QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#767901 | #9489. 0100 Insertion | ReqCxmChtChr | AC ✓ | 1533ms | 37768kb | C++14 | 3.9kb | 2024-11-20 22:36:40 | 2024-11-20 22:36:44 |
Judging History
answer
#include<bits/stdc++.h>
//#pragma GCC optimize(3)
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/hash_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
#define int long long
#define ll long long
#define ull unsigned ll
#define db double
#define ldb long db
#define mp make_pair
#define fi first
#define se second
#define pii pair<int,int>
#define pbI push_back
#define inf 1e9
#define mdI int mid=(l+r)>>1
#define lowbit(x) (x&-x)
#define rep(a,b,c) for(int a=b;a<=c;a++)
#define MAXN 520
#define gint __int128
#define MOD 998244353
int qread(){
char o=getchar();int f=1,x=0;
for(;!isdigit(o);o=getchar())if(o=='-')f*=-1;
for(;isdigit(o);o=getchar())x=x*10+o-'0';
return f*x;
}
void chmx(int &x,int y){if(y>x)x=y;}
void chmi(int &x,int y){if(y<x)x=y;}
bool FLA;
namespace MathPart{
#define rep(a,b,c) for(int a=b;a<=c;a++)
#define vep(a,b,c) for(int a=b;a>=c;a--)
void exgcd(ll a,ll b,ll &x,ll &y){if(b==0){x=1,y=0;return;}exgcd(b,a%b,y,x);y-=(a/b)*x;}
ll inv(ll a,ll p=MOD){ll x,y;exgcd(a,p,x,y);return (x+p)%p;}
gint qp(ll a,ll b,ll p=MOD){gint rs=1,bs=a;while(b){if(b&1){rs=rs*bs%p;}bs=bs*bs%p;b>>=1;}return rs;}
ll fac[MAXN],ifac[MAXN];
void initF(ll n,ll p=MOD){
fac[0]=1;rep(i,1,n){fac[i]=fac[i-1]*i%p;}
ifac[n]=inv(fac[n],p);vep(i,n-1,0){ifac[i]=ifac[i+1]*(i+1)%p;}
}
ll C(ll n,ll m){if(n<m){return 0;}return fac[n]*ifac[m]%MOD*ifac[n-m]%MOD;}
ll CC(ll n,ll m,ll p=MOD){ll rs=1;rep(i,0,m-1){rs=rs*(n-i)%p*inv(i+1,MOD)%p;}return rs;}
ll S2OL(ll n,ll m){
ll rs=0,d=1,f=1;
for(ll k=0;k<=m;k++){
rs=(rs+f*C(m,k)*qp(m-k,n,MOD)%MOD+MOD)%MOD;
d=d*max(k,1ll)%MOD;f*=-1;
}return rs*inv(d,MOD)%MOD;
}
ll phi(ll a){ll rs=a,m=sqrt(a);
rep(i,2,m){if(a%i==0){rs=rs/i*(i-1);while(a%i==0){a/=i;}}}
if(a>1){rs=rs/a*(a-1);}return rs;
}
bool MR(ll pr){if(pr<2)return 0;if(pr==3)return 1;if(pr==2)return 1;
ll a=pr-1,b=0;while(!(a&1))a>>=1,b++;
for(int i=1;i<=8;++i){
ll x=rand()%(pr-2)+2,v=qp(x,a,pr),j;if(v==1||v==pr-1)continue;
for(j=0;j<b-1;j++){v=(gint)v*v%pr;if(v==pr-1)break;}
if(v!=pr-1)return 0;
}return 1;
}
}
//using namespace MathPart;
int dp[2][MAXN*2][MAXN*2][2];//i s_i max_{j=1}^i(s_i) [s_i=0/1]
int off=500;
int n;string S;
bool FLB;
signed main(){
cerr<<((&FLB)-(&FLA))/1024.0/1024<<endl;
cin>>n;cin>>S;
reverse(S.begin(),S.end());S=" "+S;
dp[0][off][off][0]=1;
rep(i,0,n-1){
bool s=i&1;
memset(dp[!s],0,sizeof(dp[!s]));
rep(j,0,off+off){
rep(k,j,off+off){
if(S[i+1]=='0'||S[i+1]=='?'){
if(j){
dp[!s][j-1][k][0]+=dp[s][j][k][0]+dp[s][j][k][1];
dp[!s][j][k][0]%=MOD;
}
}
if(S[i+1]=='1'||S[i+1]=='?'){
if(j+3<=2*off&&k>=j+2){
dp[!s][j+3][max(k,j+3)][1]+=dp[s][j][k][0];
dp[!s][j+3][max(k,j+3)][1]%=MOD;
}
}
}
}
}
int ans=0;
rep(i,0,2*off){ans+=dp[n&1][off][i][0];ans%=MOD;}cout<<ans;
}
/*
8
0??0?100
由判定性问题展开
处理01序列的经典方法:设定数码的权值,直观折线图
(找到对目前判定方法的反例:0010问题)
下文s表示前缀和
0=-1,1=+3
对于一个1他不能匹配因为他右边下不去,
翻转一下,左边下不去导致的,
