HDU 3340 rain in acstar (line segment tree + ry)

HDU 3340 rain in acstar

Question Link

Question: give a few polygon (3-5 edges) and ask about the total area of an interval.

Idea: the polygon is divided into a trapezoid, and the area of the trapezoid is D1 + D2 at the bottom of the upper layer multiplied by the upper height/2. If the two trapezoid areas are accumulated, they can be equivalent to accumulating at the bottom of the upper and lower layers, so we can use the line segment tree, and then the given polygon points are in order. We can use the exclusion function to split an inquiry into several inquiries.

Code:

#include <cstdio>#include <cstring>#include <algorithm>#include <cmath>using namespace std;const int N = 133333;int t, n;struct Point {int x, y, id;Point() {}Point(int x, int y) {this->x = x;this->y = y;this->id = id;}void read() {scanf("%d%d", &x, &y);}} p[6];bool cmpp(Point a, Point b) {return a.x < b.x;}struct OP {int tp, l, r;double a, b;OP() {}OP(int l, int r, int tp, double a = 0.0, double b = 0.0) {this->l = l; this->r = r; this->tp = tp;this->a = a; this->b = b;}} op[N];int hash[N * 2], hn, opn;int find(int x) {return lower_bound(hash, hash + hn, x) - hash;}void build_p(int m) {p[m++] = p[0];for (int i = 0; i < m - 1; i++) {if (p[i].x < p[i + 1].x) op[opn++] = OP(p[i].x, p[i + 1].x, 1, -p[i].y, -p[i + 1].y);else op[opn++] = OP(p[i + 1].x, p[i].x, 1, p[i + 1].y, p[i].y);}}#define lson(x) ((x<<1)+1)#define rson(x) ((x<<1)+2)struct Node {int l, r;double d1, d2, s;void gao(double a, double b) {d1 += a;d2 += b;s += (a + b) * (hash[r + 1] - hash[l]) / 2;}} node[N * 8];void build(int l, int r, int x = 0) {node[x].l = l; node[x].r = r;node[x].d1 = node[x].d2 = node[x].s = 0;if (l == r) return;int mid = (l + r) / 2;build(l, mid, lson(x));build(mid + 1, r, rson(x));}double cal(double h1, double h2, double d1, double d2) {return (d2 * h1 + d1 * h2) / (h1 + h2);}void pushdown(int x) {double h1 = hash[node[lson(x)].r + 1] - hash[node[lson(x)].l];double h2 = hash[node[rson(x)].r + 1] - hash[node[rson(x)].l];double d = cal(h1, h2, node[x].d1, node[x].d2);node[lson(x)].gao(node[x].d1, d);node[rson(x)].gao(d, node[x].d2);node[x].d1 = node[x].d2 = 0;}void pushup(int x) {node[x].s = node[lson(x)].s + node[rson(x)].s;}void add(int l, int r, double a, double b, int x = 0) {if (node[x].l >= l && node[x].r <= r) {double d1 = cal(hash[node[x].l] - hash[l], hash[r + 1] - hash[node[x].l], a, b);double d2 = cal(hash[node[x].r + 1] - hash[l], hash[r + 1] - hash[node[x].r + 1], a, b);node[x].gao(d1, d2);return;}int mid = (node[x].l + node[x].r) / 2;pushdown(x);if (l <= mid) add(l, r, a, b, lson(x));if (r > mid) add(l, r, a, b, rson(x));pushup(x);}double query(int l, int r, int x = 0) {if (node[x].l >= l && node[x].r <= r) return node[x].s;int mid = (node[x].l + node[x].r) / 2;double ans = 0;pushdown(x);if (l <= mid) ans += query(l, r, lson(x));if (r > mid) ans += query(l, r, rson(x));pushup(x);return ans;}int main() {scanf("%d", &t);while (t--) {scanf("%d", &n);char ss[15];int l, r, m;hn = opn = 0;while (n--) {scanf("%s", ss);if (ss[0] == 'Q') {scanf("%d%d", &l, &r);hash[hn++] = l; hash[hn++] = r;op[opn++] = OP(l, r, 0);}else {scanf("%d", &m);for (int i = 0; i < m; i++) {p[i].read();hash[hn++] = p[i].x;}build_p(m);}}int tmp = 1;sort(hash, hash + hn);for (int i = 1; i < hn; i++)if (hash[i] != hash[i - 1])hash[tmp++] = hash[i];hn = tmp;build(0, hn - 2);for (int i = 0; i < opn; i++) {if (op[i].tp) add(find(op[i].l), find(op[i].r) - 1, op[i].a, op[i].b);else printf("%.3lf\n", query(find(op[i].l), find(op[i].r) - 1));}}return 0;}

HDU 3340 rain in acstar (line segment tree + ry)