bzoj 4009 分类： bzoj templates 2015-06-05 13:56 40人阅读 评论(0) 收藏
2015-06-05 13:56
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参考题解: /article/6139147.html
我们先把所有的盘子按照权值排序 然后考虑二分
如果能覆盖一个水果的1~mid的所有盘子数>=该水果询问的k值
说明答案在[1,mid]当中，否则在[mid+1,r]中
但是为了减少计算量 我们可以每次只计算L~mid中的盘子
需要改变的就是划分到[mid+1,r]时减去[L,mid]中累积的答案
真是一道好题，扫描线+线段树+整体二分。
复杂度：O(N∗log2N+Q∗log2Q∗log2N+P∗log2P∗log2N)≈O(N∗(log2N)2)
第一次写整体二分QAQ，真的改了好久。。。
代码写了 6k+，我是大蒟蒻！
线段树：
树状数组：
我们先把所有的盘子按照权值排序 然后考虑二分
如果能覆盖一个水果的1~mid的所有盘子数>=该水果询问的k值
说明答案在[1,mid]当中，否则在[mid+1,r]中
但是为了减少计算量 我们可以每次只计算L~mid中的盘子
需要改变的就是划分到[mid+1,r]时减去[L,mid]中累积的答案
真是一道好题，扫描线+线段树+整体二分。
复杂度：O(N∗log2N+Q∗log2Q∗log2N+P∗log2P∗log2N)≈O(N∗(log2N)2)
第一次写整体二分QAQ，真的改了好久。。。
代码写了 6k+，我是大蒟蒻！
线段树：
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
const int MAXN = 4e4+5, logN = 16, MAXP = MAXN, MAXQ = MAXP;
struct Btype{int l, r, val;}; struct Query{int id, k, gain;};
struct Node {int x, y; Node(int x = 0,int y = 0):x(x),y(y){}};
struct Edge {int v, next; Edge(int v = 0,int next = 0):v(v),next(next){}};
struct Squ {int xl, xr, yl, yr; Squ(int xl = 0,int xr = 0,int yl = 0,int yr = 0):xl(xl),xr(xr),yl(yl),yr(yr){}};
struct Issue{int x, yl, yr, val; Issue(int x = 0,int yl = 0,int yr = 0,int val = 0):x(x),yl(yl),yr(yr),val(val){}};
int n, P, Q;
Btype bowl[MAXP]; Query qu[MAXQ];
Squ ss[MAXP<<1]; int sl; Node node[MAXQ];
int read()
{
int x = 0; char c = getchar();
while(!(c >= '0' && c <= '9')) c = getchar();
while(c >= '0' && c <= '9')
x = (x<<1)+(x<<3)+(c-'0'), c = getchar();
return x;
}
void write(int x)
{
static char s[12];int sl = 0;
while(x) s[++sl] = x%10 + '0',x /= 10;
if(!sl) {putchar('0');return;}
while(sl) putchar(s[sl--]);
}
namespace TreeSolve
{
int dfn[MAXN], fc[MAXN], end[MAXN], dl;
Edge edge[MAXN<<1];int el, head[MAXN];
int fa[MAXN][logN], dep[MAXN];
void NewEdge(int u, int v)
{
edge[++el] = Edge(v,head[u]), head[u] = el;
}
void Init()
{
n = read(), P = read(), Q = read();
for(int i = 1, u, v; i < n; i++)
u = read(), v = read(),
NewEdge(u,v), NewEdge(v,u);
}
void PreLca()
{
for(int j = 1; j < logN; j++)
for(int i = 1; i <= n; i++)
fa[i][j] = fa[fa[i][j-1]][j-1];
}
int GetLca(int u,int v)
{
if(dep[u] > dep[v]) std::swap(u,v);
for(int i = logN - 1; i >= 0; i--)
if(dep[fa[v][i]] >= dep[u]) v = fa[v][i];
if(u == v) return u;
for(int i = logN - 1; i >= 0; i--)
if(fa[u][i] != fa[v][i])
u = fa[u][i], v = fa[v][i];
return fa[u][0];
}
int LinkSon(int u,int v)
{
if(dep[u] > dep[v]) std::swap(u,v);
for(int i = logN - 1; i >= 0; i--)
if(dep[fa[v][i]] > dep[u]) v = fa[v][i];
return v;
}
void DFS(int a)
{
dfn[++dl] = a, fc[a] = dl;
dep[a] = dep[fa[a][0]] + 1;
for(int i = head[a], p; i; i = edge[i].next)
