls, l, mid, s));
else
ret = std::max(ret, query(tree[p].rs, mid+1, r , s));
return ret;
}
void modify(int &p, int l, int r, int s, int t, int val){
//区间取最大值
if(!p) p = ++tot;
// printf("Modify %d %d %d %d %d %d\n", p, l, r, s ,t, val);
if(s <= l && r <= t){
tree[p].val = std::max(tree[p].val, val);
return;
}
int mid = (l+r)>>1;
push_down(p);
if(s <= mid)
modify(tree[p].ls, l, mid, s, t, val);
if(t > mid)
modify(tree[p].rs, mid+1, r ,s ,t ,val);
}
}segt;
struct Graph{
struct edge{
int to, nxt;
edge(){}
edge(int a, int b):to(a), nxt(b){}
}e[maxm];
int head[maxn];
inline void ins(int frm, int to){
static int i = 0;
++i;
e[i] = edge(to, head[frm]);
head[frm] = i;
}
void dfs(int u, int fa){
for(int i = head[u]; i; i = e[i].nxt){
int v = e[i].to;
if(v == fa) continue;
dfs(v, u);
segt.merge(roots[u], roots[v], 1, len, 0, 0);
}
segt.modify(roots[u], 1, len, v[u], len, segt.query(roots[u], 1, len, v[u]-1)+1);
// printf("ROOT %d = %d\n", u, roots[u]);
}
}G;
int main(){
scanf("%d", &n);
for(int i = 1; i <= n; ++i){
int x;
scanf("%d%d", v+i, &x);
if(x == 0) continue;
G.ins(i, x);
G.ins(x, i);
}
memcpy(tmp, v, sizeof v);
std::sort(tmp+1, tmp+1+n);
len = std::unique(tmp+1, tmp+1+n)-tmp-1;
for(int i = 1; i <= n; ++i)
v[i] = std::lower_bound(tmp+1, tmp+len+1, v[i])-tmp;
G.dfs(1, 1);
printf("%d\n", segt.query(roots[1], 1, len, len));
return 0;
}
T4
#include<cstdio>
#include<cassert>
#include<algorithm>
const int maxn = 1e5+10, maxm = 2*maxn, maxtr = 50*maxn, maxz = 1e5+5, INF = 0x3f3f3f3f;
struct max_node{
int p, val;
max_node(){p = 0, val = 0;}
max_node(int a, int b):p(a), val(b){}
bool operator <(const max_node& rhs)const{
if(val == rhs.val)
return p > rhs.p;
return val < rhs.val;
}
};
int roots[maxn];
struct Graph{
struct edge{
int to, nxt;
edge(){}
edge(int a, int b):to(a), nxt(b){}
}e[maxm];
int head[maxn];
int dep[maxn], siz[maxn], son[maxn], top[maxn], fas[maxn];
void ins(int u, int v){
static int i = 0;
++i;
e[i] = edge(v, head[u]);
head[u] = i;
}
void dfs1(int u){
siz[u] = 1;
dep[u] = dep[fas[u]]+1;
for(int i = head[u];i;i=e[i].nxt){
int v = e[i].to;
if(v == fas[u]) continue;
fas[v] = u;
dfs1(v);
if(!son[u] || siz[son[u]] < siz[v]){
son[u] = v;
}
siz[u] += siz[v];
}
}
void dfs2(int u, int tp){
top[u] = tp;
if(son[u])
dfs2(son[u], tp);
for(int i = head[u]; i; i = e[i].nxt){
int v = e[i].to;
if(v == fas[u] || v == son[u]) continue;
dfs2(v, v);
}
}
int getlca(int u, int v){
while(top[u] != top[v]){
if(dep[top[u]] > dep[top[v]]) u = fas[top[u]];
else v = fas[top[v]];
}
return dep[u] < dep[v] ? u : v;
}
}G;
struct segt{
struct node{
int ls, rs, val;
max_node key;
node(){}
}tree[maxtr];
int tot;
segt(){tot = 0;}
int newnode(){
return ++tot;
}
void push_up(int p){
int lch = tree[p].ls, rch = tree[p].rs;
tree[p].val = tree[lch].val+tree[rch].val;
tree[p].key = std::max(tree[lch].key, tree[rch].key);
}
