题目：传送门
给你一段长为n序列，m次询问，询问[L,R]区间内小于等于H的数有多少个。
数据范围，n，m<=1e5
结果：
树状数组: 249ms
主席树: 218ms
归并树: 374ms
分块:C++TLE / G++AC –(不过C++把块的大小扩大3倍也能过)
归并树: TLE
线段树: WA (求大佬找下bug，我真不知道为什么会wa，感觉对如闪电
(TLE和WA一定是我太垃圾，写残了，orz)
代码如下：
线段树：WA
#include<bits/stdc++.h>
#define lson rt<<1
#define rson rt<<1|1
#define lsonl rt<<1,l,m
#define rsonr rt<<1|1,m+1,r
using namespace std;
typedef long long LL;
const int N = 1e5+5;
int n,m,Ans[N];
struct lp{
int l,r,sum;
}cw[N<<2];
struct lh{
int val,id,l,r;
bool operator <(const lh a)const{
return val<a.val;
}
}ar[N],br[N];
void build(int rt,int l,int r){
cw[rt].l=l;cw[rt].r=r;cw[rt].sum=0;
int mid=(l+r)>>1;
if(l==r)return;
build(lson,l,mid);
build(rson,mid+1,r);
}
void update(int rt,int x){
cw[rt].sum++;
if(cw[rt].l==cw[rt].r){
return;
}
int m=(cw[rt].l+cw[rt].r)/2;
if(x<=m)update(lson,x);
else update(rson,x);
}
int query(int rt,int l,int r){
if(l=cw[rt].l&&cw[rt].r==r){
return cw[rt].sum;
}
int m=(cw[rt].l+cw[rt].r)>>1;
if(l>m) return query(rson,l,r);
else if(r<=m) return query(lson,l,r);
else{
return query(lsonl)+query(rsonr);
}
}
int main(){
int tim;
int T=0;
scanf("%d",&tim);
while(tim--){
scanf("%d%d",&n,&m);
for(int i=0;i<n;++i){
scanf("%d",&ar[i].val);
ar[i].id=i+1;
}
for(int i=0;i<m;++i){
scanf("%d%d%d",&br[i].l,&br[i].r,&br[i].val);
br[i].id=i;
}
sort(ar,ar+n);
sort(br,br+m);
build(1,1,n);
printf("Case %d:\n",++T );
for(int i=0,j=0;i<m;++i){
while(j<n&&ar[j].val<=br[i].val){
update(1,ar[j].id);
j++;
}
Ans[br[i].id]=query(1,br[i].l+1,br[i].r+1);
}
for(int i=0;i<m;++i){
printf("%d\n",Ans[i] );
}
}
return 0;
}分块：AC。。。
#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const int N = 1e6+5;
int n,m;
int block,num,belong[N],ls[N],rs[N];
int ar[N];
vector<int>bk[N];
void build(){
block=3*sqrt(n*1.0);
num=n/block;if(n%block)num++;
for(int i=1;i<=n;++i){
belong[i]=(i-1)/block+1;
}
for(int i=1;i<=num;++i){
ls[i]=(i-1)*block+1;
rs[i]=i*block;
}
rs[num]=n;
for(int i=0;i<=num;++i)bk[i].clear();
for(int i=1;i<=n;++i){
bk[belong[i]].push_back(ar[i]);
}
for(int i=1;i<=num;++i){
sort(bk[i].begin(),bk[i].end());
}
}
void get(int u,int v,int w){
int cnt=0;
if(belong[u]==belong[v]){
for(int i=u;i<=v;++i){
if(ar[i]<=w)cnt++;
}
printf("%d\n",cnt );
return;
}
for(int i=belong[u]+1;i<belong[v];++i){
int p=upper_bound(bk[i].begin(),bk[i].end(),w)-bk[i].begin();
cnt+=(p<0?0:p);
}
if(u==ls[belong[u]]){
int i=belong[u];
int p=upper_bound(bk[i].begin(),bk[i].end(),w)-bk[i].begin();
cnt+=(p<0?0:p);
}else{
for(int i=u;i<=rs[belong[u]];++i){
if(ar[i]<=w)cnt++;
}
}
if(v==rs[belong[v]]){
int i=belong[v];
int p=upper_bound(bk[i].begin(),bk[i].end(),w)-bk[i].begin();
cnt+=(p<0?0:p);
}else{
for(int i=ls[belong[v]];i<=v;++i){
if(ar[i]<=w)cnt++;
}
}
