Tsinsen-A1490 osu! 【数学期望】

 1 #include <bits/stdc++.h>
 2 #define rep(i, a, b) for (int i = a; i <= b; i++)
 3 #define drep(i, a, b) for (int i = a; i >= b; i--)
 4 #define REP(i, a, b) for (int i = a; i < b; i++)
 5 #define mp make_pair
 6 #define pb push_back
 7 #define clr(x) memset(x, 0, sizeof(x))
 8 #define xx first
 9 #define yy second
10 using namespace std;
11 typedef long long i64;
12 typedef pair<int, int> pii;
13 const int  inf = ~0U >> 1;
14 const i64 INF = ~0ULL >> 1;
15 //*******************************
16 
17 const int maxn = 500005;
18 
19 struct node {
20     double p;
21     double a21, a22, a31, a32;
22     double mul1;
23     node() {}
24     node(double _p, double _a21, double _a22, double _a31, double _a32, double _mul1) :
25         p(_p), a21(_a21), a22(_a22), a31(_a31), a32(_a32), mul1(_mul1) {}
26 
27 };
28 
29 double ans0, ans1, ans3[3];
30 
31 /* the matrix
32    {sum[i - 1], E[i - 1], 1} * {1  , 0 , 0} = {sum[i], E[i], 1}
33                                {2pi, pi, 0}
34                                {pi , pi, 1}
35  */
36 
37 double pi[maxn];
38 
39 struct Seg_Tree {
40     node T[maxn << 2];
41 
42     void Push_up(int o) {
43         T[o].p = T[o << 1].p + T[o << 1 | 1].p, T[o].mul1 = T[o << 1].mul1 + T[o << 1 | 1].mul1;
44         T[o].a21 = T[o << 1].a21 + T[o << 1].a22 * T[o << 1 | 1].a21;
45         T[o].a22 = T[o << 1].a22 * T[o << 1| 1].a22;
46         T[o].a31 = T[o << 1].a31 + T[o << 1].a32 * T[o << 1 | 1].a21 + T[o << 1 | 1].a31;
47         T[o].a32 = T[o << 1].a32 * T[o << 1 | 1].a22 + T[o << 1 | 1].a32;
48     }
49 
50     void update(int o, int l, int r, int x, double p) {
51         if (l == r) {
52             T[o] = node(p, 2 * p, p, p, p, (1 - pi[l - 1]) * p);
53             return;
54         }
55         int mid = l + r >> 1;
56         if (x > mid) update(o << 1 | 1, mid + 1, r, x, p);
57         else update(o << 1, l, mid, x, p);
58         Push_up(o);
59     }
60 
61     void query(int o, int l, int r, int ql, int qr) {
62         if (ql <= l && r <= qr) {
63             ans1 += T[o].p;
64             ans0 += T[o].mul1;
65             ans3[1] = ans3[1] + ans3[2] * T[o].a21 + T[o].a31;
66             ans3[2] = ans3[2] * T[o].a22 + T[o].a32;
67             return;
68         }
69         int mid = l + r >> 1;
70         if (ql <= mid) query(o << 1, l, mid, ql, qr);
71         if (qr > mid) query(o << 1 | 1, mid + 1, r, ql, qr);
72     }
73 } T;
74 
75 int main() {
76     int n, m;
77     scanf("%d%d", &n, &m);
78     rep(i, 1, n) scanf("%lf", &pi[i]), T.update(1, 1, n, i, pi[i]);
79     while (m--) {
80         int op;
81         scanf("%d", &op);
82         if (!op) {
83             int x, y; scanf("%d%d", &x, &y);
84             ans1 = 0, ans0 = 0, ans3[1] = ans3[2] = 0;
85             T.query(1, 1, n, x, y);
86             printf("%.2lf\n", ans1 + ans0 + pi[x - 1] * pi[x] + ans3[1]);
87         }
88         else {
89             double w; int x;
90             scanf("%d%lf", &x, &w);
91             pi[x] = w, T.update(1, 1, n, x, w);
92             if (x != n) T.update(1, 1, n, x + 1, pi[x + 1]);
93         }
94     }
95     return 0;
96 }