题意：查询区间中位数
思路：模板题，相当于区间第K大的数，主席树可以水过，但划分树是正解。但还没搞明白划分树，先上模板
#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <string>
#include <vector>
#include <algorithm>
#include <set>
#define repu(i,a,b) for(int i=a;i<b;i++)
using namespace std;
#define N 1000010
#define ll long long
#define _cle(m, a) memset(m, a, sizeof(m))
const int MAXN = ;
const int M = MAXN * ;
int n,q,m,tot;
int a[MAXN], t[MAXN];
int T[MAXN], lson[M], rson[M], c[M];
void Init_Hash()
{
for(int i = ; i <= n; i++)
t[i] = a[i];
sort(t+,t++n);
m = unique(t+,t++n) -t-;
}
int build(int l, int r)
{
int root = tot++;
c[root] = ;
if(l != r)
{
int mid = (l+r)>>;
lson[root] = build(l,mid);
rson[root] = build(mid+,r);
}
return root;
}
int Hash(int x)
{
return lower_bound(t+,t++m,x) - t;
}
int update(int root, int pos, int val)
{
int newroot = tot++, tmp = newroot;
c[newroot] = c[root] + val;
int l = , r = m;
while(l < r)
{
int mid = (l+r)>>;
if(pos <= mid)
{
lson[newroot] = tot++;
rson[newroot] = rson[root];
newroot = lson[newroot];
root = lson[root];
r = mid;
}
else
{
rson[newroot] = tot++;
lson[newroot] = lson[root];
newroot = rson[newroot];
root = rson[root];
l = mid+;
}
c[newroot] = c[root] + val;
}
return tmp;
}
int query(int left_root, int right_root, int k)
{
int l = , r = m;
while( l < r)
{
int mid = (l+r)>>;
if(c[lson[left_root]] -c[lson[right_root]] >= k )
{
r = mid;
left_root = lson[left_root];
right_root = lson[right_root];
}
else
{
l = mid + ;
k -= c[lson[left_root]] - c[lson[right_root]];
left_root = rson[left_root];
right_root = rson[right_root];
}
}
return l;
}
int main()
{
//freopen("in.txt","r", stdin);
//freopen("out.txt","w", stdout);
int kase = ;
while(scanf("%d",&n) == )
{
tot = ;
for(int i = ; i <= n; i++)
scanf("%d",&a[i]);
Init_Hash();
T[n+] = build(,m);
for(int i = n; i ; i--)
{
int pos = Hash(a[i]);
T[i] = update(T[i+],pos,);
}
printf("Case %d:\n",kase++);
scanf("%d",&q);
while(q--)
{
int l,r,k;
scanf("%d%d",&l,&r);
k = (r-l)/+;
printf("%d\n",t[query(T[l],T[r+],k)]);
}
}
return ;
}
主席树
先上KB模板
//划分树
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int MAXN=;
int tree[][MAXN];//表示每层每个位置的值
int sorted[MAXN];//已经排序好的数
int toleft[][MAXN];//toleft[p][i]表示第i层从1到i有数分入左边
void build(int l,int r,int dep){
if(l==r)return;
int mid=(l+r)>>;
int same=mid-l+;//表示等于中间值而且被分入左边的个数
for(int i=l;i<=r;i++)//注意是l,不是one
if(tree[dep][i]<sorted[mid]) same--;
int lpos=l;
int rpos=mid+;
for(int i=l;i<=r;i++){
if(tree[dep][i]<sorted[mid]) tree[dep+][lpos++]=tree[dep][i];
else if(tree[dep][i]==sorted[mid]&&same>){
tree[dep+][lpos++]=tree[dep][i];
same--;
}
else tree[dep+][rpos++]=tree[dep][i];
toleft[dep][i]=toleft[dep][l-]+lpos-l;
}
build(l,mid,dep+);
build(mid+,r,dep+);
}
//查询区间第k大的数,[L,R]是大区间,[l,r]是要查询的小区间
int query(int L,int R,int l,int r,int dep,int k){
if(l==r)return tree[dep][l];
int mid=(L+R)>>;
int cnt=toleft[dep][r]-toleft[dep][l-];
if(cnt>=k){
int newl=L+toleft[dep][l-]-toleft[dep][L-];int newr=newl+cnt-;
return query(L,mid,newl,newr,dep+,k);
}
else{
int newr=r+toleft[dep][R]-toleft[dep][r],newl=newr-(r-l-cnt);
return query(mid+,R,newl,newr,dep+,k-cnt);
}
}
int main(){
int n,m,t=;
while(~scanf("%d",&n)){
memset(tree,,sizeof(tree));
for(int i=;i<=n;i++){
scanf("%d",&tree[][i]);
sorted[i]=tree[][i];
}
sort(sorted+,sorted+n+);
build(,n,);
scanf("%d",&m);
printf("Case %d:\n",++t);
int s,t,k;
while(m--){
scanf("%d%d",&s,&t);
k=(t-s+)/;
printf("%d\n",query(,n,s,t,,k));
}
}
return ;
}
划分树