#include<iostream>
#include<stack>
#include<map>
#include<vector>
#include<string>
#include<unordered_map>
#include <queue>
#include<cstring>
#include<limits.h>
#include <cassert>
#include<cmath>
#include<set>
#include<algorithm>
#include <iomanip>
#include<numeric> //gcd(a,b)
#include<bitset>
#include <cstdlib>
#include <cstdint>
using namespace std;
#define ll long long
#define f first
//#define endl "\n"
#define s second
#define pii pair<int,int>
#define ppii pair<int,pii>
#define vi vector<int>
#define pb push_back
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define F(n) for(int i=0;i<n;i++)
#define lb lower_bound
#define ub upper_bound
#define fastio ios::sync_with_stdio(false);cin.tie(NULL);
#pragma GCC optimize ("03,unroll-loops")
using namespace std;
#define int long long
#define double long double
const int mod=998244353,mxn=3e5+5,lg=60,inf=1e18,minf=-1e18,Mxn=1e6+50000;
int dp1[Mxn+10],dp0[Mxn+10],cost[Mxn+10],rdp0[mxn+10];
int32_t main(){
fastio
int n,q;cin>>n>>q;
string a;cin>>a;
for(int i=0;i<(1LL<<n);i++)cost[i]=dp1[i]=dp0[i]=(a[i]-'0');
for(int i=0;i<n;i++)for(int j=0;j<(1LL<<n);j++)if(j&(1LL<<i))dp1[j]+=dp1[j^(1LL<<i)];
for(int i=0;i<n;i++)for(int j=(1LL<<n)-1;j>=0;j--)if(!(j&(1LL<<i)))dp0[j]+=dp0[j+(1LL<<i)];
int root=sqrt(n);
root++;
auto change=[&](int x){
int k=0;
for(int i=0;i<n;i++)if(!(x&(1LL<<i)))k+=1LL<<i;
return k;
};
//for(int i=0;i<(1LL<<n);i++)rdp0[change(i)]=dp0[i];
while(q--){
cin>>a;
reverse(all(a));
int x=0,y=0;
vector<int>o,z,c;
int bro=0;
for(int i=0;i<n;i++){
if(a[i]=='1')x+=(1LL<<i),o.pb(i),y+=(1LL<<i);
else if(a[i]=='?')c.pb(i),bro+=(1LL<<i),x+=(1LL<<i);
else z.pb(i);
}
int m=0;
int ans=0,g;
if(c.size()<=root){//5 tl
m=c.size();
for(int i=0;i<(1LL<<m);i++){
for(int j=0;j<m;j++)if((i&(1LL<<j))==0)x-=(1LL<<c[j]);
ans+=cost[x];
for(int j=0;j<m;j++)if((i&(1LL<<j))==0)x+=(1LL<<c[j]);
}
}
else if(o.size()<z.size()){
ans=dp1[x];
m=o.size();
for(int i=0;i<(1LL<<m)-1;i++){
int cnt=0;
for(int j=0;j<m;j++)if((i&(1LL<<j))==0)x-=(1LL<<o[j]),cnt++;
if(cnt%2)ans-=dp1[x];
else ans+=dp1[x];
for(int j=0;j<m;j++)if((i&(1LL<<j))==0)x+=(1LL<<o[j]);
}
/*
*/
}
else{
ans=dp0[y];
m=z.size();
for(int i=1;i<(1LL<<m);i++){
int cnt=0;
for(int j=0;j<m;j++)if((i&(1LL<<j)))y+=(1LL<<z[j]),cnt++;
if(cnt%2)ans-=dp0[y];
else ans+=dp0[y];
for(int j=0;j<m;j++)if((i&(1LL<<j)))y-=(1LL<<z[j]);
}
}
cout<<ans<<'\n';
//return 0;
//cout<<dp1[x]<<" "<<dp0[y]<<'\n';
}
}
/*
if cnt? <= sqrt(m) we can do (2^4)? bruteforce (maybe even 5)
else we can do sos dp and somehow remove the overcount
we can turn all ? into one and get sos of that bit
overcount when "1" bit that is originaly turned on switch to 0(for subset)
we can switch them off and subtract from the original answer so it cost 2^(cnt1){
we need to somehow do pie
starting from original answer-> if we turn off 1 bit
ans-(turn of x bit)-(turn of y bit)+(turn of x and y bit)