printf("%d\n",cnt );
}
int main(){
int tim;scanf("%d",&tim);
int T=0;
while(tim--){
scanf("%d%d",&n,&m);
for(int i=1;i<=n;++i){
scanf("%d",&ar[i]);
}
build();
printf("Case %d:\n",++T );
for(int i=0,u,v,w;i<m;++i){
scanf("%d%d%d",&u,&v,&w);
get(u+1,v+1,w);
}
}
return 0;
}归并树：TLE
#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const int N = 1e5+5;
int n,m;
int cw[20][N];
int ar[N];
void build(int dep,int l,int r){
if(l==r){
cw[dep][l]=ar[l];
return;
}
int mid=(l+r)>>1;
build(dep+1,l,mid);
build(dep+1,mid+1,r);
int i=l,j=mid+1,k=l;
while(i<=mid||j<=r){
if(j>r||(i<=mid&&cw[dep+1][i]<=cw[dep+1][j])){
cw[dep][k++]=cw[dep+1][i++];
}else{
cw[dep][k++]=cw[dep+1][j++];
}
}
}
int query(int dep,int l,int r,int L,int R,int key){
if(L>r||R<l)return 0;
if(L<=l&&r<=R){
return lower_bound(&cw[dep][l],&cw[dep][r]+1,key)-&cw[dep][l];
}
int mid=(l+r)>>1;
return query(dep+1,l,mid,L,R,key)+query(dep+1,mid+1,r,L,R,key);
}
int solve(int n,int L,int R,int k){
int l=1,r=n,ans=1,mid;
while(l<=r){
mid=(l+r)>>1;
int cnt=query(0,1,n,L,R,cw[0][mid]);
if(cnt>k){
r=mid-1;
ans=mid-1;
}else{
ans=mid;
l=mid+1;
}
}
return cw[0][ans];
}
int main(){
int tim,T=0;
scanf("%d",&tim);
while(tim--){
scanf("%d%d",&n,&m);
for(int i=1;i<=n;++i){
scanf("%d",&ar[i]);
}
build(0,1,n);
printf("Case %d:\n",++T );
while(m--){
int x,y,z;
scanf("%d%d%d",&x,&y,&z);
x++;y++;
int l=1,r=y-x+1,mid,ans=0,tmp;
while(l<=r){
mid=(l+r)>>1;
tmp=solve(n,x,y,mid-1);
if(tmp<=z){
l=mid+1;
ans=mid;
}else{
r=mid-1;
ans=mid-1;
}
}
printf("%d\n",ans );
}
}
return 0;
}树状数组: AC
#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
typedef unsigned long long uLL;
const int N = 1e5+5;
int n,m;
int ar[N],sum[N];
inline int lowbit(int x){
return x&(-x);
}
inline void add(int x,int d){
while(x<=n){
ar[x]+=d;
x+=lowbit(x);
}
}
inline int query(int x){
int ans=0;
while(x){
ans+=ar[x];
x-=lowbit(x);
}
return ans;
}
struct lh{
int val,id;
}br[N];
bool cmp1(lh &a,lh &b){
if(a.val!=b.val)return a.val<b.val;
return a.id<b.id;
}
struct lp{
int l,r,id,val;
}cw[N];
bool cmp2(lp &a,lp &b){
if(a.val!=b.val)return a.val<b.val;
return a.id<b.id;
}
int main(){
int tim;scanf("%d",&tim);
int T=0;
while(tim--){
scanf("%d%d",&n,&m);
for(int i=0;i<n;++i){
scanf("%d",&br[i].val);
br[i].id=i+1;
}
for(int i=0;i<m;++i){
scanf("%d%d%d",&cw[i].l,&cw[i].r,&cw[i].val);
cw[i].l++;cw[i].r++;
cw[i].id=i+1;
}
sort(br,br+n,cmp1);
sort(cw,cw+m,cmp2);
memset(ar,0,sizeof(ar));
for(int i=0,j=0;i<m;++i){
while(j<n&&br[j].val<=cw[i].val){
add(br[j].id,1);
j++;
}
sum[cw[i].id]=query(cw[i].r)-query(cw[i].l-1);
}
printf("Case %d:\n",++T );
for(int i=1;i<=m;++i){
printf("%d\n",sum[i] );
}
}
return 0;
}主席树: AC
#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const int N = 1e6+5;
