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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#548311 | #7605. Yet Another Mex Problem | six-floor-slip-liu | WA | 8ms | 25108kb | C++20 | 6.7kb | 2024-09-05 17:04:19 | 2024-09-05 17:04:20 |
Judging History
answer
#pragma GCC optimize(2)
#include<bits/stdc++.h>
#define forup(i,s,e) for(int i=(s),E123123123=(e);i<=E123123123;++i)
#define fordown(i,s,e) for(int i=(s),E123123123=(e);i>=E123123123;--i)
#define mem(a,b) memset(a,b,sizeof(a))
#ifdef DEBUG
#define msg(args...) fprintf(stderr,args)
#else
#define msg(...) void();
#endif
using namespace std;
using i64=long long;
using i128=__int128;
using pii=pair<int,i64>;
#define fi first
#define se second
#define mkp make_pair
#define gc getchar()
int read(){
int x=0,f=1;char c;
while(!isdigit(c=gc)) if(c=='-') f=-1;
while(isdigit(c)){x=(x<<1)+(x<<3)+(c^48);c=gc;}
return x*f;
}
#undef gc
const int N=2e5+5,B=650,T=310;
i64 inf=1e18;
int n,m,a[N];
i64 sum[N];
int L[T],R[T],blg[N];
deque<pii> conv[T];
i128 cross(pii a,pii b){
return a.fi*b.se-a.se*b.fi;
}
pii operator -(const pii a,const pii b){
return mkp(a.fi-b.fi,a.se-b.se);
}
bool slp(pii a,pii b,pii c){
return cross(b-a,c-b)<=0;
}
bool slp(pii a,pii b,i64 k){
return (b.se-a.se)<=(i128)(b.fi-a.fi)*k;
}
i64 dp[N];
int mex[N],tag[T];
i64 mxv[T][N];
void work(int pl,int pr,int ql,int qr,int b){
if(ql>qr) return;
if(pl==pr){
forup(i,ql,qr){
mxv[b][i]=-sum[pl]*i+dp[pl];
}
return;
}
int mid=(ql+qr)>>1,p=0;
i64 val=-inf;
forup(i,pl,pr){
if(-sum[i]*mid+dp[i]>val){
p=i;
val=-sum[i]*mid+dp[i];
}
}
mxv[b][mid]=val;
work(pl,p,mid+1,qr,b);work(p,pr,ql,mid-1,b);
}
void getconv(int j){
if(~tag[j]){
forup(k,L[j],R[j]){
mex[k]=tag[j];
}
tag[j]=-1;
}
deque<pii> &q=conv[j];
q.clear();
vector<pii> vv;
fordown(k,R[j],L[j]){
pii nw;
nw.fi=mex[k];nw.se=mex[k]*sum[k]-dp[k];
vv.push_back(nw);
}
sort(vv.begin(),vv.end(),[&](pii a,pii b){if(a.fi!=b.fi)return a.fi<b.fi;return a.se<b.se;});
for(auto i:vv){
if(q.size()&&i.fi==q.back().fi) continue;
while(q.size()>2&&slp(q[q.size()-2],q[q.size()-1],i)) q.pop_back();
q.push_back(i);
}
}
int tt[N],m0,lst[N],pp[N];
vector<pair<pii,int> > modi[N];
map<pii,int> odt;
using mit=map<pii,int>::iterator;
mit split(int x){
mit it=odt.lower_bound(mkp(x,0));
if(it->fi.fi==x) return it;
--it;
int l=it->fi.fi,r=it->fi.se,c=it->se;
odt.erase(it);
odt.insert(mkp(mkp(l,x-1),c));
return odt.insert(mkp(mkp(x,r),c)).fi;
}
signed main(){
n=read();m=read();
forup(i,1,n){
