BZOJ 3196 二逼平衡树

线段树套平衡树

上次spaly头铁卡不过去。。leaf tree轻轻松松～

#include <bits/stdc++.h>
#define INF 2147483647
#define full(a, b) memset(a, b, sizeof a)
#define FAST_IO ios::sync_with_stdio(false), cin.tie(0), cout.tie(0)
using namespace std;
typedef long long ll;
inline int lowbit(int x){ return x & (-x); }
inline int read(){
    int X = 0, w = 0; char ch = 0;
    while(!isdigit(ch)) { w |= ch == '-'; ch = getchar(); }
    while(isdigit(ch)) X = (X << 3) + (X << 1) + (ch ^ 48), ch = getchar();
    return w ? -X : X;
}
inline int gcd(int a, int b){ return b ? gcd(b, a % b) : a; }
inline int lcm(int a, int b){ return a / gcd(a, b) * b; }
template<typename T>
inline T max(T x, T y, T z){ return max(max(x, y), z); }
template<typename T>
inline T min(T x, T y, T z){ return min(min(x, y), z); }
template<typename A, typename B, typename C>
inline A fpow(A x, B p, C lyd){
    A ans = 1;
    for(; p; p >>= 1, x = 1LL * x * x % lyd)if(p & 1)ans = 1LL * x * ans % lyd;
    return ans;
}
#define newNode(a, b, c, d) (&(*pool[cnt++] = Node(a, b, c, d)))
#define merge(a, b) newNode(a->size + b->size, b->val, a, b)
#define push_up(rt) if(rt->lf->size) rt->size = rt->lf->size + rt->rf->size, rt->val = rt->rf->val
#define ratio 4
const int N = 500005;
struct Node{
    int size, val;
    Node *lf, *rf;
    Node(){}
    Node(int size, int val, Node *lf, Node *rf): size(size), val(val), lf(lf), rf(rf){}
}*null, *root[N<<2], *pool[N<<2], t[N<<2];
int cnt, n, m, a[N];

inline void maintain(Node *cur){
    if(cur->lf->size > cur->rf->size * ratio)
        cur->rf = merge(cur->lf->rf, cur->rf), pool[--cnt] = cur->lf, cur->lf = cur->lf->lf;
    if(cur->rf->size > cur->lf->size * ratio)
        cur->lf = merge(cur->lf, cur->rf->lf), pool[--cnt] = cur->rf, cur->rf = cur->rf->rf;
}

void insert(Node *cur, int val){
    if(cur->size == 1){
        cur->lf = newNode(1, min(val, cur->val), null, null);
        cur->rf = newNode(1, max(val, cur->val), null, null);
    }
    else insert(val > cur->lf->val ? cur->rf : cur->lf, val);
    push_up(cur), maintain(cur);
}

void erase(Node *cur, int val){
    if(cur->lf->size == 1 && cur->lf->val == val)
        pool[--cnt] = cur->lf, pool[--cnt] = cur->rf, *cur = *cur->rf;
    else if(cur->rf->size == 1 && cur->rf->val == val)
        pool[--cnt] = cur->lf, pool[--cnt] = cur->rf, *cur = *cur->lf;
    else erase(val > cur->lf->val ? cur->rf : cur->lf, val);
    push_up(cur), maintain(cur);
}

int find(Node *cur, int val){
    if(cur->size == 1) return 1;
    return val > cur->lf->val ? cur->lf->size + find(cur->rf, val) : find(cur->lf, val);
}

int select(Node *cur, int k){
    if(cur->size == 1) return cur->val;
    return k > cur->lf->size ? select(cur->rf, k - cur->lf->size) : select(cur->lf, k);
}

int precursor(Node *rt, int val){
    return select(rt, find(rt, val) - 1);
}

int successor(Node *rt, int val){
    return select(rt, find(rt, val + 1));
}

void buildTree(int rt, int l, int r){
    root[rt] = new Node(1, INF, null, null);
    insert(root[rt], -INF);
    for(int i = l; i <= r; i ++){
        insert(root[rt], a[i]);
    }
    if(l == r) return;
    int mid = (l + r) >> 1;
    buildTree(rt << 1, l, mid);
    buildTree(rt << 1 | 1, mid + 1, r);
}

int queryRank(int rt, int l, int r, int ql, int qr, int val){
    if(l == ql && r == qr){
        return find(root[rt], val) - 2;
    }
    int mid = (l + r) >> 1;
    if(qr <= mid) return queryRank(rt << 1, l, mid, ql, qr, val);
    else if(ql > mid) return queryRank(rt << 1 | 1, mid + 1, r, ql, qr, val);
    else return queryRank(rt << 1, l, mid, ql, mid, val) + queryRank(rt << 1 | 1, mid + 1, r, mid + 1, qr, val);
}

int querySelect(int l, int r, int k){
    int L = 0, R = 1e8;
    while(L < R){
        int mid = (L + R + 1) >> 1;
        if(queryRank(1, 1, n, l, r, mid) >= k) R = mid - 1;
        else L = mid;
    }
    return L;
}

void modify(int rt, int l, int r, int pos, int val){
    insert(root[rt], val);
    erase(root[rt], a[pos]);
    if(l == r) return;
    int mid = (l + r) >> 1;
    if(pos <= mid) modify(rt << 1, l, mid, pos, val);
    else modify(rt << 1 | 1, mid + 1, r, pos, val);
}

int queryPre(int rt, int l, int r, int ql, int qr, int val){
    if(l == ql && r == qr){
        return precursor(root[rt], val);
    }
    int mid = (l + r) >> 1;
    if(qr <= mid) return queryPre(rt << 1, l, mid, ql, qr, val);
    else if(ql > mid) return queryPre(rt << 1 | 1, mid + 1, r, ql, qr, val);
    else return max(queryPre(rt << 1, l, mid, ql, mid, val), queryPre(rt << 1 | 1, mid + 1, r, mid + 1, qr, val));
}

int querySuc(int rt, int l, int r, int ql, int qr, int val){
    if(l == ql && r == qr){
        return successor(root[rt], val);
    }
    int mid = (l + r) >> 1;
    if(qr <= mid) return querySuc(rt << 1, l, mid, ql, qr, val);
    else if(ql > mid) return querySuc(rt << 1 | 1, mid + 1, r, ql, qr, val);
    else return min(querySuc(rt << 1, l, mid, ql, mid, val), querySuc(rt << 1 | 1, mid + 1, r, mid + 1, qr, val));
}

int main(){

    //freopen("data.txt", "r", stdin);
    
    for(int i = 0; i < (N<<2); i ++) pool[i] = &t[i];
    null = new Node(0, 0, nullptr, nullptr);
    n = read(), m = read();
    for(int i = 1; i <= n; i ++) a[i] = read();
    buildTree(1, 1, n);
    while(m --){
        int opt = read();
        if(opt == 1){
            int l = read(), r = read(), k = read();
            printf("%d\n", queryRank(1, 1, n, l, r, k) + 1);
        }
        else if(opt == 2){
            int l = read(), r = read(), k = read();
            printf("%d\n", querySelect(l, r, k));
        }
        else if(opt == 3){
            int pos = read(), k = read();
            modify(1, 1, n, pos, k);
            a[pos] = k;
        }
        else if(opt == 4){
            int l = read(), r = read(), k = read();
            printf("%d\n", queryPre(1, 1, n, l, r, k));
        }
        else{
            int l = read(), r = read(), k = read();
            printf("%d\n", querySuc(1, 1, n, l, r, k));
        }
    }
    return 0;
}