题意
Sol
多年以后，我终于把这题的暴力打出来了qwq 好感动啊。。
刚开始的时候想的是：
设\(f[i][j]\)表示第\(i\)轮， 第\(j\)个人血量的期望值
转移的时候若要淦这个人，那么\(f[i][j] = (f[i - 1][j] + 1) * p + (f[i - 1][j]) * (1 - p)\)
然后发现自己傻逼了。。因为期望不能正着推。
考虑直接推概率，设\(t[k][i][j]\)表示第\(k\)轮，第\(i\)个人，血量为\(j\)的概率
这玩意儿是可以转移的，就是判一下这次打中了没有
第二问可以对每个点分别算答案，设\(g[i][j]\)表示除必须活着的人外，前\(i\)个人中，有\(j\)个活着的概率，背包转移一下
这样复杂度是\(O(qn + n^3)\)的
显然第二问看起来非常暴力，
标算的做法好像叫“退背包”，也就是从背包中删除一个元素
先不考虑某个元素必须存活，推一遍得到\(g[i][j]\)表示前\(i\)个人中，有\(j\)个存活的概率
考虑转移的式子，设\(ali[i]\)表示第\(i\)个人活着的概率
\(g[i][j] = g[i - 1][j - 1] * ali[i] + g[i - 1][j] * (1 - ali[i])\)
而我们要得到的实际上就是\(g[i-1][j]\)这一项
那么\(g[i - 1][j] = \frac{g[i][j] - g[i - 1][j - 1] * ali[i]}{1 - ali[i]}\)
倒着推一遍即可，注意当\(1 - ali[i] = 0\)的时候需要特判，此时\(g[i - 1][j] = g[i][j + 1]\)
70分
#include<bits/stdc++.h>
//#define int long long
using namespace std;
const int MAXN = 201, mod = 998244353;
int f[2][MAXN], g[MAXN][MAXN], t[2][MAXN][MAXN];
// f: expect
inline int read() {
char c = getchar(); int x = 0, f = 1;
while(c < '0' || c > '9') {if(c == '-') f = -1; c = getchar();}
while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
return x * f;
}
int N, a[MAXN], Q, em[MAXN];
int fp(int a, int p) {
int base = 1;
while(p) {
if(p & 1) base = 1ll * base * a % mod;
a = 1ll * a * a % mod; p >>= 1;
}
return base;
}
int inv(int a) {
return fp(a, mod - 2);
}
int add(int x, int y) {
if(x + y < 0) return x + y + mod;
else return x + y >= mod ? x + y - mod : x + y;
}
int mul(int x, int y) {
x = (x + mod) % mod; y = (y + mod) % mod;
return 1ll * x * y % mod;
}
int solve(int id, int o, int N) {//这里dp的时候不能直接表示有j个活着，必须表示除i之外有j个活着。。
memset(g, 0, sizeof(g));
g[0][0] = 1;
for(int i = 1; i <= N; i++) {
for(int j = 0; j <= N; j++) {
if(em[i] ^ id) {
g[i][j] = mul(g[i - 1][j], t[o][em[i]][0]);
if(j) g[i][j] = add(g[i][j], mul(g[i - 1][j - 1], 1 - t[o][em[i]][0]));
}
else g[i][j] = g[i - 1][j];
}
}
int ans = 0;
for(int i = 0; i < N; i++)
ans = add(ans, mul(mul(1 - t[o][id][0], g[N][i]), inv(i + 1)));
return ans;
}
signed main() {
// freopen("a.in", "r", stdin);
// freopen("b.out", "w", stdout);
N = read();
for(int i = 1; i <= N; i++) a[i] = read(), t[0][i][a[i]] = 1, f[0][i] = a[i];
Q = read();
int o = 1;
for(int i = 1; i <= Q; i++, o ^= 1) {
int opt = read();
memcpy(t[o], t[o ^ 1], sizeof(t[o]));
if(opt == 0) {//
int id = read(), u = read(), v = read(), p = 1ll * u * inv(v) % mod;
t[o][id][0] = add(t[o][id][0], mul(p, t[o][id][1]));
for(int j = 1; j <= a[id]; j++) t[o][id][j] = add(mul(p, t[o ^ 1][id][j + 1]), mul(1 - p, t[o ^ 1][id][j]));
} else if(opt == 1) {
int k = read(), cnt = 0;
for(int i = 1; i <= k; i++) em[++cnt] = read();
for(int i = 1; i <= k; i++) printf("%d ", solve(em[i], o, cnt)); puts("");