void update(int p, int val, int s){
tree[p].val += val;
tree[p].key = max_node(s, tree[p].val);
//不能被负数的救济粮拐跑
}
void modify(int &p, int l, int r, int s, int val){
if(!p) p = newnode();
// printf("Modify %d in %d %d at %d val %d key %d %d \n", p, l, r, s, val, tree[p].key.p, tree[p].key.val);
if(l == r){
// printf("RET %d in %d %d at %d val %d key %d %d\n", p, l, r, s , val, tree[p].key.p ,tree[p].key.val);
return update(p, val, s);
}
int mid = (l+r)>>1;
if(s <= mid)
modify(tree[p].ls, l, mid, s, val);
else
modify(tree[p].rs, mid+1, r, s, val);
push_up(p);
// printf("Modify pushup %d val %d key %d %d\n", p,tree[p].val, tree[p].key.val, tree[p].key.p);
}
int Query(int p){
return tree[p].key.p;
}
void merge(int &rt, int p, int l, int r){
// printf("MERGE %d FROM %d IN %d %d\n", rt, p, l, r);
if(!p) return;
if(!rt) return rt = p, void();
if(l == r){
assert(l == r);
update(rt, tree[p].val, l);
return;
}
int mid = (l+r)>>1;
merge(tree[rt].ls, tree[p].ls, l, mid);
merge(tree[rt].rs, tree[p].rs, mid+1, r);
push_up(rt);
// printf("Merge pushup %d val %d key %d %d\n", p,tree[p].val, tree[p].key.val, tree[p].key.p);
}
}segt;
int n, m;
int ans[maxn];
void dfs(int u, int fa){
for(int i = G.head[u];i;i=G.e[i].nxt){
int v = G.e[i].to;
if(v == fa) continue;
dfs(v, u);
segt.merge(roots[u], roots[v], 1, maxz);
}
// printf("%d %d\n", u, roots[u]);
ans[u] = segt.Query(roots[u]);
}
int main(){
scanf("%d%d", &n, &m);
for(int i = 1; i <= n-1; ++i){
int u,v;
scanf("%d%d", &u, &v);
G.ins(u,v);
G.ins(v,u);
}
G.dfs1(1);
G.dfs2(1, 1);
/*
for(int i = 1; i <= n; ++i){
for(int j = 1 ; j <= n; ++j){
if(i == j) continue;
printf("%d %d %d\n", i, j, G.getlca(i, j));
}
}*/
for(int i = 1; i <= m; ++i){
int x,y,z;
scanf("%d%d%d", &x, &y, &z);
int mylca = G.getlca(x, y), falca = G.fas[mylca];
segt.modify(roots[x], 1, maxz, z, 1);
segt.modify(roots[y], 1, maxz, z, 1);
segt.modify(roots[mylca], 1, maxz, z, -1);
// printf("add %d %d %d %d\n", x, y, mylca, falca);
if(falca)segt.modify(roots[falca], 1, maxz, z, -1);
}
dfs(1, 0);
for(int i = 1; i <= n; ++i){
printf("%d\n", ans[i]);
}
return 0;
}
T5
#include<cstdio>
#include<algorithm>
#include<cstring>
const int maxn = 200000+10, maxtr = 32*maxn, maxm = 2*maxn;
int n;
int v[maxn], tmp[maxn];
int roots[maxn];
int len;
struct segment_tree{
struct node{
int ls, rs, val, lazy;
}tree[maxtr];
int tot;
segment_tree(){
tot = 0;
}
int newnode(){
return ++tot;
}
void update(int p, int val){
tree[p].val += val;
tree[p].lazy += val;
}
void push_down(int p){
int ls = tree[p].ls, rs = tree[p].rs;
if(ls)update(ls, tree[p].lazy);
if(rs)update(rs, tree[p].lazy);
tree[p].lazy = 0;
}
void merge(int &rt, int p, int l, int r, int ladd, int radd){
// printf("MERGE %d %d %d %d %d %d\n",rt, p, l, r, ladd, radd);
ladd = std::max(ladd, tree[rt].val), radd = std::max(radd, tree[p].val);
if(!rt || !p){
