4821. [Sdoi2017]相关分析

https://hydro.ac/d/bzoj/record/63a45a58b053be17396a0036

BZOJ/4821/4821.cpp

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