so if cnt%2==1 then we subtract
else we add back in
}
cnt1 can be at most 16,worst case is all 1 (2^16)
we can also do sos dp where 0 is now the "switchable" value
so if cnt0<cnt1 we take do from 0 dp else from 1
tc-> worst case q*(2^m)*m
pre com time is m*(2^m+1)
q*(x*(2^x)+(2^(m-x)/2))
*/
Compilation message
snake_escaping.cpp: In function 'int32_t main()':
snake_escaping.cpp:68:14: warning: comparison of integer expressions of different signedness: 'std::vector<long long int>::size_type' {aka 'long unsigned int'} and 'long long int' [-Wsign-compare]
68 | if(c.size()<=root){//5 tl
| ~~~~~~~~^~~~~~
snake_escaping.cpp:67:13: warning: unused variable 'g' [-Wunused-variable]
67 | int ans=0,g;
| ^
snake_escaping.cpp:49:7: warning: variable 'change' set but not used [-Wunused-but-set-variable]
49 | auto change=[&](int x){
| ^~~~~~
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
6488 KB |
Output is correct |
2 |
Correct |
1 ms |
6492 KB |
Output is correct |
3 |
Correct |
2 ms |
6492 KB |
Output is correct |
4 |
Correct |
2 ms |
6488 KB |
Output is correct |
5 |
Correct |
1 ms |
6492 KB |
Output is correct |
6 |
Correct |
1 ms |
6492 KB |
Output is correct |
7 |
Correct |
2 ms |
6492 KB |
Output is correct |
8 |
Correct |
1 ms |
6492 KB |
Output is correct |
9 |
Correct |
2 ms |
6492 KB |
Output is correct |
10 |
Correct |
2 ms |
6492 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
6488 KB |
Output is correct |
2 |
Correct |
1 ms |
6492 KB |
Output is correct |
3 |
Correct |
2 ms |
6492 KB |
Output is correct |
4 |
Correct |
2 ms |
6488 KB |
Output is correct |
5 |
Correct |
1 ms |
6492 KB |
Output is correct |
6 |
Correct |
1 ms |
6492 KB |
Output is correct |
7 |
Correct |
2 ms |
6492 KB |
Output is correct |
8 |
Correct |
1 ms |
6492 KB |
Output is correct |
9 |
Correct |
2 ms |
6492 KB |
Output is correct |
10 |
Correct |
2 ms |
6492 KB |
Output is correct |
11 |
Correct |
363 ms |
21308 KB |
Output is correct |
12 |
Correct |
395 ms |
20820 KB |
Output is correct |
13 |
Correct |
471 ms |
20092 KB |
Output is correct |
14 |
Correct |
481 ms |
20232 KB |
Output is correct |
15 |
Correct |
362 ms |
21260 KB |
Output is correct |
16 |
Correct |
481 ms |
20292 KB |
Output is correct |
17 |
Correct |
481 ms |
20560 KB |
Output is correct |
18 |
Correct |
254 ms |
22332 KB |
Output is correct |
19 |
Correct |
352 ms |
19284 KB |
Output is correct |
20 |
Correct |
419 ms |
21276 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
6488 KB |
Output is correct |
2 |
Correct |
1 ms |
6492 KB |
Output is correct |
3 |
Correct |
2 ms |
6492 KB |
Output is correct |
4 |
Correct |
2 ms |
6488 KB |
Output is correct |
5 |
Correct |
1 ms |
6492 KB |
Output is correct |
6 |
Correct |
1 ms |
6492 KB |
Output is correct |
7 |
Correct |
2 ms |
6492 KB |
Output is correct |
8 |
Correct |