if(rt) update(rt, radd);//这里相当与单点merge的递归到了叶子，这里是递归到了区间，
if(p) update(p, ladd), rt = p;//加上另外的子树的影响
//不知道y这里有没有用
return;
}
push_down(rt);
push_down(p);
int mid = (l+r)>>1;
merge(tree[rt].ls, tree[p].ls, l, mid, ladd, radd);
merge(tree[rt].rs, tree[p].rs, mid+1, r, ladd, radd);
tree[rt].val = ladd+radd;
}
int query(int p, int l, int r, int s){//单点查询
if(!p) return 0;
if(l == r) return tree[p].val;
int mid = (l+r)>>1;
int ret = tree[p].val;//懒惰标记永久化
push_down(p);
if(s <= mid)
ret = std::max(ret, query(tree[p].ls, l, mid, s));
else
ret = std::max(ret, query(tree[p].rs, mid+1, r , s));
return ret;
}
void modify(int &p, int l, int r, int s, int t, int val){
//区间取最大值
if(!p) p = newnode();
// printf("Modify %d %d %d %d %d %d\n", p, l, r, s ,t, val);
if(s <= l && r <= t){
tree[p].val = std::max(tree[p].val, val);
return;
}
int mid = (l+r)>>1;
push_down(p);
if(s <= mid)
modify(tree[p].ls, l, mid, s, t, val);
if(t > mid)
modify(tree[p].rs, mid+1, r ,s ,t ,val);
}
}segt;
struct Graph{
struct edge{
int to, nxt;
edge(){}
edge(int a, int b):to(a), nxt(b){}
}e[maxm];
int head[maxn];
void ins(int frm, int to){
static int i = 0;
++i;
e[i] = edge(to, head[frm]);
head[frm] = i;
}
void dfs(int u, int fa){
for(int i = head[u]; i; i = e[i].nxt){
int v = e[i].to;
if(v == fa) continue;
dfs(v, u);
segt.merge(roots[u], roots[v], 1, len, 0, 0);
}
segt.modify(roots[u], 1, len, 1, v[u], segt.query(roots[u], 1, len, v[u])+1);
// printf("ROOT %d = %d\n", u, roots[u]);
}
}G;
int main(){
scanf("%d", &n);
for(int i = 1; i <= n; ++i){
scanf("%d", v+i);
}
for(int i = 2; i <= n; ++i){
int x;
scanf("%d", &x);
G.ins(i, x);
G.ins(x, i);
}
memcpy(tmp, v, sizeof v);
std::sort(tmp+1, tmp+1+n);
len = std::unique(tmp+1, tmp+1+n)-tmp-1;
for(int i = 1; i <= n; ++i)
v[i] = std::lower_bound(tmp+1, tmp+len+1, v[i])-tmp;
G.dfs(1, 1);
printf("%d\n", segt.query(roots[1], 1, len, 1));
return 0;
}
T5
#include<cstdio>
#include<algorithm>
typedef long long ll;
const int maxn = 1e5+10, maxe = 2*maxn, maxtr = 32*maxn, maxq = maxn;
int siz[maxn];
int roots[maxn];
int n, q;
struct Graph{
struct edge{
int to, nxt;
edge(){}
edge(int a, int b):to(a), nxt(b){}
}e[maxe];
int head[maxn];
void ins(int frm, int to){
static int i = 0;
++i;
e[i] = edge(to, head[frm]);
head[frm] = i;
}
int dfn[maxn], tim;
void dfs(int u){
//printf("%d", u);
siz[u] = 1;
dfn[u] = ++tim;
for(int i = head[u]; i; i = e[i].nxt){
int v = e[i].to;
if(dfn[v]) continue;
dfs(v);
siz[u] += siz[v];
}
}
void graph_prework(){
for(int i = 1; i <= n; ++i){
if(!dfn[i]){
dfs(i);
}
}
}
}G;
struct segt{
struct node{
int ls, rs, val;
node(){}
}tree[maxtr];
int tot;
segt(){
tot = 0;
}
void push_up(int rt){
tree[rt].val = tree[tree[rt].ls].val + tree[tree[rt].rs].val;
}
int newnode(){
return ++tot;
}
void update(int p, int val){
tree[p].val += val;
}
void modify(int &rt, int l, int r, int s){
if(!rt) rt = newnode();
