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4821. [Sdoi2017]相关分析
https://hydro.ac/d/bzoj/record/63a45a58b053be17396a0036
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BZOJ/4821/4821.cpp
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BZOJ/4821/4821.cpp
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#include <iostream>
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#include <iomanip>
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using std::cin;
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using std::cout;
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const char endl = '\n';
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const int N = 1e5 + 5;
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struct node {
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int l, r;
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__int128 sum_x, sum_y, sum_xx, sum_xy;
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__int128 lazy_s, lazy_t;
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bool covered;
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node(const int &_l = 0, const int &_r = 0)
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: l(_l),
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r(_r),
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sum_x(0),
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sum_y(0),
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sum_xx(0),
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sum_xy(0),
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lazy_s(0),
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lazy_t(0),
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covered(false) {}
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node operator+(const node &rhs) const {
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node res;
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res.l = l;
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res.r = rhs.r;
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res.sum_x = sum_x + rhs.sum_x;
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res.sum_y = sum_y + rhs.sum_y;
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res.sum_xx = sum_xx + rhs.sum_xx;
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res.sum_xy = sum_xy + rhs.sum_xy;
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return res;
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}
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} tr[N << 2];
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int n, m, x[N], y[N];
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__int128 square_sum(__int128 x) {
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return x * (x + 1) * (2 * x + 1) / 6;
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}
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__int128 square_sum(__int128 l, __int128 r) {
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return square_sum(r) - square_sum(l - 1);
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}
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/// Add (s, t) to each element under tr[u]
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void modify_node(int u, __int128 s, __int128 t) {
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tr[u].lazy_s += s;
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tr[u].lazy_t += t;
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tr[u].sum_xx += 2 * s * tr[u].sum_x + s * s * (tr[u].r - tr[u].l + 1);
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tr[u].sum_xy += t * tr[u].sum_x + s * tr[u].sum_y + s * t * (tr[u].r - tr[u].l + 1);
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tr[u].sum_x += s * (tr[u].r - tr[u].l + 1);
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tr[u].sum_y += t * (tr[u].r - tr[u].l + 1);
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}
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/// x[i] = y[i] = i
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void change_node(int u) {
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tr[u].lazy_s = tr[u].lazy_t = 0;
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tr[u].sum_x = tr[u].sum_y = static_cast<__int128>(tr[u].l + tr[u].r) * (tr[u].r - tr[u].l + 1) / 2;
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tr[u].sum_xx = tr[u].sum_xy = square_sum(tr[u].l, tr[u].r);
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tr[u].covered = true;
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}
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void pushup(int u) {
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tr[u] = tr[u << 1] + tr[u << 1 | 1];
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}
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void pushdown(int u) {
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if (tr[u].covered) {
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change_node(u << 1);
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change_node(u << 1 | 1);
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tr[u].covered = false;
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}
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modify_node(u << 1, tr[u].lazy_s, tr[u].lazy_t);
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modify_node(u << 1 | 1, tr[u].lazy_s, tr[u].lazy_t);
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tr[u].lazy_s = tr[u].lazy_t = 0;
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}
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void build(int u, int l, int r) {
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tr[u] = node(l, r);
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if (l == r) {
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tr[u].sum_x = x[l];
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tr[u].sum_y = y[l];
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tr[u].sum_xx = static_cast<__int128>(x[l]) * x[l];
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tr[u].sum_xy = static_cast<__int128>(x[l]) * y[l];
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return;
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}
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int mid = l + r >> 1;
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build(u << 1, l, mid);
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build(u << 1 | 1, mid + 1, r);
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pushup(u);
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}
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void modify(int u, int l, int r, __int128 s, __int128 t) {
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if (l <= tr[u].l && tr[u].r <= r) {
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modify_node(u, s, t);
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return;
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}
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int mid = tr[u].l + tr[u].r >> 1;
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pushdown(u);
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if (l <= mid) modify(u << 1, l, r, s, t);
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if (r > mid) modify(u << 1 | 1, l, r, s, t);
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pushup(u);
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}
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void change(int u, int l, int r, __int128 s, __int128 t) {
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if (l <= tr[u].l && tr[u].r <= r) {
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change_node(u);
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modify_node(u, s, t);
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return;
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}
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int mid = tr[u].l + tr[u].r >> 1;
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pushdown(u);
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if (l <= mid) change(u << 1, l, r, s, t);
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if (r > mid) change(u << 1 | 1, l, r, s, t);
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pushup(u);
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}
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node query(int u, int l, int r) {
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if (l <= tr[u].l && tr[u].r <= r) return tr[u];
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int mid = tr[u].l + tr[u].r >> 1;
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node res;
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pushdown(u);
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if (l <= mid) res = res + query(u << 1, l, r);
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if (r > mid) res = res + query(u << 1 | 1, l, r);
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return res;
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}
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int main() {
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std::ios::sync_with_stdio(false);
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cin.tie(nullptr);
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cin >> n >> m;
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for (int i = 1; i <= n; i++) {
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cin >> x[i];
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}
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for (int i = 1; i <= n; i++) {
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cin >> y[i];
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}
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build(1, 1, n);
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while (m--) {
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int op, l, r;
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cin >> op >> l >> r;
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if (op == 1) {
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auto res = query(1, l, r);
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double x = static_cast<double>(res.sum_xy) - static_cast<double>(res.sum_x) * res.sum_y / (r - l + 1),
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y = static_cast<double>(res.sum_xx) - static_cast<double>(res.sum_x) * res.sum_x / (r - l + 1);
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cout << std::fixed << std::setprecision(10) << x / y << endl;
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} else if (op == 2) {
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int s, t;
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cin >> s >> t;
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modify(1, l, r, s, t);
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} else { // op == 3
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int s, t;
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cin >> s >> t;
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change(1, l, r, s, t);
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}
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}
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return 0;
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}
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