题目链接
树链剖分学习笔记,可以看这里
这道题还真挺好的,以前不会做,现在想了发现,学过树链剖分之后,剩下的部分就是处理去反那块比较的不容易些了,但是想了一下午,现在还是给我敲出来了,我们主要难处理的就是关于求反,那么怎么处理求反?
一开始读题的时候,我还在想,是不是求反是与此数的最大2次幂系数开始,后来推了测试样例,发现,是直接对64为比特位都求反,那么我们似乎可以推一个公式了,因为2^64-1就是满unsigned long long,而且之前用过无符号类型就是在哈希里,它会在满了之后自动向前重新开始,所以相当于是在自动取模,那么,怎么处理去反呢?
去反可以看作111111......11111-X,那么,换句话说,不就是相当于想乘以“-1”在加上unsigned long long的满值吗?那么建树不就是完成了吗?
#include <iostream>
#include <cstdio>
#include <cmath>
#include <string>
#include <cstring>
#include <algorithm>
#include <limits>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#define lowbit(x) ( x&(-x) )
#define pi 3.141592653589793
#define e 2.718281828459045
using namespace std;
typedef unsigned long long ull;
typedef long long ll;
const int maxN = 1e5+5;
const ull INF=(ull)0-(ull)1;
int N, Q, cnt, head[maxN], root[maxN], depth[maxN], size[maxN], W_son[maxN], top[maxN], id[maxN], num;
ull tree[maxN<<2], lazy[maxN<<2], mult[maxN<<2];
struct Eddge
{
int nex, to;
Eddge(int a=-1, int b=0):nex(a), to(b) {}
}edge[maxN<<1];
void addEddge(int u, int v)
{
edge[cnt] = Eddge(head[u], v);
head[u] = cnt++;
}
void dfs1(int u, int fa, int deep)
{
root[u] = fa;
depth[u] = deep;
size[u] = 1;
int maxxSon = -1;
for(int i=head[u]; i!=-1; i=edge[i].nex)
{
int v = edge[i].to;
if(v == fa) continue;
dfs1(v, u, deep+1);
size[u] += size[v];
if(maxxSon < size[v])
{
maxxSon = size[v];
W_son[u] = v;
}
}
}
void dfs2(int x, int topf)
{
top[x] = topf;
id[x] = ++num;
if(!W_son[x]) return;
dfs2(W_son[x], topf);
for(int i=head[x]; i!=-1; i=edge[i].nex)
{
int y = edge[i].to;
if(y==W_son[x] || y==root[x]) continue;
dfs2(y, y);
}
}
void buildTree(int rt, int l, int r)
{
lazy[rt] = 0; mult[rt] = 1;
if(l == r)
{
tree[rt] = 0;
return;
}
int mid = (l + r)>>1;
buildTree(rt<<1, l, mid);
buildTree(rt<<1|1, mid+1, r);
tree[rt] = 0;
}
void pushup(int rt)
{
tree[rt] = tree[rt<<1] + tree[rt<<1|1];
}
void pushdown(int rt, int l, int r)
{
if(mult[rt]!=1)
{
mult[rt<<1]*=mult[rt]; lazy[rt<<1]*=mult[rt];
mult[rt<<1|1]*=mult[rt]; lazy[rt<<1|1]*=mult[rt];
tree[rt<<1]*=mult[rt];
tree[rt<<1|1]*=mult[rt];
mult[rt] = 1;
}
if(lazy[rt])
{
lazy[rt<<1] += lazy[rt];
lazy[rt<<1|1] += lazy[rt];
int mid = (l + r)>>1;
tree[rt<<1] += lazy[rt]*(mid - l + 1);
tree[rt<<1|1] += lazy[rt]*(r - mid);
lazy[rt] = 0;
}
}
void update_add(int rt, int l, int r, int ql, int qr, ull val)
{
if(ql<=l && qr>=r)
{
lazy[rt] += val;
tree[rt] += val*(r - l + 1);
return;
}
int mid = (l + r)>>1;
pushdown(rt, l, r);