1 ms |
6492 KB |
Output is correct |
9 |
Correct |
2 ms |
6492 KB |
Output is correct |
10 |
Correct |
2 ms |
6492 KB |
Output is correct |
11 |
Correct |
363 ms |
21308 KB |
Output is correct |
12 |
Correct |
395 ms |
20820 KB |
Output is correct |
13 |
Correct |
471 ms |
20092 KB |
Output is correct |
14 |
Correct |
481 ms |
20232 KB |
Output is correct |
15 |
Correct |
362 ms |
21260 KB |
Output is correct |
16 |
Correct |
481 ms |
20292 KB |
Output is correct |
17 |
Correct |
481 ms |
20560 KB |
Output is correct |
18 |
Correct |
254 ms |
22332 KB |
Output is correct |
19 |
Correct |
352 ms |
19284 KB |
Output is correct |
20 |
Correct |
419 ms |
21276 KB |
Output is correct |
21 |
Correct |
385 ms |
24108 KB |
Output is correct |
22 |
Correct |
413 ms |
24440 KB |
Output is correct |
23 |
Correct |
540 ms |
23428 KB |
Output is correct |
24 |
Correct |
623 ms |
23300 KB |
Output is correct |
25 |
Correct |
421 ms |
25124 KB |
Output is correct |
26 |
Correct |
607 ms |
23796 KB |
Output is correct |
27 |
Correct |
622 ms |
23636 KB |
Output is correct |
28 |
Correct |
265 ms |
26332 KB |
Output is correct |
29 |
Correct |
387 ms |
22100 KB |
Output is correct |
30 |
Correct |
415 ms |
24344 KB |
Output is correct |
31 |
Correct |
506 ms |
24144 KB |
Output is correct |
32 |
Correct |
579 ms |
24136 KB |
Output is correct |
33 |
Correct |
520 ms |
23164 KB |
Output is correct |
34 |
Correct |
646 ms |
23308 KB |
Output is correct |
35 |
Correct |
584 ms |
23636 KB |
Output is correct |
36 |
Correct |
269 ms |
22168 KB |
Output is correct |
37 |
Correct |
395 ms |
24304 KB |
Output is correct |
38 |
Correct |
397 ms |
22292 KB |
Output is correct |
39 |
Correct |
551 ms |
23856 KB |
Output is correct |
40 |
Correct |
624 ms |
23244 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
6488 KB |
Output is correct |
2 |
Correct |
1 ms |
6492 KB |
Output is correct |
3 |
Correct |
2 ms |
6492 KB |
Output is correct |
4 |
Correct |
2 ms |
6488 KB |
Output is correct |
5 |
Correct |
1 ms |
6492 KB |
Output is correct |
6 |
Correct |
1 ms |
6492 KB |
Output is correct |
7 |
Correct |
2 ms |
6492 KB |
Output is correct |
8 |
Correct |
1 ms |
6492 KB |
Output is correct |
9 |
Correct |
2 ms |
6492 KB |
Output is correct |
10 |
Correct |
2 ms |
6492 KB |
Output is correct |
11 |
Correct |
49 ms |
28592 KB |
Output is correct |
12 |
Correct |
50 ms |
28656 KB |
Output is correct |
13 |
Correct |
70 ms |
28404 KB |
Output is correct |
14 |
Correct |
95 ms |
28404 KB |
Output is correct |
15 |
Correct |
55 ms |
28660 KB |
Output is correct |
16 |
Correct |
129 ms |
28688 KB |
Output is correct |
17 |
Correct |
117 ms |
28892 KB |
Output is correct |
18 |
Correct |
46 ms |
28684 KB |
Output is correct |
19 |
Correct |
56 ms |
28492 KB |
Output is correct |
20 |
Correct |
56 ms |
28672 KB |
Output is correct |
