[Luogu] 相关分析
不想调了
#include <bits/stdc++.h> const int N = 1e5 + 10; #define LL long long #define gc getchar() int fjs; struct Node { LL xy, x, y, x_2, lenst, lens, lent, lentt; LL S_2, T_2/*用于 2 操作*/, S_1, T_1/*用于 3 操作*/; bool flag1/*用于 2 操作*/, flag2/*用于 3 操作*/; int size; int l, r; }; Node T[N << 2]; int impx[N], impy[N]; Node operator + (const Node &a, const Node &b) { Node ret; ret.x = a.x + b.x; ret.y = a.y + b.y; ret.xy = a.xy + b.xy; ret.x_2 = a.x_2 + b.x_2; ret.size = a.size + b.size; return ret; } int n, Ty, Len; inline LL read() { LL x = 0, f = 1; char c = gc; while(c < '0' || c > '9') {if(c == '-') f = -1; c = gc;} while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = gc; return x * f; } #define lson jd << 1 #define rson jd << 1 | 1 void Build_tree(int l, int r, int jd) { T[jd].size = (r - l + 1); T[jd].l = l; T[jd].r = r; if(l == r) { int x_ = impx[l], y_ = impy[l]; T[jd].x = x_; T[jd].y = y_; T[jd].xy = x_ * y_; T[jd].x_2 = x_ * x_; return ; } int mid = (l + r) >> 1; Build_tree(l, mid, lson); Build_tree(mid + 1, r, rson); T[jd] = T[lson] + T[rson]; } void Clear_1(int jd) { T[jd].flag1 = T[jd].lenst = T[jd].lens = T[jd].lent = T[jd].lentt = 0; T[jd].S_1 = T[jd].T_1 = 0; } void Clear_2(int jd) { T[jd].flag2 = 0; T[jd].S_2 = T[jd].T_2 = 0; } void Down_1(int jd) { T[lson].flag1 = T[rson].flag1 = ++ fjs; T[lson].S_1 += T[jd].S_1; T[rson].S_1 += T[jd].S_1; T[lson].T_1 += T[jd].T_1; T[rson].T_1 += T[jd].T_1; T[lson].lenst += T[jd].lenst; T[rson].lenst += T[jd].lenst; T[lson].lens += T[jd].lens; T[rson].lens += T[jd].lens; T[lson].lent += T[jd].lent; T[rson].lent += T[jd].lent; T[lson].lentt += T[jd].lentt; T[rson].lentt += T[jd].lentt; int s = T[jd].S_1, t = T[jd].T_1; T[lson].xy += (t * T[lson].x + s * T[lson].y + T[jd].lenst); T[lson].x_2 += (2 * t * T[lson].x + T[jd].lentt); T[lson].x += T[jd].lens; T[lson].y += T[jd].lent; T[rson].xy += (t * T[rson].x + s * T[rson].y + T[jd].lenst); T[rson].x_2 += (2 * t * T[rson].x + T[jd].lentt); T[rson].x += T[jd].lens; T[rson].y += T[jd].lent; Clear_1(jd); } void Work_1(int, int, int, int, int, int, int); void Down_2(int jd) { T[lson].flag2 = T[rson].flag2 = ++ fjs; T[lson].S_2 = T[rson].S_2 = T[jd].S_2; T[lson].T_2 = T[rson].T_2 = T[jd].T_2; int l, r; l = T[lson].l, r = T[lson].r; T[lson].xy = T[lson].x_2 = (r * (r + 1) * (2 * r + 1) / 6) - (l * (l - 1) * (2 * l - 1)) / 6; T[lson].x = T[lson].y = (l + r) / 2 * (r - l + 1); Work_1(1, n, 1, l, r, T[jd].S_2, T[jd].T_2); l = T[rson].l, r = T[rson].r; T[rson].xy = T[rson].x_2 = (r * (r + 1) * (2 * r + 1) / 6) - (l * (l - 1) * (2 * l - 1)) / 6; T[rson].x = T[rson].y = (l + r) / 2 * (r - l + 1); Work_1(1, n, 1, l, r, T[jd].S_2, T[jd].T_2); Clear_2(jd); } void Work_1(int l, int r, int jd, int x, int y, int s, int t) { if(x <= l && r <= y) { T[jd].flag1 = ++ fjs; T[jd].S_1 = s; T[jd].T_1 = s; T[jd].xy += (t * T[jd].x + s * T[jd].y + Len * s * t); T[jd].x_2 += (2 * t * T[jd].x + Len * t * t); T[jd].x += Len * s; T[jd].y += Len * t; T[jd].lenst += Len * s * t; T[jd].lens += Len * s; T[jd].lent += Len * t; T[jd].lentt += Len * t * t; return ; } if(T[jd].flag2 > T[jd].flag1) Down_1(jd), Down_2(jd); else Down_2(jd), Down_1(jd); int mid = (l + r) >> 1; if(x <= mid) Work_1(l, mid, lson, x, y, s, t); if(y > mid) Work_1(mid + 1, r, rson, x, y, s, t); T[jd] = T[lson] + T[rson]; } void Work_2(int l, int r, int jd, int x, int y, int s, int t) { if(x <= l && r <= y) { T[jd].flag2 = ++ fjs; T[jd].S_2 = s; T[jd].T_2 = t; T[jd].xy = T[jd].x_2 = (r * (r + 1) * (2 * r + 1)) / 6 - (l * (l - 1) * (2 * l - 1)) / 6; T[jd].x = T[jd].y = (l + r) / 2 * (r - l + 1); Work_1(1, n, 1, l, r, s, t); return ; } if(T[jd].flag2 > T[jd].flag1) Down_1(jd), Down_2(jd); else Down_2(jd), Down_1(jd); int mid = (l + r) >> 1; if(x <= mid) Work_2(l, mid, lson, x, y, s, t); if(y > mid) Work_2(mid + 1, r, rson, x, y, s, t); T[jd] = T[lson] + T[rson]; } int Sec_A_xy(int l, int r, int jd, int x, int y) { if(x <= l && r <= y) return T[jd].xy; if(T[jd].flag2 > T[jd].flag1) Down_1(jd), Down_2(jd); else Down_2(jd), Down_1(jd); int mid = (l + r) >> 1; if(y <= mid) return Sec_A_xy(l, mid, lson, x, y); else if(x > mid) return Sec_A_xy(mid + 1, r, rson, x, y); else return Sec_A_xy(l, mid, lson, x, y) + Sec_A_xy(mid + 1, r, rson, x, y); } int Sec_A_x(int l, int r, int jd, int x, int y) { if(x <= l && r <= y) return T[jd].x; if(T[jd].flag2 > T[jd].flag1) Down_1(jd), Down_2(jd); else Down_2(jd), Down_1(jd); int mid = (l + r) >> 1; if(y <= mid) return Sec_A_x(l, mid, lson, x, y); else if(x > mid) return Sec_A_x(mid + 1, r, rson, x, y); else return Sec_A_x(l, mid, lson, x, y) + Sec_A_x(mid + 1, r, rson, x, y); } int Sec_A_y(int l, int r, int jd, int x, int y) { if(x <= l && r <= y) return T[jd].y; if(T[jd].flag2 > T[jd].flag1) Down_1(jd), Down_2(jd); else Down_2(jd), Down_1(jd); int mid = (l + r) >> 1; if(y <= mid) return Sec_A_y(l, mid, lson, x, y); else if(x > mid) return Sec_A_y(mid + 1, r, rson, x, y); else return Sec_A_y(l, mid, lson, x, y) + Sec_A_y(mid + 1, r, rson, x, y); } int Sec_A_x_2(int l, int r, int jd, int x, int y) { if(x <= l && r <= y) return T[jd].x_2; if(T[jd].flag2 > T[jd].flag1) Down_1(jd), Down_2(jd); else Down_2(jd), Down_1(jd); int mid = (l + r) >> 1; if(y <= mid) return Sec_A_x_2(l, mid, lson, x, y); else if(x > mid) return Sec_A_x_2(mid + 1, r, rson, x, y); else return Sec_A_x_2(l, mid, lson, x, y) + Sec_A_x_2(mid + 1, r, rson, x, y); } int main() { freopen("gg.in", "r", stdin); n = read(); Ty = read(); for(int i = 1; i <= n; i ++) impx[i] = read(); for(int i = 1; i <= n; i ++) impy[i] = read(); Build_tree(1, n, 1); for(; Ty; Ty --) { int opt = read(), l = read(), r = read(); Len = (r - l + 1); if(opt == 1) { double a = Sec_A_xy(1, n, 1, l, r) * 1.0; double b = Sec_A_x(1, n, 1, l, r) * 1.0; double c = Sec_A_y(1, n, 1, l, r) * 1.0; double d = Sec_A_x_2(1, n, 1, l, r) * 1.0; double Ans = (a - b * c / (double)Len) / (double)(1.0 * d - 1.0 * b * b / (double)Len); printf("%.10lf\n", Ans); continue ; } int s = read(), t = read(); if(opt == 2) Work_1(1, n, 1, l, r, s, t); else if(opt == 3) Work_2(1, n, 1, l, r, s, t); } return 0; }