if(ql>mid) update_add(rt<<1|1, mid+1, r, ql, qr, val);
else if(qr<=mid) update_add(rt<<1, l, mid, ql, qr, val);
else
{
update_add(rt<<1, l, mid, ql, qr, val);
update_add(rt<<1|1, mid+1, r, ql, qr, val);
}
pushup(rt);
}
void update_multi(int rt, int l, int r, int ql, int qr, ull val)
{
if(ql<=l && qr>=r)
{
lazy[rt] *= val;
mult[rt] *= val;
tree[rt] *= val;
return;
}
pushdown(rt, l, r);
int mid = (l + r)>>1;
if(ql>mid) update_multi(rt<<1|1, mid+1, r, ql, qr, val);
else if(qr<=mid) update_multi(rt<<1, l, mid, ql, qr, val);
else
{
update_multi(rt<<1, l, mid, ql, qr, val);
update_multi(rt<<1|1, mid+1, r, ql, qr, val);
}
pushup(rt);
}
void update_Range_add(int x, int y, ull val)
{
while(top[x] != top[y])
{
if(depth[top[x]] < depth[top[y]]) swap(x, y);
update_add(1, 1, N, id[top[x]], id[x], val);
x = root[top[x]];
}
if(depth[x] > depth[y]) swap(x, y);
update_add(1, 1, N, id[x], id[y], val);
}
void update_Range_Multi(int x, int y, ull val)
{
while(top[x] != top[y])
{
if(depth[top[x]] < depth[top[y]]) swap(x, y);
update_multi(1, 1, N, id[top[x]], id[x], val);
x = root[top[x]];
}
if(depth[x] > depth[y]) swap(x, y);
update_multi(1, 1, N, id[x], id[y], val);
}
ull query(int rt, int l, int r, int ql, int qr)
{
if(ql<=l && qr>=r) return tree[rt];
pushdown(rt, l, r);
int mid = (l + r)>>1;
if(ql>mid) return query(rt<<1|1, mid+1, r, ql, qr);
else if(qr<=mid) return query(rt<<1, l, mid, ql, qr);
else
{
ull ans = query(rt<<1, l, mid, ql, qr);
ans += query(rt<<1|1, mid+1, r, ql, qr);
return ans;
}
}
ull query_Range(int x, int y)
{
ull ans = 0;
while(top[x] != top[y])
{
if(depth[top[x]] < depth[top[y]]) swap(x, y);
ans += query(1, 1, N, id[top[x]], id[x]);
x = root[top[x]];
}
if(depth[x] > depth[y]) swap(x, y);
ans += query(1, 1, N, id[x], id[y]);
return ans;
}
void init()
{
cnt = num = 0;
memset(head, -1, sizeof(head));
memset(W_son, 0, sizeof(W_son));
}
int main()
{
while(scanf("%d", &N)!=EOF)
{
init();
for(int i=2; i<=N; i++)
{
int e1; scanf("%d", &e1);
addEddge(i, e1);
addEddge(e1, i);
}
dfs1(1, 1, 0);
dfs2(1, 1);
buildTree(1, 1, N);
scanf("%d", &Q);
while(Q--)
{
int op, u, v;
ull x;
scanf("%d", &op);
if(op == 1)
{
scanf("%d%d%llu", &u, &v, &x);
update_Range_Multi(u, v, x);
}
else if(op == 2)
{
scanf("%d%d%llu", &u, &v, &x);
update_Range_add(u, v, x);
}
else if(op == 3)
{
scanf("%d%d", &u, &v);
update_Range_Multi(u, v, -1);
update_Range_add(u, v, INF);
}
else
{
scanf("%d%d", &u, &v);
printf("%llu\n", query_Range(u, v));
}
}
}
return 0;
}