主席树学习

Posted 2022-09-02 nublity

求区间第k小

题目链接：https://www.luogu.org/problem/P3834

#include<bits/stdc++.h>

#define ll long long
#define ull unsigned long long
#define met(a, x) memset(a,x,sizeof(a))
#define inf 0x3f3f3f3f
#define Rint register int

using namespace std;
const ll mod = 1e9 + 7;
const int N = 2e5 + 10;
const int M = 3e6 + 10;
int a[N], b[N], c[N], cnt;
int sum[N << 5], L[N << 5], R[N << 5];

inline int build(int l, int r) 
    int rt = ++cnt;
    sum[rt] = 0;
    if (l < r) 
        int mid = (l + r) / 2;
        L[rt] = build(l, mid);
        R[rt] = build(mid + 1, r);
    
    return rt;


inline int update(int pre, int l, int r, int x) 
    int rt = ++cnt;
    L[rt] = L[pre], R[rt] = R[pre], sum[rt] = sum[pre] + 1;
    if (l < r) 
        int mid = (l + r) / 2;
        if (x <= mid)L[rt] = update(L[pre], l, mid, x);
        else R[rt] = update(R[pre], mid + 1, r, x);
    
    return rt;


inline int query(int u, int v, int l, int r, int k) 
    if (l >= r)return l;
    int x = sum[L[v]] - sum[L[u]];
    int mid = (l + r) / 2;
    if (x >= k)return query(L[u], L[v], l, mid, k);
    else return query(R[u], R[v], mid + 1, r, k - x);


int main() 
   // freopen("in","r",stdin);
//    freopen("out","w",stdout);
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n, m;
    cin >> n >> m;
    for (int i = 1; i <= n; i++) 
        cin >> a[i];
        b[i] = a[i];
    
    sort(b + 1, b + 1 + n);
    int len = unique(b + 1, b + 1 + n) - (b + 1);
    c[0] = build(1, len);
    for (int i = 1; i <= n; i++) 
        int t = lower_bound(b + 1, b + 1 + len, a[i]) - b;
        c[i] = update(c[i - 1], 1, len, t);
    
    while (m--) 
        int x, y, z;
        cin >> x >> y >> z;
        int t = query(c[x - 1], c[y], 1, len, z);
        cout << b[t] << endl;
    
    return 0;

动态主席树，求区间第k小

题目链接：https://www.luogu.org/problem/P2617