if(l == r){
return update(rt, 1);
}
int mid = (l+r)>>1;
if(s <= mid)
modify(tree[rt].ls, l, mid, s);
else
modify(tree[rt].rs, mid+1, r, s);
push_up(rt);
}
int query(int rt, int l, int r, int s,int t){
if(!rt) return 0;
if(s <= l && r <= t){
return tree[rt].val;
}
int mid = (l+r)>>1;
int ans = 0;
if(s <= mid)
ans = query(tree[rt].ls, l, mid, s, t);
if(t > mid)
ans += query(tree[rt].rs, mid+1, r, s, t);
return ans;
}
void merge(int &rt, int p, int l, int r){
//printf("MERGE %d %d %d %d\n", rt, p, l, r);
if(!p) return;
if(!rt) return rt = p, void();
if(l == r){
return update(rt, tree[p].val);
//好像直接+1就行
}
int mid = (l+r)>>1;
merge(tree[rt].ls, tree[p].ls, l, mid);
merge(tree[rt].rs, tree[p].rs, mid+1, r);
push_up(rt);
}
}segt;
struct input_t{
int opt, x, y;
input_t(){}
input_t(int a, int b, int c):opt(a), x(b), y(c){}
}inputs[maxq];
struct DSU{
int fa[maxn];
int sizun[maxn];//联通块的大小
void init(int len){
for(int i = 1; i <= len; ++i){
fa[i] = i;
sizun[i] = 1;
}
}
int find(int x){
return x == fa[x]?x:fa[x] = find(fa[x]);
}
void merge(int x, int y){
int fx = find(x), fy = find(y);
int &sx = sizun[fx], &sy = sizun[fy];
fa[fy] = fx;
sizun[fx] += sy;
/*
if(sx >= sy){
sizun[fx] += sy;
fa[fy] = fx;
}else{
sizun[fy] += sx;
fa[fx] = fy;
}*/
}
int getsiz(int x){
return sizun[find(x)];
}
}un;
int main(){
scanf("%d%d", &n, &q);
for(int i = 1; i <= q; ++i){
int x, y;
char opt;
scanf(" %c%d%d", &opt, &x, &y);
opt = opt == 'A'?1:2;
inputs[i] = input_t(opt, x, y);
if(opt == 1)
{
G.ins(x, y);
G.ins(y, x);
}
}
G.graph_prework();
un.init(n);
/*
for(int i = 1; i <= n; ++i){
printf("%d ", siz[i]);
}
puts("");
for(int i = 1 ; i<= n; ++i){
printf("%d ", G.dfn[i]);
}
puts("");
*/
for(int i = 1; i <= n; ++i){
segt.modify(roots[i], 1, n, G.dfn[i]);
}
for(int i = 1; i <= q; ++i){
int opt = inputs[i].opt, x = inputs[i].x, y = inputs[i].y;
if(G.dfn[x] > G.dfn[y]) std::swap(x, y);
//x是y的父亲
if(opt == 1){
//printf("MERGE %d %d\n", x, y);
segt.merge(roots[un.find(x)], roots[un.find(y)], 1, n);
roots[y] = roots[x];
un.merge(x, y);
}else{
ll sizsub = segt.query(roots[un.find(y)], 1, n, G.dfn[y], G.dfn[y]+siz[y]-1), sizall = un.getsiz(x);
ll ans = sizsub*(sizall-sizsub);
//printf("l r %d %d x y %d %d sub %lld all %lld\n", G.dfn[y],G.dfn[y]+siz[y]-1, x, y, sizsub, sizall);
printf("%lld\n", ans);
}
}
return 0;
}
T6
#include<cstdio>
#include<algorithm>
typedef long long ll;
const int maxn = 1e5+10, maxe = 2*maxn, maxtr = 32*maxn, maxq = maxn;
int siz[maxn];
int roots[maxn];
int n, q;
struct Graph{
struct edge{
int to, nxt;
edge(){}
edge(int a, int b):to(a), nxt(b){}
}e[maxe];
int head[maxn];
void ins(int frm, int to){
static int i = 0;
++i;
e[i] = edge(to, head[frm]);
head[frm] = i;
}
int dfn[maxn], tim;
void dfs(int u){
//printf("%d", u);
siz[u] = 1;
dfn[u] = ++tim;
for(int i = head[u]; i; i = e[i].nxt){
int v = e[i].to;
if(dfn[v]) continue;
