hdu4417 Super Mario (主席树+二分)

题目：http://acm.hdu.edu.cn/showproblem.php?pid=4417

题意：求区间内不大于x的数有多少个。

分析：二分枚举答案，用主席树查询即可。复杂度q*log(n)*log(n)。

代码：

#include <iostream>
#include <cstdio>
#include <algorithm>
using namespace std;

typedef long long LL;
typedef unsigned long long ULL;
const LL INF = 1E9+9;

const int maxn = 1e5+6;
const int LOG = 20;

struct node
{
int l,r;
int sum;
}Node[maxn*LOG];
int root[maxn],node_cnt;
void build(int l,int r,int &rt)
{
rt=node_cnt++;
Node[rt].sum=0;
if(l==r)
return ;
int m=(l+r)>>1;
build(l,m,Node[rt].l);
build(m+1,r,Node[rt].r);
}
void update(int v,int l,int r,int &rt,int pre)
{
rt=node_cnt++;
Node[rt]=Node[pre];
Node[rt].sum++;
if(l==r)
return ;
int m=(l+r)>>1;
if(v<=m)
update(v,l,m,Node[rt].l,Node[pre].l);
else
update(v,m+1,r,Node[rt].r,Node[pre].r);
}
int query(int k,int l,int r,int r1,int r2)
{
if(l==r)
return r;
int lnum=Node[Node[r2].l].sum-Node[Node[r1].l].sum;
int m=(l+r)>>1;
if(k<=lnum)
return query(k,l,m,Node[r1].l,Node[r2].l);
else
return query(k-lnum,m+1,r,Node[r1].r,Node[r2].r);
}

int a[maxn],numbers[maxn],num_cnt;

void solve(int L,int R,int X)
{
int c=Node[root[R]].sum-Node[root[L-1]].sum;
int ans=0,down=1,up=c,mid;
while(down<=up)
{
mid=(down+up)>>1;
int q= query(mid,1,num_cnt,root[L-1],root[R]);
if(numbers[q]<=X)
{
down=mid+1;
if(mid>ans)
ans=mid;
}
else
up=mid-1;
}
printf("%d\n",ans);
}

int main()
{
int nCase;
scanf("%d",&nCase);
for(int T=1;T<=nCase;T++)
{
int n,m;
scanf("%d%d",&n,&m);
for(int i=1;i<=n;i++)
{
scanf("%d",&a[i]);
numbers[i]=a[i];
}
sort(numbers+1,numbers+1+n);
num_cnt=unique(numbers+1,numbers+n+1)-numbers-1;
node_cnt=0;
build(1,num_cnt,root[0]);
for(int i=1;i<=n;i++)
{
int pos=lower_bound(numbers+1,numbers+num_cnt+1,a[i])-numbers;
update(pos,1,num_cnt,root[i],root[i-1]);
}
printf("Case %d:\n",T);
while(m--)
{
int L,R,X;
scanf("%d%d%d",&L,&R,&X);
solve(L+1,R+1,X);
}
}
return 0;
}