int n,m;
struct lp{
int l,r,sum;
}cw[N*20];
int rak[N],ar[N],br[N],tot;
void update(int l,int r,int last,int &cur,int x){
cw[++tot]=cw[last];
cw[tot].sum++;
cur=tot;
if(l==r)return;
int mid=(l+r)>>1;
if(x<=mid)update(l,mid,cw[last].l,cw[cur].l,x);
else update(mid+1,r,cw[last].r,cw[cur].r,x);
}
int query(int l,int r,int last,int cur,int k){
if(l==r)return cw[cur].sum-cw[last].sum;
int mid=(l+r)>>1;
if(k<=mid)return query(l,mid,cw[last].l,cw[cur].l,k);
else {
int ans=query(mid+1,r,cw[last].r,cw[cur].r,k);
ans+=cw[cw[cur].l].sum-cw[cw[last].l].sum;
return ans;
}
}
int main(){
int tim;scanf("%d",&tim);
int T=0;
while(tim--){
scanf("%d%d",&n,&m);
for(int i=1;i<=n;++i){
scanf("%d",&ar[i]);
br[i]=ar[i];
}
sort(br+1,br+1+n);
int k=1;
for(int i=2;i<=n;++i){
if(br[i]!=br[i-1]){
br[++k]=br[i];
}
}
tot=0;cw[0].l=cw[0].r=cw[0].sum=0;
memset(rak,0,sizeof(rak));
for(int i=1;i<=n;++i){
int p=lower_bound(br+1,br+1+k,ar[i])-br;
update(1,k,rak[i-1],rak[i],p);
}
printf("Case %d:\n",++T );
for(int i=0,u,v,w;i<m;++i){
scanf("%d%d%d",&u,&v,&w);
u++;v++;
int p=upper_bound(br+1,br+1+k,w)-br-1;
if(p)printf("%d\n",query(1,k,rak[u-1],rak[v],p) );
else printf("0\n");
}
}
return 0;
}划分树：AC
#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const int N = 1e5+5;
int n,m,sor[N];
struct lp{
int cnt[N];
int num[N];
}cw[22];
void build(int l,int r,int d){
if(l==r)return;
cw[d].num[0]=cw[d].cnt[0]=0;
int same=0,mid=(l+r)>>1;
for(int i=mid;i>=l;--i){
if(sor[mid]==sor[i])same++;
else break;
}
int lpos=l,rpos=mid+1,cnt=0;
for(int i=l;i<=r;++i){
if(cw[d].num[i]<sor[mid]){
cw[d+1].num[lpos++]=cw[d].num[i];
cnt++;
}else if(cw[d].num[i]==sor[mid]&&same){
same--;cnt++;
cw[d+1].num[lpos++]=cw[d].num[i];
}else{
cw[d+1].num[rpos++]=cw[d].num[i];
}
cw[d].cnt[i]=cnt;
}
build(l,mid,d+1);
build(mid+1,r,d+1);
}
int query(int l,int r,int L,int R,int k,int d){
if(l==r)return cw[d].num[l];
int mid=(l+r)>>1,newl,newr,left=0,sum_in_left;
if(l==L){
sum_in_left=cw[d].cnt[R];
}else{
left=cw[d].cnt[L-1];
sum_in_left=cw[d].cnt[R]-left;
}
if(k<=sum_in_left){
newl=l+left;
newr=newl+sum_in_left-1;
return query(l,mid,newl,newr,k,d+1);
}else{
newl=mid+L-l+1-left;
newr=newl+R-L+1-sum_in_left-1;
return query(mid+1,r,newl,newr,k-sum_in_left,d+1);
}
}
int main(){
int tim;scanf("%d",&tim);
int T=0;
while(tim--){
scanf("%d%d",&n,&m);
for(int i=1;i<=n;++i){
scanf("%d",&sor[i]);
cw[0].num[i]=sor[i];
}
sort(sor+1,sor+1+n);
build(1,n,0);
printf("Case %d:\n",++T );
for(int i=0,u,v,w;i<m;++i){
scanf("%d%d%d",&u,&v,&w);
u++;v++;
int l=1,r=v-u+1,mid,ans=0,tmp;
while(l<=r){
mid=(l+r)>>1;
tmp=query(1,n,u,v,mid,0);
if(tmp<=w){
l=mid+1;
ans=mid;
}else{
r=mid-1;
ans=mid-1;
}
}
printf("%d\n",ans );
}
}
return 0;
}