21 |
Correct |
67 ms |
28656 KB |
Output is correct |
22 |
Correct |
90 ms |
28616 KB |
Output is correct |
23 |
Correct |
61 ms |
28388 KB |
Output is correct |
24 |
Correct |
126 ms |
28604 KB |
Output is correct |
25 |
Correct |
104 ms |
28400 KB |
Output is correct |
26 |
Correct |
42 ms |
28656 KB |
Output is correct |
27 |
Correct |
51 ms |
28660 KB |
Output is correct |
28 |
Correct |
54 ms |
28436 KB |
Output is correct |
29 |
Correct |
72 ms |
28404 KB |
Output is correct |
30 |
Correct |
153 ms |
28564 KB |
Output is correct |
31 |
Correct |
59 ms |
28404 KB |
Output is correct |
32 |
Correct |
121 ms |
28404 KB |
Output is correct |
33 |
Correct |
132 ms |
28424 KB |
Output is correct |
34 |
Correct |
39 ms |
28404 KB |
Output is correct |
35 |
Correct |
89 ms |
28616 KB |
Output is correct |
36 |
Correct |
86 ms |
28404 KB |
Output is correct |
37 |
Correct |
92 ms |
28428 KB |
Output is correct |
38 |
Correct |
98 ms |
28472 KB |
Output is correct |
39 |
Correct |
87 ms |
28432 KB |
Output is correct |
40 |
Correct |
88 ms |
28632 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
6488 KB |
Output is correct |
2 |
Correct |
1 ms |
6492 KB |
Output is correct |
3 |
Correct |
2 ms |
6492 KB |
Output is correct |
4 |
Correct |
2 ms |
6488 KB |
Output is correct |
5 |
Correct |
1 ms |
6492 KB |
Output is correct |
6 |
Correct |
1 ms |
6492 KB |
Output is correct |
7 |
Correct |
2 ms |
6492 KB |
Output is correct |
8 |
Correct |
1 ms |
6492 KB |
Output is correct |
9 |
Correct |
2 ms |
6492 KB |
Output is correct |
10 |
Correct |
2 ms |
6492 KB |
Output is correct |
11 |
Correct |
363 ms |
21308 KB |
Output is correct |
12 |
Correct |
395 ms |
20820 KB |
Output is correct |
13 |
Correct |
471 ms |
20092 KB |
Output is correct |
14 |
Correct |
481 ms |
20232 KB |
Output is correct |
15 |
Correct |
362 ms |
21260 KB |
Output is correct |
16 |
Correct |
481 ms |
20292 KB |
Output is correct |
17 |
Correct |
481 ms |
20560 KB |
Output is correct |
18 |
Correct |
254 ms |
22332 KB |
Output is correct |
19 |
Correct |
352 ms |
19284 KB |
Output is correct |
20 |
Correct |
419 ms |
21276 KB |
Output is correct |
21 |
Correct |
385 ms |
24108 KB |
Output is correct |
22 |
Correct |
413 ms |
24440 KB |
Output is correct |
23 |
Correct |
540 ms |
23428 KB |
Output is correct |
24 |
Correct |
623 ms |
23300 KB |
Output is correct |
25 |
Correct |
421 ms |
25124 KB |
Output is correct |
26 |
Correct |
607 ms |
23796 KB |
Output is correct |
27 |
Correct |
622 ms |
23636 KB |
Output is correct |
28 |
Correct |
265 ms |
26332 KB |
Output is correct |
29 |
Correct |
387 ms |
22100 KB |
Output is correct |
30 |
Correct |
415 ms |
24344 KB |
Output is correct |
31 |
Correct |
506 ms |
24144 KB |
Output is correct |
32 |
Correct |
579 ms |
24136 KB |
Output is correct |
33 |
Correct |
520 ms |
23164 KB |