充要条件:无相邻1,最后非1,和=0,每一个i处的1,存在一个j使得s_j=s_i-1(知其下降过程连续,实际上和最大值等价)
必要性:递归构造可得
充分性:取第一个最大的s_i(一定为1),由条件知s_{i-1}=s_i-3,s_{i-2}=s_i-2,找到如是j(j最小),s_{i+1}=s_i-1,s_{i+2}=s_i-2(最大性)
观察[j+1,i-1]平的,j+2向下(否则没有最小性),找到(j+1,j+2,i,i+1)这一组,随后可以删除、拼接、归纳
跳出区间dp套路
*/
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 24ms
memory: 37708kb
input:
8 0??0?100
output:
2
result:
ok "2"
Test #2:
score: 0
Accepted
time: 14ms
memory: 37584kb
input:
4 ?10?
output:
1
result:
ok "1"
Test #3:
score: 0
Accepted
time: 77ms
memory: 37620kb
input:
28 ???????????0???0??????1???0?
output:
2023
result:
ok "2023"
Test #4:
score: 0
Accepted
time: 11ms
memory: 37612kb
input:
4 ????
output:
1
result:
ok "1"
Test #5:
score: 0
Accepted
time: 16ms
memory: 37760kb
input:
8 11111111
output:
0
result:
ok "0"
Test #6:
score: 0
Accepted
time: 1385ms
memory: 37700kb
input:
500 ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????...
output:
870731023
result:
ok "870731023"
Test #7:
score: 0
Accepted
time: 1380ms
memory: 37640kb
input:
500 ???????????????????0???????????????????????????????????????0??????????????????????1???????????????????????????????????????00????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????1???????????????????????????????????...
output:
763641704
result:
ok "763641704"
Test #8:
score: 0
Accepted
time: 951ms
memory: 37708kb
input:
344 ?0???????????1???????0?0?????0?????????????0?0????0?0??1??0?????0??0???1?????0????00?????1?????1????????1?????10????0??????????1????0???1????????0???10?????1?0?0???1??????????0??0???1?0??00??0???????001????????1????1??????1?0????1??????????????????1????1????????????0???????????01?1??????0?0?????...
output:
273835616
result:
ok "273835616"
Test #9:
score: 0
Accepted
time: 409ms
memory: 37700kb
input:
152 ?1???1??????????????????00??????????0?????0????????0??1?????0????0????????0????010???????????????1??1??????0?10??1????0???????????????1?????0???1???????
output:
539361138
result:
ok "539361138"
Test #10:
score: 0
Accepted
time: 595ms
memory: 37760kb
input:
216 ???????1?????1??1????1???1?????????????0?1???????????????????????????????????????????????1?????????????????10???0???1???????????????????????1????????????0???????0??????0?????????1???????????????????????1?????????0???
output:
336079328
result:
ok "336079328"
Test #11:
score: 0
Accepted
time: 866ms
memory: 37640kb
input:
316 ??????00?????????????????????1??????????????????0?????????????????0??0??????0???1??1?????????0??????????????????????0?????????0?0?1??0?????1?1??????1?1?????????????????????????????????0??????????????????????10???????1???????????1?????????????1????1????????????0????????????????1????1???0??0??1???...
output:
919261244
result:
ok "919261244"
Test #12:
score: 0
Accepted
time: 865ms
memory: 37692kb
input:
340 ?0?001??1?0????1?????1???01?????????1??01??0???1???1?????????????0?1??????1??1?10??0????????10?????1????1?010???1?????????????1???????1????01???????1???????00???1?0?00??0????????00???0??????1??1?1?????10??1????0??1????1????0????????0????0??????00?0??00???1??001????????0?1?????????????????0???1??...
