2018.湘潭邀请赛.C.2018

C. Just h-index

The h-index of an author is the largest h where he has at least h papers with citations not less than h.

Bobo has published n papers with citations a1,a2,a3,……,an respectively. One day,he raises q questions. The i-th question is described by two integers l(i) and r(i), asking the h-index of Bobo if has only published papers with citations a(li),a(li+1),……,a(ri).()中为下标。

题意：
题目背景和第A题相近，不同的是：
A题第二行依次给出 0 到 n 次项的系数
C题第二行依次给出 n 个不同项的次幂，这些幂次可能相同可能不同，然后有 q 个询问，
每个询问给出一个有区间 [l,r]，问每个区间解
思路：
用主席树求区间第K小的结果，二分答案求解即可
下面用的是kuangbin的主席树模板

Input

（1）

5 3
1 5 3 2 1
1 3
2 4
1 5
（2）
5 6
1 2 3 4 5
1 1
1 2
1 3
1 4
1 5
3 5
（3）
5 5
5 5 5 5 5
1 5
2 5
3 5
4 5

5 5

output

(1)

(2）

(3)

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


const int MAXN = 100010;
const int M = MAXN * 30;
int n,q,m,tot;
int a[MAXN], t[MAXN];
int T[M], lson[M], rson[M], c[M];


void Init_hash()
{
    for(int i = 1; i <= n;i++)
        t[i] = a[i];
    sort(t+1,t+1+n);
    m = unique(t+1,t+1+n)-t-1;
}
int build(int l,int r)
{
    int root = tot++;
    c[root] = 0;
    if(l != r)
    {
        int mid = (l+r)>>1;
        lson[root] = build(l,mid);
        rson[root] = build(mid+1,r);
    }
    return root;
}
int hash(int x)
{
    return lower_bound(t+1,t+1+m,x) - t;
}
int update(int root,int pos,int val)
{
    int newroot = tot++, tmp = newroot;
    c[newroot] = c[root] + val;
    int l = 1, r = m;
    while(l < r)
    {
        int mid = (l+r)>>1;
        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+1;
        }
        c[newroot] = c[root] + val;
    }
    return tmp;
}
int query(int left_root,int right_root,int k)
{
    int l = 1, r = m;
    while( l < r)
    {
        int mid = (l+r)>>1;
        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 + 1;
            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);
    while(scanf("%d%d",&n,&q) == 2)
    {
        tot = 0;
        for(int i = 1;i <= n;i++)
            scanf("%d",&a[i]);
        Init_hash();
        T[n+1] = build(1,m);
        for(i = n;i ;i--)
        {
            int pos = hash(a[i]);
            T[i] = update(T[i+1],pos,1);
        }
        while(q--)
        {
            int l,r,k;
            scanf("%d%d",&l,&r);
            int ll = 1,rr = r - l + 2; //答案的范围是 1 ~ r-l+1
            while(ll<rr) {
            	int mid = ll + rr >> 1;
            	int w = t[query(T[l],T[r+1],r-l+1-mid+1)];  // 求区间[l,r]第k小 (k=r-l+1-mid+1)
            	//cout<<ll<<" "<<rr<<" "<<mid<<" "<<w<<endl;
            	if(w >= mid ) ll = mid + 1;  // 如果去年第 k 小 w >= mid，则mid满足条件，ll 调整为 mid + 1 
            	else rr = mid;  //mid 不符合 条件
            }
            printf("%d\n",rr-1);//最后 ll == rr，rr 为 答案加一
        }
    }
    return 0;
}

2018.湘潭邀请赛.C.2018

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