a[i]=read();
sum[i]=sum[i-1]+a[i];
pp[i]=lst[a[i]];
lst[a[i]]=i;
}
int t=n/B;
forup(i,1,t){
L[i]=R[i-1]+1;R[i]=i*B;
forup(j,L[i],R[i]) blg[j]=i;
}
if(R[t]!=n){
++t;
L[t]=R[t-1]+1;R[t]=n;
forup(j,L[t],R[t]) blg[j]=t;
}
forup(i,1,t) tag[i]=-1;
fordown(i,n,0){
mex[i]=mex[i+1];
while(tt[mex[i]]) ++mex[i];
++tt[a[i]];
}
forup(i,0,n) tt[i]=0;
int lpos=0;
forup(i,1,n){
if(mex[i]!=mex[i-1]){
odt.insert(mkp(mkp(lpos,i-1),mex[i-1]));
lpos=i;
}
}
// forup(i,0,n){
// msg("%d ",mex[i]);
// }msg("|\n");
odt.insert(mkp(mkp(lpos,n),mex[n]));
fordown(i,n,1){
mit st=split(pp[i]);
int r=pp[i]-1;
for(mit it=st;it!=odt.end()&&it->se>=a[i];odt.erase(prev(++it))){
modi[i].push_back(*it);
r=it->fi.se;
}
if(r>=pp[i])odt.insert(mkp(mkp(pp[i],r),a[i]));
mex[i]=0;
}
mex[0]=0;
forup(i,1,n){
++tt[a[i]];
while(tt[m0]) ++m0;
dp[i]=0;
if(i<=m){
dp[i]=max(dp[i],m0*sum[i]);
}
vector<int> sv;
for(auto j:modi[i]){
int l=j.fi.fi,r=j.fi.se,c=j.se;
if(r==0) continue;
if(l==0) l=1;
if(blg[r]==blg[l]){
if(~tag[blg[l]]){
int p=blg[l];
forup(k,L[p],R[p]) mex[k]=tag[p];
tag[p]=-1;
}
forup(k,l,r){
mex[k]=c;
}
sv.push_back(blg[l]);
}else{
if(~tag[blg[l]]){
int p=blg[l];
forup(k,L[p],R[p]) mex[k]=tag[p];
tag[p]=-1;
}
if(~tag[blg[r]]){
int p=blg[r];
forup(k,L[p],R[p]) mex[k]=tag[p];
tag[p]=-1;
}
forup(k,l,R[blg[l]]) mex[k]=c;
forup(k,L[blg[r]],r) mex[k]=c;
sv.push_back(blg[l]);sv.push_back(blg[r]);
forup(j,blg[l]+1,blg[r]-1) tag[j]=c;
}
}
// forup(j,1,n){
// int mm=mex[j];
// if(~tag[blg[j]]) mm=tag[blg[j]];
// msg("%d ",mm);
// }msg("|");
fordown(j,i-1,max(L[blg[i]],i-m)){
int mm=mex[j];
if(~tag[blg[j]]) mm=tag[blg[j]];
dp[i]=max(dp[i],dp[j]+mm*(sum[i]-sum[j]));
}
sort(sv.begin(),sv.end());
sv.erase(unique(sv.begin(),sv.end()),sv.end());
for(auto j:sv){
getconv(j);
}
if(i-m>=1&&blg[i]!=blg[i-m]){
fordown(j,blg[i]-1,blg[i-m]+1){
if(~tag[j]){
dp[i]=max(dp[i],tag[j]*sum[i]+mxv[j][tag[j]]);
// msg("[%d]A %d %d %d %lld|%lld\n",i,L[j],R[j],tag[j],mxv[j][tag[j]],tag[j]*sum[i]+mxv[j][tag[j]]);
}else{
while(conv[j].size()>=2&&slp(conv[j][0],conv[j][1],sum[i])) conv[j].pop_front();
dp[i]=max(dp[i],conv[j].front().fi*sum[i]-conv[j].front().se);
// if(i==10){
// for(auto k:conv[j]){
// msg("(%d,%d,%lld)",k.fi,k.se,k.fi*sum[i]-k.se);
// }
// }
// msg("[%d]B %d %d %d %lld|%lld(%d)\n",i,L[j],R[j],conv[j].front().fi,-conv[j].front().se,conv[j].front().fi*sum[i]-conv[j].front().se,(int)conv[j].size());
}
}
fordown(j,R[blg[i-m]],i-m){
int mm=mex[j];
if(~tag[blg[j]]) mm=tag[blg[j]];
