HDU 4251 --- 主席树（划分树是正解）

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