if((p = edge[i].v) != fa[a][0])
fa[p][0] = a, DFS(p);
end[a] = dl;
}
void GetSqu()
{
for(int i = 1, u, v, k; i <= P; i++)
{
u = read(), v = read(), k = read();
int t = GetLca(u, v);
if(t == u || t == v)
{
bowl[i].l = sl + 1;
if(u != t) std::swap(u,v);
int w = LinkSon(u,v);
if(fc[w] > 1)
ss[++sl] = Squ(1,fc[w]-1,fc[v],end[v]);
if(end[w] < n)
ss[++sl] = Squ(fc[v],end[v],end[w]+1,n);
bowl[i].r = sl;
}
else
{
bowl[i].l = sl + 1;
if(fc[u] > fc[v]) std::swap(u,v);
ss[++sl] = Squ(fc[u],end[u],fc[v],end[v]);
bowl[i].r = sl;
}
bowl[i].val = k;
}
}
void GetNode()
{
for(int i = 1, u, v, k; i <= Q; i++)
{
u = read(), v = read(), k = read();
if(fc[u] > fc[v]) std::swap(u,v);
node[i] = Node(fc[u],fc[v]);
qu[i].id = i, qu[i].k = k - 1;
}
}
void Main()
{
Init(), DFS(1), PreLca(), GetSqu(), GetNode();
}
}
namespace SegSolve
{
#define L(x) ((x)<<1)
#define R(x) (((x)<<1)|1)
bool cmpb(const Btype &a, const Btype &b){return a.val < b.val;}
bool cmpis(const Issue &a, const Issue &b){return a.x < b.x;}
bool cmpid(const Query &a, const Query &b){return a.id < b.id;}
bool cmpq(const Query &a, const Query &b){return node[a.id].x < node[b.id].x;}
int tree[MAXN<<2];
void PushDown(int x)
{
tree[L(x)] += tree[x];
tree[R(x)] += tree[x];
tree[x] = 0;
}
void Add(int l,int r,int ll,int rr,int s,int val)
{
if(l == ll && r == rr)
tree[s] += val;
else
{
PushDown(s);
int mid = (ll + rr)>>1;
if(r <= mid)
Add(l,r,ll,mid,L(s),val);
else if(l > mid)
Add(l,r,mid+1,rr,R(s),val);
else
Add(l,mid,ll,mid,L(s),val),
Add(mid+1,r,mid+1,rr,R(s),val);
}
}
int Ask(int k,int ll,int rr,int s)
{
if(ll == rr)
return tree[s];
else
{
PushDown(s);
int mid = (ll + rr)>>1;
if(k <= mid)
return Ask(k,ll,mid,L(s));
else
return Ask(k,mid+1,rr,R(s));
}
}
int segroll(int bl,int br,int ql,int qr)
{
static Issue hp[MAXP<<2]; int hl = 0;
static Query tmp[MAXQ]; int tl = 0;
for(int i = bl; i <= br; i++)
for(int j = bowl[i].l; j <= bowl[i].r; j++)
{
hp[++hl] = Issue(ss[j].xl,ss[j].yl,ss[j].yr,1);
hp[++hl] = Issue(ss[j].xr+1,ss[j].yl,ss[j].yr,-1);
}
std::sort(hp+1, hp+hl+1, cmpis);
int p = ql, ret = ql - 1;
for(int i = 1; i <= hl; i++)
{
while(p <= qr && node[qu[p].id].x < hp[i].x)
qu[p++].gain = Ask(node[qu[p].id].y,1,n,1);
Add(hp[i].yl,hp[i].yr,1,n,1,hp[i].val);
}
while(p <= qr) qu[p++].gain = 0;
for(int i = ql; i <= qr; i++)
if(qu[i].gain <= qu[i].k)
{
qu[i].k -= qu[i].gain;
tmp[++tl] = qu[i];
}
else
qu[++ret] = qu[i];
for(int i = 1; i <= tl; i++)
qu[ret+i] = tmp[i];
return ret;
}
void Solve(int pl,int pr,int ql,int qr)
{
if(pl == pr)
{
for(int i = ql; i <= qr; i++)
qu[i].gain = bowl[pl].val;
return;
}
int mid = (pl + pr)>>1;
int div = segroll(pl, mid, ql, qr);
