hdu 3473 Minimum Sum 划分树

http://acm.hdu.edu.cn/showproblem.php?pid=3473

对于xl,xl+1……xr，使得[xi-x]和最小，显然x应当为其中的中位数。中位数可以通过求K大数解决，划分树可搞。

对于求和，分为两部分，小于x的部分，大于y的部分，在建树的时候也保存下来分到左子树中的数的和。

最终的和为ave*(lnum-rnum)+rsum-lsum

ave为中位数，lnum为左子数的数量，也就是小于中位数的数量，rnum为右子数，lsum表示小于中位数部分的和

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#define ls (rt<<1)
#define rs ((rt<<1)|1)
#define mid ((t[rt].l+t[rt].r)>>1)
#define ll long long
const int maxn = 100010;
struct node {
    int l , r;
}t[maxn<<2];
int sa[maxn],num[20][maxn],cnt[20][maxn];
ll Lsum[20][maxn],sum[maxn];
int n , q;
void build(int l,int r,int rt,int deep) {
    t[rt].l = l; t[rt].r = r;
    if(l == r) return;
    int mid_val = sa[mid],lsum=mid-l+1;
    for(int i=l;i<=r;i++)
        if(num[deep][i] < mid_val)
            lsum --;
    int L = l , R = mid + 1;
    for(int i=l;i<=r;i++) {
        if(i == l) cnt[deep][i] = 0;
        else cnt[deep][i] = cnt[deep][i-1];
        Lsum[deep][i]=Lsum[deep][i-1];
        if(num[deep][i]<mid_val || num[deep][i]==mid_val && lsum>0) {
            num[deep+1][L++] = num[deep][i];
            cnt[deep][i] ++;
            Lsum[deep][i]+=(ll)num[deep][i];
            if(num[deep][i] == mid_val)
                lsum --;
        }
        else num[deep+1][R++] = num[deep][i];
    }
    build(l,mid,ls,deep+1);
    build(mid+1,r,rs,deep+1);
}
int lnum;
ll lsum;
int query(int l,int r,int rt,int k,int deep) {
    if(l == r) return num[deep][l];
    int s1 , s2;
    if(t[rt].l == l) s1 = 0;
    else s1 = cnt[deep][l-1];
    s2 = cnt[deep][r] - s1;
    if(k <= s2)
        return query(t[rt].l+s1,t[rt].l+s1+s2-1,ls,k,deep+1);
    int b1 = l-1-t[rt].l+1-s1;
    int b2 = r-l+1-s2;
    lnum += s2;
    lsum = (ll)lsum+Lsum[deep][r]-Lsum[deep][l-1];
    return query(mid+1+b1,mid+1+b1+b2-1,rs,k-s2,deep+1);
}
int main() {
    int T , cas = 1;
    scanf("%d" , &T);
    while(T--) {
        printf("Case #%d:
" , cas++);
        scanf("%d" , &n);
        sum[0] = 0;
        for(int i=1;i<=n;i++) {
            scanf("%d",&num[1][i]);
            sa[i] = num[1][i];
            sum[i] = (ll)sum[i-1] + sa[i];
        }
        sort(sa+1,sa+1+n);
        build(1,n,1,1);
        scanf("%d",&q);
        while(q--) {
            int l , r,  k;
            scanf("%d%d",&l,&r);
            l ++; r ++;
            k = (r-l+2)>>1;
            lnum = lsum = 0;
            int ave = query(l,r,1,k,1);
            printf("%I64d
",ave*(lnum-(r-l+1-lnum))+sum[r]-sum[l-1]-lsum-lsum);
        }
        puts("");
    }
    return 0;
}