ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#203542 | #3566. T1 | snow_trace | 100 | 111ms | 3324kb | C++11 | 1.9kb | 2024-02-27 10:07:23 | 2024-02-27 13:03:15 |
answer
#include<bits/stdc++.h>
using namespace std;
#define int long long
const int mod = 998244353;
int n;
int a[100005];
int qp(int p,int q){
int ans = 1,pro = p%mod;
while(q){
if(q&1)ans = ans*pro%mod;
pro = pro*pro%mod;q>>=1;
}return ans;
}struct poly{
int k,b;
poly(){};
poly(int K,int B) : k(K%mod),b(B%mod){}
friend poly operator*(poly a,poly b){
poly c(0,0);
c.k = (a.b*b.k+a.k*b.b)%mod;
c.b = (a.b*b.b+a.k*b.k)%mod;
return c;
}
};
poly p[100005];
poly NTT(int l,int r){//最分治NTT的一集
// cout << l << " " << r << endl;
if(l>r)return poly(0,1);
if(l == r)return p[l];
int mid = l+r>>1;return NTT(l,mid)*NTT(mid+1,r);
}
signed main(){
ios::sync_with_stdio(0);cin.tie(0);
cin>>n;for(int i = 1;i<=n;i++)cin >> a[i];
int ans = 0;
for(int i = 31;i>=0;i--){
vector<int>pp;
for(int j = 1;j<=n;j++){
if(a[j]>>i&1)pp.push_back(a[j]);
}int pro = 1,tot =0 ;
for(int j = 1;j<=n;j++){
if(a[j]>>i&1)tot++;
else pro = pro*(a[j]+1)%mod;
}for(int j = 0;j<pp.size();j++){
p[j+1].k = 1+pp[j]-(1ll<<i);
p[j+1].b = (1ll<<i);
//cout << p[j+1].k << " " << p[j+1].b << endl;
}
auto res = NTT(1,pp.size());
// cout << " " << pp.size() << " " << res.b << endl;
ans = ans+(pro*res.b%mod*qp(1ll<<i,mod-2));ans%=mod;
for(int j = 1;j<=n;j++)if(a[j]>>i&1){
a[j]-=(1ll<<i);pro = pro*(a[j]+1)%mod;
}
if(tot%2 == 0)ans = ans-pro*qp(1ll<<i,mod-2);;ans%=mod;ans+=mod;ans%=mod;
if(tot%2 == 1)break;
}cout << ans << endl;
return 0;
}/*
一般来说,如果你看到 998244353,又看到 n = 1e5,又看到 2s,那大概就又是一个毒瘤题。
由特殊性质的启发可以想到。
如果最高位有个元素没被消掉就拿他干点事情。
生成函数 \prod (ai*x+bi)
但是我们只需要求偶数项之和。
于是我们上分治 NTT(确信)
分治,然后算二项式的乘法。
这题真是令人感到难绷。
原来不分治也是对的。
*/
Details
小提示:点击横条可展开更详细的信息
Subtask #1:
score: 10
Accepted
Test #1:
score: 10
Accepted
time: 0ms
memory: 1272kb
input:
10 3 5 0 1 0 3 5 4 2 5
output:
13248
result:
ok 1 number(s): "13248"
Subtask #2:
score: 10
Accepted
Test #2:
score: 10
Accepted
time: 24ms
memory: 3232kb
input:
100000 25 0 7 1 42 27 29 17 26 23 11 4 24 40 31 10 6 16 26 26 46 27 7 32 9 33 17 15 4 44 36 29 19 17...
output:
460821675
result:
ok 1 number(s): "460821675"
Subtask #3:
score: 10
Accepted
Test #3:
score: 10
Accepted
time: 23ms
memory: 3232kb
input:
100000 14 25 9 27 9 33 48 28 10 29 28 39 50 33 8 18 38 0 34 25 13 7 30 48 13 39 14 11 40 8 32 3 7 16...
output:
885189946
result:
ok 1 number(s): "885189946"
Subtask #4:
score: 10
Accepted
Test #4:
score: 10
Accepted
time: 13ms
memory: 2040kb
input:
100000 999998102 402961903 309346107 445160702 274308544 145846539 341002420 77841978 313436667 3206...
output:
714756233
result:
ok 1 number(s): "714756233"
Subtask #5:
score: 10
Accepted
Test #5:
score: 10
Accepted
time: 13ms
memory: 2044kb
input:
100000 999998479 400795186 127605328 439009686 279338791 222344190 32214702 347490239 390113609 1737...
output:
885251777
result:
ok 1 number(s): "885251777"
Subtask #6:
score: 10
Accepted
Test #6:
score: 10
Accepted
time: 13ms
memory: 2044kb
input:
100000 999980995 341927799 474797020 355936070 215296904 77682610 413850993 194378088 233473841 3566...
output:
99729538
result:
ok 1 number(s): "99729538"
Subtask #7:
score: 10
Accepted
Test #7:
score: 10
Accepted
time: 1ms
memory: 1320kb
input:
2000 540706819 309629779 17707890 194083691 334726587 456162964 498417390 246765617 957682339 604730...
output:
800177499
result:
ok 1 number(s): "800177499"
Subtask #8:
score: 10
Accepted
Test #8:
score: 10
Accepted
time: 0ms
memory: 1320kb
input:
2000 101722906 988313572 550840902 777765553 778991206 95817204 989809443 357040014 425595004 794587...
output:
443206431
result:
ok 1 number(s): "443206431"
Subtask #9:
score: 10
Accepted
Test #9:
score: 10
Accepted
time: 19ms
memory: 3320kb
input:
100000 327468559 836395032 98737045 14714567 147268924 355455125 829199457 117664948 79547712 117935...
output:
252529800
result:
ok 1 number(s): "252529800"
Subtask #10:
score: 10
Accepted
Test #10:
score: 10
Accepted
time: 5ms
memory: 3324kb
input:
100000 334373908 573410989 584461609 757523993 595819683 93095595 866600961 552146722 657326632 1804...
output:
633437866
result:
ok 1 number(s): "633437866"