if(ql <= div) Solve(pl, mid, ql, div);
if(div < qr) Solve(mid+1, pr, div+1, qr);
}
void Main()
{
std::sort(bowl+1,bowl+P+1,cmpb);
std::sort(qu+1, qu+Q+1, cmpq);
Solve(1,P,1,Q);
std::sort(qu+1,qu+Q+1,cmpid);
for(int i = 1; i <= Q; i++)
write(qu[i].gain), putchar('\n');
}
}
int main()
{
#ifndef ONLINE_JUDGE
freopen("bzoj4009.in","r",stdin);
freopen("bzoj4009.out","w",stdout);
#endif
TreeSolve::Main();
SegSolve::Main();
#ifndef ONLIE_JUDGE
fclose(stdin);
fclose(stdout);
#endif
return 0;
}树状数组：
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
const int MAXN = 4e4+5, logN = 16, MAXP = MAXN, MAXQ = MAXP;
struct Btype{int l, r, val;}; struct Query{int id, k, gain;};
struct Node {int x, y; Node(int x = 0,int y = 0):x(x),y(y){}};
struct Edge {int v, next; Edge(int v = 0,int next = 0):v(v),next(next){}};
struct Squ {int xl, xr, yl, yr; Squ(int xl = 0,int xr = 0,int yl = 0,int yr = 0):xl(xl),xr(xr),yl(yl),yr(yr){}};
struct Issue{int x, yl, yr, val; Issue(int x = 0,int yl = 0,int yr = 0,int val = 0):x(x),yl(yl),yr(yr),val(val){}};
int n, P, Q;
Btype bowl[MAXP]; Query qu[MAXQ];
Squ ss[MAXP<<1]; int sl; Node node[MAXQ];
int read()
{
int x = 0; char c = getchar();
while(!(c >= '0' && c <= '9')) c = getchar();
while(c >= '0' && c <= '9')
x = (x<<1)+(x<<3)+(c-'0'), c = getchar();
return x;
}
void write(int x)
{
static char s[12];int sl = 0;
while(x) s[++sl] = x%10 + '0',x /= 10;
if(!sl) {putchar('0');return;}
while(sl) putchar(s[sl--]);
}
namespace TreeSolve
{
int dfn[MAXN], fc[MAXN], end[MAXN], dl;
Edge edge[MAXN<<1];int el, head[MAXN];
int fa[MAXN][logN], dep[MAXN];
void NewEdge(int u, int v)
{
edge[++el] = Edge(v,head[u]), head[u] = el;
}
void Init()
{
n = read(), P = read(), Q = read();
for(int i = 1, u, v; i < n; i++)
u = read(), v = read(),
NewEdge(u,v), NewEdge(v,u);
}
void PreLca()
{
for(int j = 1; j < logN; j++)
for(int i = 1; i <= n; i++)
fa[i][j] = fa[fa[i][j-1]][j-1];
}
int GetLca(int u,int v)
{
if(dep[u] > dep[v]) std::swap(u,v);
for(int i = logN - 1; i >= 0; i--)
if(dep[fa[v][i]] >= dep[u]) v = fa[v][i];
if(u == v) return u;
for(int i = logN - 1; i >= 0; i--)
if(fa[u][i] != fa[v][i])
u = fa[u][i], v = fa[v][i];
return fa[u][0];
}
int LinkSon(int u,int v)
{
if(dep[u] > dep[v]) std::swap(u,v);
for(int i = logN - 1; i >= 0; i--)
if(dep[fa[v][i]] > dep[u]) v = fa[v][i];
return v;
}
void DFS(int a)
{
dfn[++dl] = a, fc[a] = dl;
dep[a] = dep[fa[a][0]] + 1;
for(int i = head[a], p; i; i = edge[i].next)
if((p = edge[i].v) != fa[a][0])
fa[p][0] = a, DFS(p);
end[a] = dl;
}
void GetSqu()
{
for(int i = 1, u, v, k; i <= P; i++)
{
u = read(), v = read(), k = read();
int t = GetLca(u, v);
if(t == u || t == v)
{
bowl[i].l = sl + 1;
