第K大/小数

第K小数

#include<bits/stdc++.h>
using namespace std;
const int N = 1e5 + 10;
vector<int> num;
int n,m;
int a[N];
int root[N],idx;
struct node
{
    int l,r;
    int cnt;
}tr[N*21];
int find(int x)
{
    return lower_bound(num.begin(),num.end(),x) - num.begin();
}
int build(int l,int r)
{
    int p = ++idx;
    if(l == r)  return p;
    int mid = l + r >> 1;
    tr[p].l = build(l,mid) , tr[p].r = build(mid+1,r);
    return p;
}
int insert(int p,int l,int r,int x)
{
    int q = ++idx;
    tr[q] = tr[p];
    if(l == r)
    {
        tr[q].cnt++;
        return q;
    }
    int mid = l + r >> 1;
    if(x <= mid)    tr[q].l = insert(tr[p].l,l,mid,x);
    else tr[q].r = insert(tr[p].r,mid+1,r,x);
    tr[q].cnt = tr[tr[q].l].cnt + tr[tr[q].r].cnt;
    return q;
}
int query(int p,int q,int l,int r,int k)
{
    if(l == r)  return l;
    int mid = l + r >> 1;
    int cnt = tr[tr[p].l].cnt - tr[tr[q].l].cnt;
    if(k <= cnt)    return query(tr[p].l,tr[q].l,l,mid,k);
    else return query(tr[p].r,tr[q].r,mid + 1 , r, k - cnt);
}
int main()
{
    cin>>n>>m;
    for(int i = 1 ; i <= n ; i ++ )
    {
        cin>>a[i];
        num.push_back(a[i]);
    }
    sort(num.begin(),num.end());
    num.erase(unique(num.begin(),num.end()) , num.end());
    root[0] = build(0,num.size()-1);
    for(int i = 1 ; i <= n ; i ++ )
    {
        root[i] = insert(root[i-1],0,num.size()-1,find(a[i]));
    }
    while(m--)
    {
        int l,r,k;
        cin>>l>>r>>k;
        cout<<num[query(root[r],root[l-1],0,num.size()-1,k)]<<"\n";
    }
    return 0;
}

第K大数

#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;
#define ios ios::sync_with_stdio(false),cin.tie(0),cout.tie(0);
#define fi first
#define se second
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> PII;
typedef vector<int> VI;
inline ll qmi(int a, int b, int p){ ll res = 1 % p; while (b){ if (b & 1) res = res * a % p; a = a * (ll)a % p; b >>= 1;} return res;}
inline ll qm(ll a, ll b){ ll res = 1 ; while (b){ if (b & 1) res = res * a ; a = a * (ll)a ; b >>= 1;} return res;}
inline ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}
inline ll lcm(ll x, ll y) { return x / gcd(x, y) * y;}
inline ll maxll(ll x, ll y) { return x > y ? x : y; }
inline ll minll(ll x, ll y) { return x < y ? x : y; }
const int mod=1000000007 , N = 1e5 + 10;
struct node
{
	int l,r,cnt;
}tr[N*40];
int root[N],idx;
int n,m;
VI num;
int a[N];
int build(int l,int r)
{
	int u = ++idx;
	if(l == r)
	{
		return u;
	}
	int mid = l + r >> 1;
	tr[u].l = build(l,mid) , tr[u].r = build(mid+1,r);
	return u;
}
int find(int x)
{
	return lower_bound(num.begin(),num.end() , x) - num.begin();
}
void insert(int &u,int p,int l,int r,int x)
{
	u = ++idx;
	tr[u] = tr[p];
	tr[u].cnt ++;
	if(l == r)	return ;
	int mid = l + r >> 1;
	if(x <= mid)	insert(tr[u].l,tr[p].l,l,mid,x);
	else insert(tr[u].r , tr[p].r , mid+1,r,x);
}
int query(int p,int q,int l,int r,int x)
{
	if(l == r)	return r;
	int cnt = tr[tr[p].r].cnt - tr[tr[q].r].cnt;
	int mid = l + r >> 1;
	if(x > cnt)	return query(tr[p].l,tr[q].l,l,mid,x-cnt);
	else return query(tr[p].r,tr[q].r,mid+1,r,x);
}
void solve()
{
	ios
	cin>>n;
	num.clear();
	idx = 0;
	for(int i = 1 ; i <= n ; i ++ )	cin>>a[i],num.push_back(a[i]);
	cin>>m;
	sort(num.begin(),num.end());
	num.erase(unique(num.begin() , num.end()) , num.end());
	root[0] = build(0,num.size()-1);
	for(int i = 1 ; i <= n ; i ++ )
		insert(root[i],root[i-1],0,num.size()-1,find(a[i]));
	while( m -- )
	{
		int l,r,k;
		cin>>l>>r>>k;
		l ++ , r ++ ;
		cout<<num[query(root[r],root[l-1],0,num.size()-1,k)]<<"\n";
	}
}
int main(){
	// int t;
	// cin>>t;
	// while(t--)
	// {
		solve();
	// }
	return 0;
}

区间小于或大于K的数的个数/和

const int mod=1000000007 , N = 2e5 + 10;
int a[N];
int n,m;
int root[N],idx;
struct node
{
	int l,r;
	ll sum,cnt;
}tr[N*40];
void insert(int &p,int u,int l,int r,int x)
{
	p = ++idx;
	tr[p] = tr[u];
	tr[p].cnt ++;
	tr[p].sum += x;
	if(l == r)
	{	
		return ;
	}
	int mid = l + r >> 1;
	if(x <= mid)	 insert(tr[p].l,tr[u].l,l,mid,x);
	else insert(tr[p].r,tr[u].r,mid+1,r,x);
	return ;
}
ll query1(int p,int q,int l,int r,int lk,int rk)
{
	if(l >= lk && r <= rk)	return tr[p].sum - tr[q].sum;
	int mid = l + r >> 1;
	ll sum = 0;
	if(lk <= mid)	sum += query1(tr[p].l,tr[q].l,l,mid,lk,rk);
	if(rk > mid)	sum += query1(tr[p].r,tr[q].r,mid+1,r,lk,rk);
	return sum;
}
ll query2(int p,int q,int l,int r,int lk,int rk,int k)
{
	if(l >= lk && r <= rk)
	{
		return (ll)(tr[p].cnt - tr[q].cnt)*k - (tr[p].sum - tr[q].sum);
	}
	int mid = l + r >> 1;
	ll sum = 0;
	if(lk <= mid)	sum += query2(tr[p].l,tr[q].l,l,mid,lk,rk,k);
	if(rk > mid)	sum += query2(tr[p].r,tr[q].r,mid+1,r,lk,rk,k);
	return sum;
}
void solve()
{
	cin>>n>>m;
	for(int i = 1 ; i <= n ; i ++ )	cin>>a[i],num.push_back(a[i]);
	int len = 1e9;
	for(int i = 1 ; i <= n ; i ++ )
		insert(root[i],root[i-1],0,len,a[i]);
	while(m -- )
	{
		int l,r,k;
		cin>>l>>r>>k;
		ll ans = 0;
		ans += query1(root[r],root[l-1],0,len,0,k/2);
		ans += query2(root[r],root[l-1],0,len,k/2+1,k,k);
		cout<<ans<<"\n";
	}
}
int main(){
		solve();
	return 0;
}