}
}
for(int i = 1; i <= N; i++) {
int ans = 0;
for(int j = 1; j <= a[i]; j++)
ans = add(ans, mul(j, t[o ^ 1][i][j]));
printf("%d ", ans);
}
return 0;
}
/*
*/
100分
#include<bits/stdc++.h>
//#define int long long
using namespace std;
const int MAXN = 201, mod = 998244353;
int f[2][MAXN], g[MAXN][MAXN], t[2][MAXN][MAXN];
// f: expect
inline int read() {
char c = getchar(); int x = 0, f = 1;
while(c < '0' || c > '9') {if(c == '-') f = -1; c = getchar();}
while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
return x * f;
}
int N, a[MAXN], Q, em[MAXN], ans[MAXN], ali[MAXN], tp[MAXN], Inv[MAXN];
int add(int x, int y) {
if(x + y < 0) return x + y + mod;
else return x + y >= mod ? x + y - mod : x + y;
}
int mul(int x, int y) {
x = (x + mod) % mod; y = (y + mod) % mod;
return 1ll * x * y % mod;
}
int fp(int a, int p) {
int base = 1;
while(p) {
if(p & 1) base = 1ll * base * a % mod;
a = 1ll * a * a % mod; p >>= 1;
}
return base;
}
int inv(int a) {
a = add(a, mod);
return fp(a, mod - 2);
}
void Pre(int o, int N) {
// memset(g, 0, sizeof(g));
g[0][0] = 1;
for(int i = 1; i <= N; i++) {
ali[i] = (1 - t[o][em[i]][0] + mod) % mod;//alive
for(int j = 0; j <= i; j++) {
g[i][j] = mul(g[i - 1][j], t[o][em[i]][0]);
if(j) g[i][j] = add(g[i][j], mul(g[i - 1][j - 1], ali[i]));
}
}
}
int solve(int id, int o, int N) {
//memset(tp, 0, sizeof(tp));
if(!ali[id]) return 0;
if(ali[id] == 1) {
for(int i = 1; i <= N; i++) tp[i - 1] = g[N][i];
} else {
int down = inv(1 - ali[id]);
tp[0] = mul(g[N][0], down);
for(int i = 1; i <= N; i++)
tp[i] = mul(g[N][i] - mul(tp[i - 1], ali[id]), down);
}
int ans = 0;
for(int i = 1; i <= N; i++)
ans = add(ans, mul(mul(ali[id], tp[i - 1]), Inv[i]));
return ans;
}
signed main() {
//freopen("faceless10.in", "r", stdin);
// freopen("b.out", "w", stdout);
N = read();
for(int i = 1; i <= N; i++) a[i] = read(), t[0][i][a[i]] = 1, f[0][i] = a[i], Inv[i] = inv(i);
Q = read();
int o = 1;
for(int i = 1; i <= Q; i++, o ^= 1) {
int opt = read();
memcpy(t[o], t[o ^ 1], sizeof(t[o]));
if(opt == 0) {//
int id = read(), u = read(), v = read(), p = 1ll * u * inv(v) % mod;
t[o][id][0] = add(t[o][id][0], mul(p, t[o][id][1]));
for(int j = 1; j <= a[id]; j++) t[o][id][j] = add(mul(p, t[o ^ 1][id][j + 1]), mul(1 - p, t[o ^ 1][id][j]));
} else if(opt == 1) {
int k = read();
for(int i = 1; i <= k; i++) em[i] = read();
Pre(o, k);
for(int i = k; i >= 1; i--) ans[i] = solve(i, o, k);
for(int i = 1; i <= k; i++) printf("%d ", ans[i]); puts("");
}
}
for(int i = 1; i <= N; i++) {
int ans = 0;
for(int j = 1; j <= a[i]; j++)
ans = add(ans, mul(j, t[o ^ 1][i][j]));
printf("%d ", ans);
}
return 0;
}
/*
*/