dp[i]=max(dp[i],dp[j]+mm*(sum[i]-sum[j]));
}
}
if(i==R[blg[i]]){
work(L[blg[i]],R[blg[i]],0,n,blg[i]);
getconv(blg[i]);
}
// msg("{%d %lld}\n",i,dp[i]);
}
// msg("|\n");
printf("%lld\n",dp[n]);
}
/*
13 7
6 9 0 12 6 1 9 0 3 4 6 9 12
*/
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 2ms
memory: 12192kb
input:
5 3 3 4 0 0 3
output:
10
result:
ok 1 number(s): "10"
Test #2:
score: 0
Accepted
time: 0ms
memory: 10144kb
input:
8 4 0 1 2 0 3 1 4 1
output:
26
result:
ok 1 number(s): "26"
Test #3:
score: 0
Accepted
time: 2ms
memory: 12132kb
input:
10 5 0 2 0 1 2 1 0 2 2 1
output:
33
result:
ok 1 number(s): "33"
Test #4:
score: 0
Accepted
time: 2ms
memory: 14244kb
input:
20 10 3 1 3 2 3 3 0 1 3 0 2 3 3 3 3 1 3 0 0 3
output:
160
result:
ok 1 number(s): "160"
Test #5:
score: 0
Accepted
time: 0ms
memory: 12068kb
input:
30 10 14 15 10 1 14 1 8 0 12 8 6 15 1 8 9 12 15 10 11 12 7 10 10 3 3 10 8 14 13 13
output:
172
result:
ok 1 number(s): "172"
Test #6:
score: 0
Accepted
time: 0ms
memory: 12172kb
input:
40 3 0 4 2 4 3 1 5 5 2 3 4 2 1 1 1 5 5 4 1 3 3 0 1 0 2 0 1 4 2 1 5 3 0 4 0 0 0 5 3 3
output:
51
result:
ok 1 number(s): "51"
Test #7:
score: 0
Accepted
time: 0ms
memory: 10432kb
input:
50 20 29 6 30 26 8 11 22 26 24 8 30 25 19 12 28 19 28 4 13 9 2 23 30 15 21 5 30 5 19 17 25 29 2 28 20 16 0 4 26 23 22 30 3 25 29 5 29 24 11 27
output:
378
result:
ok 1 number(s): "378"
Test #8:
score: 0
Accepted
time: 0ms
memory: 12120kb
input:
80 15 2 13 20 11 12 10 19 17 3 7 10 2 14 11 9 17 19 11 17 15 10 18 11 11 14 5 20 8 8 12 13 17 14 19 11 20 13 2 12 2 19 12 6 7 3 4 11 16 1 12 4 16 17 4 1 2 5 11 17 12 13 7 8 12 2 4 15 20 18 1 1 13 1 14 6 5 20 12 12 11
output:
0
result:
ok 1 number(s): "0"
Test #9:
score: 0
Accepted
time: 1ms
memory: 10076kb
input:
100 30 41 50 33 22 1 34 7 14 31 44 46 49 49 23 33 12 9 41 25 23 22 1 49 45 45 8 10 49 37 23 48 17 32 44 38 21 29 27 23 27 47 44 6 12 7 2 18 12 9 43 20 26 26 8 14 25 18 48 2 41 49 7 48 38 10 45 34 27 17 12 1 19 9 29 50 13 25 21 9 13 26 15 6 9 5 13 47 30 26 17 40 0 21 6 25 24 22 31 43 16
output:
1308
result:
ok 1 number(s): "1308"
Test #10:
score: 0
Accepted
time: 2ms
memory: 12128kb
input:
200 30 1 26 8 2 6 36 43 49 15 48 39 7 12 18 28 46 13 6 24 17 43 44 31 17 30 5 40 19 13 24 26 1 23 39 34 29 28 2 22 23 32 21 32 5 38 11 18 10 15 14 16 7 40 40 35 30 8 3 46 25 36 50 13 37 16 42 39 9 24 5 8 2 15 17 24 35 39 26 5 24 39 23 47 17 23 49 21 30 36 46 26 15 0 24 23 25 12 16 12 18 42 30 20 0 5...
