版权声明：本人版权意识薄弱，请随意转载 https://blog.csdn.net/Ike940067893/article/details/88785599
题意
给定一棵树,设计数据结构支持以下操作
1 u v d 表示将路径 (u,v) 加d(d>=0)
2 u v 表示询问路径 (u,v) 上点权绝对值的和
分析
绝对值之和不好处理,那么我们开两棵线段树,一个存正数,一个存负数.然后对于两棵线段树,都要维护子树sz(有效节点数),sum(有效节点权值之和),lz(加法懒标记).特别的,因为负数可能会加到正数,那么修改一个区间的时候,询问一下这个区间最大的负数加上d有没有变成正数,如果有就暴力从负数线段树中删去这个节点,加入正数线段树中.又题目中满足每一次加的数都是非负的,也就是说一个数最多从负变成正一次,那么时间复杂度均摊是 的(每次删除/插入是 的).注意细节就行了…
CODE
看着我7000B的代码陷入沉思…为毛打个线段树板题都要220行+
(其实两棵树大多数函数可以直接复制)
#include <cstdio>
#include <cctype>
#include <cstring>
#include <algorithm>
using namespace std;
typedef long long LL;
char cb[1<<15],*cs=cb,*ct=cb;
#define getc() (cs==ct&&(ct=(cs=cb)+fread(cb,1,1<<15,stdin),cs==ct)?0:*cs++)
template<class T>inline void read(T &res) {
char ch; int flg = 1; for(;!isdigit(ch=getc());)if(ch=='-')flg=-flg;
for(res=ch-'0';isdigit(ch=getc());res=res*10+ch-'0'); res*=flg;
}
const int MAXN = 100005;
const LL INF = 1e16;
int n, m, cnt, tmr, w[MAXN], a[MAXN], fir[MAXN], fa[MAXN], dfn[MAXN], top[MAXN], sz[MAXN], son[MAXN], dep[MAXN];
struct edge { int to, nxt; }e[MAXN<<1];
inline void Add(int u, int v) { e[cnt] = (edge){ v, fir[u] }, fir[u] = cnt++; }
void dfs(int x, int ff) { //树剖
dep[x] = dep[fa[x]=ff] + (sz[x]=1);
for(int v, i = fir[x]; ~i; i = e[i].nxt)
if((v=e[i].to) != ff) {
dfs(v, x), sz[x] += sz[v];
if(sz[v] > sz[son[x]]) son[x] = v;
}
}
void dfs2(int x, int tp) {
top[x] = tp; w[dfn[x] = ++tmr] = a[x];
if(son[x]) dfs2(son[x], tp);
for(int v, i = fir[x]; ~i; i = e[i].nxt)
if((v=e[i].to) != fa[x] && v != son[x])
dfs2(v, v);
}
struct node { //写个结构体存最大值以及坐标
LL val; int id;
node(){}
node(LL v, int i):val(v), id(i){}
inline node operator +(const node &o)const {
if(val < o.val) return o;
else return *this;
}
};
namespace PositiveTree { //正线段树
LL sum[MAXN<<2], lz[MAXN<<2]; int sz[MAXN<<2];
inline void update(int i) {
sum[i] = sum[i<<1] + sum[i<<1|1];
sz[i] = sz[i<<1] + sz[i<<1|1];
}
inline void pushdown(int i) {
if(lz[i]) {
lz[i<<1] += lz[i]; sum[i<<1] += 1ll * sz[i<<1] * lz[i];
lz[i<<1|1] += lz[i]; sum[i<<1|1] += 1ll * sz[i<<1|1] * lz[i];
lz[i] = 0;
}
}
void build(int i, int l, int r) {
if(l == r) {
sum[i] = w[l] >= 0 ? w[l] : 0;
sz[i] = w[l] >= 0 ? 1 : 0;
return;
}
int mid = (l + r) >> 1;
build(i<<1, l, mid);
build(i<<1|1, mid+1, r);
update(i);
}
void insert(int i, int l, int r, int x, int y, int val) {
if(x == l && y == r) {
sum[i] += 1ll * sz[i] * val;
lz[i] += val;
return;
}
int mid = (l + r) >> 1;
pushdown(i);
if(y <= mid) insert(i<<1, l, mid, x, y, val);
else if(x > mid) insert(i<<1|1, mid+1, r, x, y, val);
else insert(i<<1, l, mid, x, mid, val), insert(i<<1|1, mid+1, r, mid+1, y, val);
update(i);
}
void modify(int i, int l, int r, int x, int val) {
if(l == r) {
sum[i] = val, sz[i] = 1; return;
}
int mid = (l + r) >> 1;
pushdown(i);
if(x <= mid) modify(i<<1, l, mid, x, val);
else modify(i<<1|1, mid+1, r, x, val);
update(i);
}
LL querysum(int i, int l, int r, int x, int y) {
if(x == l && y == r) return sum[i];
int mid = (l + r) >> 1;
pushdown(i);
LL res;
if(y <= mid) res = querysum(i<<1, l, mid, x, y);
else if(x > mid) res = querysum(i<<1|1, mid+1, r, x, y);
else res = querysum(i<<1, l, mid, x, mid) + querysum(i<<1|1, mid+1, r, mid+1, y);
update(i);
return res;
}
}
namespace NegativeTree { //负线段树
node mx[MAXN<<2];
LL sum[MAXN<<2], lz[MAXN<<2]; int sz[MAXN<<2];