output:
743485908
result:
ok "743485908"
Test #13:
score: 0
Accepted
time: 1037ms
memory: 37768kb
input:
392 ??????0??????????10???????????????????????1????????1???????0???????????0??????????????101???????????????????????0??????????0??0??????????1?????1???????????????????1?0?????????????1???????????????????????1????????0???0?????1????????????????0??????1?????????????0????????????????0?????????????????1...
output:
213859453
result:
ok "213859453"
Test #14:
score: 0
Accepted
time: 264ms
memory: 37708kb
input:
96 ????????0??1??1??????????????????????????1?0?????0??????1?????????1?0?????00??????????1???1?????
output:
860127276
result:
ok "860127276"
Test #15:
score: 0
Accepted
time: 293ms
memory: 37608kb
input:
116 ???????????????????????????????01?1???????????????0?00????0?????????????????1?0?????????????????1???????????????00??
output:
717954632
result:
ok "717954632"
Test #16:
score: 0
Accepted
time: 759ms
memory: 37612kb
input:
280 ?????1????0??0??????1????????0????0?1?0????????00???0???????0????0???????????1?0?1???????????1?????10????1??????100??????????1?1?????01?1??????0????01??1???1?????0????????0?1?0???????????01??00??????1?????????????????1?1?????????1????????????????0????????????????????????0????????
output:
553679844
result:
ok "553679844"
Test #17:
score: 0
Accepted
time: 683ms
memory: 37704kb
input:
260 ????????0????0???????????????1???????0?00??0???????????????0??????0?????1?????????????????????????????????????0???????1????????0??????????????????????1???????????????????1?0????1???????00?0????10???????????0?1?10??????????????????0??0???????1???????1??1???????
output:
121486637
result:
ok "121486637"
Test #18:
score: 0
Accepted
time: 1379ms
memory: 37636kb
input:
500 ??0????1???1??????1?1??????????????????????????????????0??0??????????????????????1???????01????????0???0???????????????????????1????????1??????????????1????????0?1???0?????0???????????????????0??????????????1????????0???????0?0??????????????0???????1???????1??????????????????????????0????0??????...
output:
397451125
result:
ok "397451125"
Test #19:
score: 0
Accepted
time: 1324ms
memory: 37672kb
input:
500 ??????1???????????????????0????????????????????????0??????0???????????1??????????10???0???0?????????????1??1????????0??????1???????????00????????????0???????????????????1??0???0????0?????????????0?????????????????????????????????????0????0??????????1??????????????????????????????????????????????...
output:
248838567
result:
ok "248838567"
Test #20:
score: 0
Accepted
time: 1285ms
memory: 37676kb
input:
500 ?0??0????1???????????????????????????1????????????????????0????????1????????????????1????0?????????????1???????????1?0????????????????????0?????????????0????0????????????1????????1????????????????0???0?1???1???1???????????1?????1???0??????????1????????1?????1???0?1???????????1???????????????????...
output:
53824210
result:
ok "53824210"
Test #21:
score: 0
Accepted
time: 196ms
memory: 37684kb
input:
76 ????0????????0??0???1??0??????00?0????0???1??????1?0????0?1?????????????1???
output:
205686585
result:
ok "205686585"
Test #22:
score: 0
Accepted
time: 60ms
memory: 37644kb
input:
24 ?0?0?????0??????????????
output:
587
result:
ok "587"
Test #23:
score: 0
Accepted
time: 196ms
memory: 37756kb
input:
76 ?????0?????????????????0????????????????????????????1???0???????????????????
output:
83575746
result:
ok "83575746"
Test #24:
score: 0
Accepted
time: 75ms
memory: 37760kb
input:
28 00???0???0?0??0???0???0?????
output:
859
result:
ok "859"
Test #25:
score: 0
Accepted
time: 118ms
memory: 37704kb
input:
44 ?00??1???00??1???0??1?100??1?0???0??1???0???
output:
63
result:
ok "63"
Test #26:
score: 0
Accepted
time: 1140ms
memory: 37672kb
input:
444 ???0???0???????????????1?????1??????0?????1??????1??????????10?1???????????????????????????????1?1??00?0??0????0??????????1???????101?0????10??????????????0?0???????1???????????????1????????0?????????1????????????1???0??????????????????????????0??????1??????????0???10??1???????????01????????????...