output:
3389
result:
ok 1 number(s): "3389"
Test #11:
score: 0
Accepted
time: 1ms
memory: 10388kb
input:
300 30 39 28 33 6 10 36 27 31 1 1 9 41 27 39 48 30 43 49 0 11 39 36 15 40 43 28 18 15 17 23 4 9 37 32 5 34 3 4 45 44 18 24 6 23 18 21 40 7 18 38 35 14 5 44 4 10 25 34 14 8 23 43 28 11 22 13 44 16 30 49 40 13 21 32 50 30 29 31 27 35 1 30 10 49 42 33 46 30 47 48 13 5 5 41 22 3 26 26 33 20 34 41 46 27 ...
output:
6636
result:
ok 1 number(s): "6636"
Test #12:
score: 0
Accepted
time: 2ms
memory: 10104kb
input:
400 30 25 30 7 36 38 37 10 15 37 6 4 49 42 34 43 13 46 40 1 6 35 29 50 13 30 23 48 12 43 23 32 44 28 28 1 41 2 31 44 40 5 1 6 17 50 5 40 5 48 36 32 47 20 24 25 42 17 40 8 43 9 10 43 34 30 36 48 48 37 18 21 23 26 20 24 2 44 10 22 46 38 12 50 4 9 17 19 30 6 25 1 20 33 33 21 6 15 11 27 22 2 25 22 30 8 ...
output:
5312
result:
ok 1 number(s): "5312"
Test #13:
score: 0
Accepted
time: 0ms
memory: 10372kb
input:
500 30 11 7 6 40 43 14 47 49 22 9 25 32 6 4 12 48 25 31 2 26 30 46 10 36 43 46 2 34 45 48 11 28 43 22 47 47 1 32 41 36 41 3 31 8 31 14 12 2 2 8 0 30 34 5 46 46 6 20 25 27 46 3 34 8 36 33 27 4 19 10 3 32 33 9 49 24 9 15 18 6 0 20 13 11 28 1 18 30 18 4 12 34 39 50 20 35 30 47 46 24 46 36 49 34 21 10 7...
output:
9118
result:
ok 1 number(s): "9118"
Test #14:
score: 0
Accepted
time: 0ms
memory: 12184kb
input:
600 30 49 8 31 19 46 14 31 32 33 39 20 15 46 25 6 32 2 48 28 20 26 39 44 9 5 43 31 30 23 47 39 10 33 42 44 3 26 7 15 6 28 31 5 2 11 24 11 1 6 6 21 10 25 36 16 26 23 27 19 10 33 47 49 7 43 5 32 37 24 3 9 17 39 49 24 20 50 20 15 18 12 27 3 43 46 36 43 31 28 32 50 50 44 43 19 13 20 6 15 26 14 45 25 11 ...
output:
9497
result:
ok 1 number(s): "9497"
Test #15:
score: 0
Accepted
time: 2ms
memory: 12480kb
input:
700 200 190 11 82 65 81 32 130 4 124 52 155 181 166 29 44 49 187 134 155 130 127 17 76 156 59 155 171 194 110 2 102 122 48 191 31 25 83 154 184 56 38 175 50 190 162 191 116 198 170 173 160 177 184 194 195 64 120 27 154 192 96 160 183 196 76 109 15 81 9 189 120 55 42 17 192 20 100 53 29 197 181 152 1...