inline void update(int i) {
sum[i] = sum[i<<1] + sum[i<<1|1];
mx[i] = mx[i<<1] + mx[i<<1|1];
sz[i] = sz[i<<1] + sz[i<<1|1];
}
inline void pushdown(int i) {
if(lz[i]) {
lz[i<<1] += lz[i]; sum[i<<1] += 1ll * sz[i<<1] * lz[i]; mx[i<<1].val += lz[i];
lz[i<<1|1] += lz[i]; sum[i<<1|1] += 1ll * sz[i<<1|1] * lz[i]; mx[i<<1|1].val += lz[i];
lz[i] = 0;
}
}
void build(int i, int l, int r) {
if(l == r) {
mx[i] = node(w[l] < 0 ? w[l] : -INF, l);
sz[i] = w[l] < 0 ? 1 : 0;
sum[i] = w[l] < 0 ? w[l] : 0; return;
}
int mid = (l + r) >> 1;
build(i<<1, l, mid);
build(i<<1|1, mid+1, r);
update(i);
}
void insert(int i, int l, int r, int x, int y, int val) {
if(x == l && y == r) {
sum[i] += 1ll * sz[i] * val;
lz[i] += val;
mx[i].val += val;
return;
}
int mid = (l + r) >> 1;
pushdown(i);
if(y <= mid) insert(i<<1, l, mid, x, y, val);
else if(x > mid) insert(i<<1|1, mid+1, r, x, y, val);
else insert(i<<1, l, mid, x, mid, val), insert(i<<1|1, mid+1, r, mid+1, y, val);
update(i);
}
void modify(int i, int l, int r, int x) {
if(l == r) {
sum[i] = sz[i] = 0, mx[i].val = -INF; return;
}
int mid = (l + r) >> 1;
pushdown(i);
if(x <= mid) modify(i<<1, l, mid, x);
else modify(i<<1|1, mid+1, r, x);
update(i);
}
node querymx(int i, int l, int r, int x, int y) {
if(x == l && y == r) return mx[i];
int mid = (l + r) >> 1;
pushdown(i);
node res;
if(y <= mid) res = querymx(i<<1, l, mid, x, y);
else if(x > mid) res = querymx(i<<1|1, mid+1, r, x, y);
else res = querymx(i<<1, l, mid, x, mid) + querymx(i<<1|1, mid+1, r, mid+1, y);
update(i);
return res;
}
LL querysum(int i, int l, int r, int x, int y) {
if(x == l && y == r) return sum[i];
int mid = (l + r) >> 1;
pushdown(i);
LL res;
if(y <= mid) res = querysum(i<<1, l, mid, x, y);
else if(x > mid) res = querysum(i<<1|1, mid+1, r, x, y);
else res = querysum(i<<1, l, mid, x, mid) + querysum(i<<1|1, mid+1, r, mid+1, y);
update(i);
return res;
}
void ADD(int l, int r, int val) {
if(r < l) return;
node res = querymx(1, 1, n, l, r);
if(res.val + val >= 0) {
modify(1, 1, n, res.id); //暴力在负线段树中删
PositiveTree::modify(1, 1, n, res.id, res.val + val); //暴力在正线段树中插入
ADD(l, res.id-1, val);
ADD(res.id+1, r, val);
}
else insert(1, 1, n, l, r, val);
}
}
inline void Plus(int u, int v, int d) {
while(top[u]!=top[v]) {
if(dep[top[u]] < dep[top[v]]) swap(u, v);
PositiveTree::insert(1, 1, n, dfn[top[u]], dfn[u], d);
NegativeTree::ADD(dfn[top[u]], dfn[u], d);
u = fa[top[u]];
}
if(dep[u] < dep[v]) swap(u, v);
PositiveTree::insert(1, 1, n, dfn[v], dfn[u], d);
NegativeTree::ADD(dfn[v], dfn[u], d);
}
inline LL Query(int u, int v) {
LL res = 0;
while(top[u]!=top[v]) {
if(dep[top[u]] < dep[top[v]]) swap(u, v);
res += - NegativeTree::querysum(1, 1, n, dfn[top[u]], dfn[u]) + PositiveTree::querysum(1, 1, n, dfn[top[u]], dfn[u]);
u = fa[top[u]];
}
if(dep[u] < dep[v]) swap(u, v);
return res - NegativeTree::querysum(1, 1, n, dfn[v], dfn[u]) + PositiveTree::querysum(1, 1, n, dfn[v], dfn[u]);
}
int main() {
memset(fir, -1, sizeof fir);
read(n), read(m);
for(int i = 1; i <= n; ++i) read(a[i]);
for(int x, y, i = 1; i < n; ++i)
read(x), read(y), Add(x, y), Add(y, x);
dfs(1, 0), dfs2(1, 1);
NegativeTree::build(1, 1, n);
PositiveTree::build(1, 1, n);
int op, u, v, d;
while(m--) {
read(op), read(u), read(v);
if(op == 1) read(d), Plus(u, v, d);
else printf("%lld\n", Query(u, v));
}
}