Output is correct |
34 |
Correct |
646 ms |
23308 KB |
Output is correct |
35 |
Correct |
584 ms |
23636 KB |
Output is correct |
36 |
Correct |
269 ms |
22168 KB |
Output is correct |
37 |
Correct |
395 ms |
24304 KB |
Output is correct |
38 |
Correct |
397 ms |
22292 KB |
Output is correct |
39 |
Correct |
551 ms |
23856 KB |
Output is correct |
40 |
Correct |
624 ms |
23244 KB |
Output is correct |
41 |
Correct |
49 ms |
28592 KB |
Output is correct |
42 |
Correct |
50 ms |
28656 KB |
Output is correct |
43 |
Correct |
70 ms |
28404 KB |
Output is correct |
44 |
Correct |
95 ms |
28404 KB |
Output is correct |
45 |
Correct |
55 ms |
28660 KB |
Output is correct |
46 |
Correct |
129 ms |
28688 KB |
Output is correct |
47 |
Correct |
117 ms |
28892 KB |
Output is correct |
48 |
Correct |
46 ms |
28684 KB |
Output is correct |
49 |
Correct |
56 ms |
28492 KB |
Output is correct |
50 |
Correct |
56 ms |
28672 KB |
Output is correct |
51 |
Correct |
67 ms |
28656 KB |
Output is correct |
52 |
Correct |
90 ms |
28616 KB |
Output is correct |
53 |
Correct |
61 ms |
28388 KB |
Output is correct |
54 |
Correct |
126 ms |
28604 KB |
Output is correct |
55 |
Correct |
104 ms |
28400 KB |
Output is correct |
56 |
Correct |
42 ms |
28656 KB |
Output is correct |
57 |
Correct |
51 ms |
28660 KB |
Output is correct |
58 |
Correct |
54 ms |
28436 KB |
Output is correct |
59 |
Correct |
72 ms |
28404 KB |
Output is correct |
60 |
Correct |
153 ms |
28564 KB |
Output is correct |
61 |
Correct |
59 ms |
28404 KB |
Output is correct |
62 |
Correct |
121 ms |
28404 KB |
Output is correct |
63 |
Correct |
132 ms |
28424 KB |
Output is correct |
64 |
Correct |
39 ms |
28404 KB |
Output is correct |
65 |
Correct |
89 ms |
28616 KB |
Output is correct |
66 |
Correct |
86 ms |
28404 KB |
Output is correct |
67 |
Correct |
92 ms |
28428 KB |
Output is correct |
68 |
Correct |
98 ms |
28472 KB |
Output is correct |
69 |
Correct |
87 ms |
28432 KB |
Output is correct |
70 |
Correct |
88 ms |
28632 KB |
Output is correct |
71 |
Correct |
536 ms |
52932 KB |
Output is correct |
72 |
Correct |
587 ms |
52852 KB |
Output is correct |
73 |
Correct |
1018 ms |
51376 KB |
Output is correct |
74 |
Correct |
1537 ms |
51856 KB |
Output is correct |
75 |
Correct |
704 ms |
43724 KB |
Output is correct |
76 |
Correct |
1906 ms |
50252 KB |
Output is correct |
77 |
Correct |
1796 ms |
52132 KB |
Output is correct |
78 |
Correct |
336 ms |
55792 KB |
Output is correct |
79 |
Correct |
557 ms |
49864 KB |
Output is correct |
80 |
Correct |
599 ms |
52860 KB |
Output is correct |
81 |
Correct |
903 ms |
52956 KB |
Output is correct |
82 |
Correct |
1421 ms |
51712 KB |
Output is correct |
83 |
Correct |
739 ms |
51112 KB |
Output is correct |
84 |
Execution timed out |
2066 ms |
51804 KB |
Time limit exceeded |
85 |
Halted |
0 ms |
0 KB |
- |