dfs(v);
siz[u] += siz[v];
}
}
void graph_prework(){
for(int i = 1; i <= n; ++i){
if(!dfn[i]){
dfs(i);
}
}
}
}G;
struct segt{
struct node{
int ls, rs, val;
node(){}
}tree[maxtr];
int tot;
segt(){
tot = 0;
}
void push_up(int rt){
tree[rt].val = tree[tree[rt].ls].val + tree[tree[rt].rs].val;
}
int newnode(){
return ++tot;
}
void update(int p, int val){
tree[p].val += val;
}
void modify(int &rt, int l, int r, int s){
if(!rt) rt = newnode();
if(l == r){
return update(rt, 1);
}
int mid = (l+r)>>1;
if(s <= mid)
modify(tree[rt].ls, l, mid, s);
else
modify(tree[rt].rs, mid+1, r, s);
push_up(rt);
}
int query(int rt, int l, int r, int s,int t){
if(!rt) return 0;
if(s <= l && r <= t){
return tree[rt].val;
}
int mid = (l+r)>>1;
int ans = 0;
if(s <= mid)
ans = query(tree[rt].ls, l, mid, s, t);
if(t > mid)
ans += query(tree[rt].rs, mid+1, r, s, t);
return ans;
}
void merge(int &rt, int p, int l, int r){
//printf("MERGE %d %d %d %d\n", rt, p, l, r);
if(!p) return;
if(!rt) return rt = p, void();
if(l == r){
return update(rt, tree[p].val);
//好像直接+1就行
}
int mid = (l+r)>>1;
merge(tree[rt].ls, tree[p].ls, l, mid);
merge(tree[rt].rs, tree[p].rs, mid+1, r);
push_up(rt);
}
}segt;
struct input_t{
int opt, x, y;
input_t(){}
input_t(int a, int b, int c):opt(a), x(b), y(c){}
}inputs[maxq];
struct DSU{
int fa[maxn];
int sizun[maxn];//联通块的大小
void init(int len){
for(int i = 1; i <= len; ++i){
fa[i] = i;
sizun[i] = 1;
}
}
int find(int x){
return x == fa[x]?x:fa[x] = find(fa[x]);
}
void merge(int x, int y){
int fx = find(x), fy = find(y);
int &sx = sizun[fx], &sy = sizun[fy];
fa[fy] = fx;
sizun[fx] += sy;
/*
if(sx >= sy){
sizun[fx] += sy;
fa[fy] = fx;
}else{
sizun[fy] += sx;
fa[fx] = fy;
}*/
}
int getsiz(int x){
return sizun[find(x)];
}
}un;
int main(){
scanf("%d%d", &n, &q);
for(int i = 1; i <= q; ++i){
int x, y;
char opt;
scanf(" %c%d%d", &opt, &x, &y);
opt = opt == 'A'?1:2;
inputs[i] = input_t(opt, x, y);
if(opt == 1)
{
G.ins(x, y);
G.ins(y, x);
}
}
G.graph_prework();
un.init(n);
/*
for(int i = 1; i <= n; ++i){
printf("%d ", siz[i]);
}
puts("");
for(int i = 1 ; i<= n; ++i){
printf("%d ", G.dfn[i]);
}
puts("");
*/
for(int i = 1; i <= n; ++i){
segt.modify(roots[i], 1, n, G.dfn[i]);
}
for(int i = 1; i <= q; ++i){
int opt = inputs[i].opt, x = inputs[i].x, y = inputs[i].y;
if(G.dfn[x] > G.dfn[y]) std::swap(x, y);
//x是y的父亲
if(opt == 1){
//printf("MERGE %d %d\n", x, y);
segt.merge(roots[un.find(x)], roots[un.find(y)], 1, n);
roots[y] = roots[x];
un.merge(x, y);
}else{
ll sizsub = segt.query(roots[un.find(y)], 1, n, G.dfn[y], G.dfn[y]+siz[y]-1), sizall = un.getsiz(x);
ll ans = sizsub*(sizall-sizsub);
//printf("l r %d %d x y %d %d sub %lld all %lld\n", G.dfn[y],G.dfn[y]+siz[y]-1, x, y, sizsub, sizall);
printf("%lld\n", ans);
}
}
for(int i = 5; i <= 9; ++i){
//printf("SIZ = %d\n", segt.query(roots[9], 1, n, i, i));
}
return 0;
}
