Luogu P3834 【模板】可持久化线段树 2(主席树)(整体二分)

题目描述

https://www.luogu.com.cn/problem/P3834

Solution

整体二分的板子

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#include <iostream>
#include <cstdio>
#include <algorithm>
#include <vector>
#define maxn 200010
#define lowbit(i) ((i) & (-i))
using namespace std;

int n, m, a[maxn];

vector<int> v[maxn];

int b[maxn], cnt;
void init_hash() {
for (int i = 1; i <= n; ++i) b[i] = a[i];
sort(b + 1, b + n + 1); cnt = unique(b + 1, b + n + 1) - b - 1;
for (int i = 1; i <= n; ++i) a[i] = lower_bound(b + 1, b + cnt + 1, a[i]) - b;
}

int Bit[maxn];
void add(int i, int v) { while (i <= n) Bit[i] += v, i += lowbit(i); }

int get_sum(int i) {
int s = 0;
while (i) s += Bit[i], i -= lowbit(i);
return s;
}

struct Query {
int l, r, k, id;
} Q[maxn], t1[maxn], t2[maxn]; int ans[maxn];

int l, r;
inline void add(int x) { for (auto u : v[x]) add(u, 1); }

inline void del(int x) { for (auto u : v[x]) add(u, -1); }

void update(int L, int R) {
while (r < R) add(++r);
while (l > L) add(--l);
while (r > R) del(r--);
while (l < L) del(l++);
}

void solve(int l, int r, int L, int R) {
if (L > R) return ;
if (l == r) {
for (int i = L; i <= R; ++i) ans[Q[i].id] = b[l];
return ;
} int m = l + r >> 1, c1 = 0, c2 = 0; update(l, m);
for (int i = L; i <= R; ++i) {
int l = Q[i].l, r = Q[i].r, k = Q[i].k, v;
v = get_sum(r) - get_sum(l - 1);
if (k <= v) t1[++c1] = Q[i];
else t2[++c2] = Q[i], t2[c2].k -= v;
}
for (int i = 1; i <= c1; ++i) Q[L + i - 1] = t1[i];
for (int i = 1; i <= c2; ++i) Q[L + c1 + i - 1] = t2[i];
solve(l, m, L, L + c1 - 1); solve(m + 1, r, L + c1, R);
}

int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr); cout.tie(nullptr);

cin >> n >> m;
for (int i = 1; i <= n; ++i) cin >> a[i]; init_hash();
for (int i = 1; i <= n; ++i) v[a[i]].push_back(i);
for (int i = 1; i <= m; ++i) cin >> Q[i].l >> Q[i].r >> Q[i].k, Q[i].id = i;
add(l = r = 1); solve(1, cnt, 1, m);
for (int i = 1; i <= m; ++i) cout << ans[i] << "\n";
return 0;
}