output:
847293915
result:
ok "847293915"
Test #27:
score: 0
Accepted
time: 1352ms
memory: 37676kb
input:
484 ?????1?1???????????1?????1??????????0?1???????????1?????0?1???0000?1?1?0?00????1????0?0?00?????????????????????1????????1?01??????01??1?????0??????0???000?????????1????????0?1??01?????0???1???0?????1???0???????0?????1?1?0??0???????01????????0???1???0??0???0?????????????????1??????1???10??1010???...
output:
679474848
result:
ok "679474848"
Test #28:
score: 0
Accepted
time: 1259ms
memory: 37708kb
input:
456 ?????0???????????????0?????1???????0???1??????????????????1??????1?????????????1??????1??????????0??????????????1????????????????????1??????????1???0???0??1???1????????00??0?????1???0?????????????1?0??1??1?1???0???1????????????0???????????????0?0??0?????0????????01?????????????????????????????10...
output:
920943116
result:
ok "920943116"
Test #29:
score: 0
Accepted
time: 1436ms
memory: 37636kb
input:
484 ????????????????????????????????0????1???1???????1????????1?????????0?????1??1??????????????????????1???????01???????????????????1??1???????????????1?1?0?0??1????????1??1???????????????????????????0?????????????0?????????????1????0??????1?????????0?0??????????1????????????1??????????????????????...
output:
453361220
result:
ok "453361220"
Test #30:
score: 0
Accepted
time: 1253ms
memory: 37672kb
input:
448 ?1?01??1????01?10????1???0????????????10????0??????1????1??????1?????1?0??1????101?1????1??????????????0?????1???0???????01?0?1?1????1???1?01?????????????0?1???1???01????0???????????????1??????01?1??????1?1?1??0???0?????????1????????1??1?0?1?0???????????????1?????1???0?0?????0????0??0???????????...
output:
84175678
result:
ok "84175678"
Test #31:
score: 0
Accepted
time: 1397ms
memory: 37708kb
input:
480 ?0?????????????????????0???00???1???0?????1?????????1??????????1?????1????????0??????????1????0???10?????????1????1????0?????0???01??????????0?????0???0?????????0???????01??????????????0????????0?????1????1?0??0?0????????????????1???1??01????????????1????0??????0??????1??1???????????????????????...
output:
247404334
result:
ok "247404334"
Test #32:
score: 0
Accepted
time: 1533ms
memory: 37688kb
input:
492 ??????00??????0??0??????????1???1?1?010????????????????????00???1???0?????0???????1?????????0???????1?????????????1???10???0?????????????????0??????????????0??????1???0????0?0???0??100?0?????????1??1????1???????????1????1??0?????????00??????1??1??????1????01?1?0??????0???????1????????????1??0???...
output:
487405442
result:
ok "487405442"
Test #33:
score: 0
Accepted
time: 1225ms
memory: 37712kb
input:
456 ????1???????????1???1????0????????????????????????????????????1???????0?????1???1?1??????????????????????????1?????????1?00??????????10?0????????????1??????????1?0????????1?1?????????????????0??????0???????1???????????????????????????0????????0??????1??????????0??1???????????????????????????????...
output:
884555628
result:
ok "884555628"
Test #34:
score: 0
Accepted
time: 1222ms
memory: 37672kb
input:
460 ??????1????1??????????0??0?????????????????0?????0???????????1?????????????1???????????01???????0????????????0???0???????????????????????????1???0????0??????????0??0??????1????0???????????????01?????????????0???????????????????????????????1????0????0????1??????1???????1???0??????????????????????...
output:
244536851
result:
ok "244536851"
Test #35:
score: 0
Accepted
time: 1177ms
memory: 37608kb
input:
456 ???????1?1????????????????00??????????1??1?0???????0??????0??????????0??1?????0??1???0?1??1?1?1???00?10?0???01??????????????0???01?0??000?1????1????????0????1?1????1???01???0?????1?0??????????1???0???1?1??????????01???1?????0???????0?1????1???1?0??0????1????0?0??1????????????0???0?????0??????01?...
output:
890392505
result:
ok "890392505"
Extra Test:
score: 0
Extra Test Passed