首先将(x, y)变换为((x + y) / 2, (x - y) / 2)
然后变成查询区间中位数的问题，把x, y分开做
离散化完直接用主席树维护区间和
1 /************************************************************** 2 Problem: 2735 3 User: rausen 4 Language: C++ 5 Result: Accepted 6 Time:5960 ms 7 Memory:81280 kb 8 ****************************************************************/ 9 10 #include <cstdio> 11 #include <algorithm> 12 13 using namespace std; 14 typedef long long ll; 15 typedef double lf; 16 const int N = 1e5 + 5; 17 const int M = 4e6 + 5; 18 19 int n, Q; 20 int x[N], y[N], tx[N], ty[N]; 21 22 struct chair_node { 23 chair_node *ls, *rs; 24 int cnt; 25 ll sum; 26 } *chair_root_x[N], *chair_root_y[N], mempool[M], *cnt_chair = mempool, *null; 27 28 inline int read() { 29 int x = 0, sgn = 1; 30 char ch = getchar(); 31 while (ch < '0' || '9' < ch) { 32 if (ch == '-') sgn = -1; 33 ch = getchar(); 34 } 35 while ('0' <= ch && ch <= '9') { 36 x = x * 10 + ch - '0'; 37 ch = getchar(); 38 } 39 return sgn * x; 40 } 41 42 #define Cnt p -> cnt 43 #define Sum p -> sum 44 #define Ls p -> ls 45 #define Rs p -> rs 46 #define mid (l + r >> 1) 47 void chair_modify(chair_node *&p, int l, int r, int pos, int d) { 48 *(++cnt_chair) = *p, p = cnt_chair, ++Cnt, Sum += d; 49 if (l == r) return; 50 if (pos <= mid) chair_modify(Ls, l, mid, pos, d); 51 else chair_modify(Rs, mid + 1, r, pos, d); 52 } 53 54 ll chair_query(chair_node *p, chair_node *q, int rank) { 55 int l = 1, r = n, cnt = 0, t; 56 ll res = 0; 57 while (l < r) { 58 t = p -> ls -> cnt - q -> ls -> cnt; 59 if (rank <= t) { 60 cnt += p -> rs -> cnt - q -> rs -> cnt, res += p -> rs -> sum - q -> rs -> sum; 61 p = p -> ls, q = q -> ls, r = mid; 62 } else { 63 cnt -= t, res -= p -> ls -> sum - q -> ls -> sum; 64 rank -= t, p = p -> rs, q = q -> rs, l = mid + 1; 65 } 66 } 67 return res - Sum / Cnt * cnt; 68 } 69 #undef mid 70 #undef Ls 71 #undef Rs 72 #undef Sum 73 #undef Cnt 74 75 int main() { 76 int i, j, x1, y1, tmp; 77 n = read(), Q = read(); 78 for (i = 1; i <= n; ++i) x[i] = read(); 79 for (i = 1; i <= n; ++i) { 80 tmp = read(); 81 y[i] = x[i] - tmp, x[i] += tmp; 82 } 83 for (i = 1; i <= n; ++i) tx[i] = x[i]; 84 sort(tx + 1, tx + n + 1); 85 for (i = 1; i <= n; ++i) x[i] = lower_bound(tx + 1, tx + n + 1, x[i]) - tx; 86 for (i = 1; i <= n; ++i) ty[i] = y[i]; 87 sort(ty + 1, ty + n + 1); 88 for (i = 1; i <= n; ++i) y[i] = lower_bound(ty + 1, ty + n + 1, y[i]) - ty; 89 90 null = cnt_chair; 91 null -> ls = null -> rs = null, null -> cnt = null -> sum = 0; 92 chair_root_x[0] = chair_root_y[0] = null; 93 for (i = 1; i <= n; ++i) { 94 chair_modify(chair_root_x[i] = chair_root_x[i - 1], 1, n, x[i], tx[x[i]]); 95 chair_modify(chair_root_y[i] = chair_root_y[i - 1], 1, n, y[i], ty[y[i]]); 96 } 97 while (Q--) { 98 x1 = read(), y1 = read(), tmp = (y1 - x1 + 2) / 2; 99 printf("%.2lf ", (lf) (chair_query(chair_root_x[y1], chair_root_x[x1 - 1], tmp) + chair_query(chair_root_y[y1], chair_root_y[x1 - 1], tmp)) / 2.0); 100 } 101 return 0; 102 }