if(u != t) std::swap(u,v);
int w = LinkSon(u,v);
if(fc[w] > 1)
ss[++sl] = Squ(1,fc[w]-1,fc[v],end[v]);
if(end[w] < n)
ss[++sl] = Squ(fc[v],end[v],end[w]+1,n);
bowl[i].r = sl;
}
else
{
bowl[i].l = sl + 1;
if(fc[u] > fc[v]) std::swap(u,v);
ss[++sl] = Squ(fc[u],end[u],fc[v],end[v]);
bowl[i].r = sl;
}
bowl[i].val = k;
}
}
void GetNode()
{
for(int i = 1, u, v, k; i <= Q; i++)
{
u = read(), v = read(), k = read();
if(fc[u] > fc[v]) std::swap(u,v);
node[i] = Node(fc[u],fc[v]);
qu[i].id = i, qu[i].k = k - 1;
}
}
void Main()
{
Init(), DFS(1), PreLca(), GetSqu(), GetNode();
}
}
namespace SegSolve
{
#define L(x) ((x)<<1)
#define R(x) (((x)<<1)|1)
bool cmpb(const Btype &a, const Btype &b){return a.val < b.val;}
bool cmpis(const Issue &a, const Issue &b){return a.x < b.x;}
bool cmpid(const Query &a, const Query &b){return a.id < b.id;}
bool cmpq(const Query &a, const Query &b){return node[a.id].x < node[b.id].x;}
int tree[MAXN<<2];
int lowbit(int x)
{
return x&-x;
}
void Add(int x,int c)
{
while(x <= n)
{
tree[x] += c;
x += lowbit(x);
}
}
void Change(int l, int r, int val)
{
Add(l, val), Add(r+1, -val);
}
int Ask(int x)
{
int ret = 0;
while(x > 0)
{
ret += tree[x];
x -= lowbit(x);
}
return ret;
}
int segroll(int bl,int br,int ql,int qr)
{
static Issue hp[MAXP<<2]; int hl = 0;
static Query tmp[MAXQ]; int tl = 0;
for(int i = bl; i <= br; i++)
for(int j = bowl[i].l; j <= bowl[i].r; j++)
{
hp[++hl] = Issue(ss[j].xl,ss[j].yl,ss[j].yr,1);
hp[++hl] = Issue(ss[j].xr+1,ss[j].yl,ss[j].yr,-1);
}
std::sort(hp+1, hp+hl+1, cmpis);
int p = ql, ret = ql - 1;
for(int i = 1; i <= hl; i++)
{
while(p <= qr && node[qu[p].id].x < hp[i].x)
qu[p++].gain = Ask(node[qu[p].id].y);
Change(hp[i].yl,hp[i].yr,hp[i].val);
}
while(p <= qr) qu[p++].gain = 0;
for(int i = ql; i <= qr; i++)
if(qu[i].gain <= qu[i].k)
{
qu[i].k -= qu[i].gain;
tmp[++tl] = qu[i];
}
else
qu[++ret] = qu[i];
for(int i = 1; i <= tl; i++)
qu[ret+i] = tmp[i];
return ret;
}
void Solve(int pl,int pr,int ql,int qr)
{
if(pl == pr)
{
for(int i = ql; i <= qr; i++)
qu[i].gain = bowl[pl].val;
return;
}
int mid = (pl + pr)>>1;
int div = segroll(pl, mid, ql, qr);
if(ql <= div) Solve(pl, mid, ql, div);
if(div < qr) Solve(mid+1, pr, div+1, qr);
}
void Main()
{
std::sort(bowl+1,bowl+P+1,cmpb);
std::sort(qu+1, qu+Q+1, cmpq);
Solve(1,P,1,Q);
std::sort(qu+1,qu+Q+1,cmpid);
for(int i = 1; i <= Q; i++)
write(qu[i].gain), putchar('\n');
}
}
int main()
{
#ifndef ONLINE_JUDGE
freopen("bzoj4009.in","r",stdin);
freopen("bzoj4009.out","w",stdout);
#endif
TreeSolve::Main();
SegSolve::Main();
#ifndef ONLIE_JUDGE
fclose(stdin);
fclose(stdout);
#endif
return 0;
}
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