output:
142372
result:
ok 1 number(s): "142372"
Test #16:
score: 0
Accepted
time: 3ms
memory: 16368kb
input:
800 200 197 112 65 12 115 42 97 158 105 122 140 175 154 63 192 103 43 87 11 114 164 35 179 101 171 13 104 179 185 78 96 75 93 19 191 108 136 161 152 183 123 199 99 197 147 185 82 112 6 157 178 180 200 47 95 15 153 71 89 172 182 98 187 19 129 126 59 166 2 75 135 86 64 37 58 64 148 195 45 165 125 115 ...
output:
193511
result:
ok 1 number(s): "193511"
Test #17:
score: 0
Accepted
time: 0ms
memory: 10232kb
input:
900 200 27 187 75 160 123 52 39 137 85 65 149 67 65 122 140 57 101 39 143 200 100 153 57 47 7 172 62 140 34 153 91 4 61 148 51 165 64 92 119 10 183 97 48 2 58 53 48 1 43 117 71 84 115 176 96 192 109 14 124 51 168 137 191 168 182 143 4 50 71 162 75 16 86 158 50 84 120 60 137 158 69 53 32 24 59 94 178...
output:
387825
result:
ok 1 number(s): "387825"
Test #18:
score: 0
Accepted
time: 0ms
memory: 12468kb
input:
1000 500 120 156 148 83 1 52 17 33 164 176 165 3 66 161 99 132 190 83 124 139 172 30 67 87 132 61 36 8 116 128 162 151 166 24 84 160 52 180 80 120 36 82 97 159 0 83 60 45 195 47 186 166 91 191 88 146 167 133 147 38 126 182 82 23 0 31 70 8 77 118 85 50 55 144 56 115 34 58 57 13 89 132 37 6 11 105 187...
output:
1033863
result:
ok 1 number(s): "1033863"
Test #19:
score: 0
Accepted
time: 0ms
memory: 14684kb
input:
2000 200 39 181 151 81 34 229 56 147 86 128 55 47 211 141 215 97 28 16 235 144 172 198 92 48 226 86 113 233 119 81 123 222 129 200 61 21 246 55 6 66 65 2 5 10 109 239 236 164 185 98 3 236 123 21 131 125 46 235 67 83 205 214 243 111 173 99 2 240 159 66 80 211 96 185 167 187 218 38 105 194 199 57 33 1...
output:
399183
result:
ok 1 number(s): "399183"
Test #20:
score: 0
Accepted
time: 8ms
memory: 20536kb
input:
3000 600 92 85 85 10 57 53 30 1 89 14 70 26 72 73 14 70 30 58 50 78 4 75 79 48 73 40 88 92 5 83 21 57 6 16 30 80 9 76 42 81 17 94 24 72 76 67 85 85 17 68 21 1 14 68 41 86 74 53 73 60 30 70 63 47 100 92 45 67 22 14 69 31 26 56 53 30 43 69 62 52 39 10 47 17 72 93 5 65 32 41 69 88 41 2 14 46 81 49 65 1...
output:
14762368
result:
ok 1 number(s): "14762368"
Test #21:
score: 0
Accepted
time: 4ms
memory: 20668kb
input:
4000 100 1073 699 498 1797 203 458 1112 1140 1749 1900 725 1926 579 396 1711 183 1673 300 1551 370 411 1926 1712 1191 411 54 1170 1324 551 860 68 1864 564 684 766 1300 1715 1849 303 1649 1375 1603 1885 605 403 687 1702 500 1801 1173 1842 443 125 405 1711 1951 1692 671 1983 1247 1451 1279 1075 1230 6...
output:
213208
result:
ok 1 number(s): "213208"
Test #22:
score: 0
Accepted
time: 0ms
memory: 20688kb
input:
5000 400 288 870 939 422 710 726 995 841 2 582 912 28 195 718 252 721 488 416 228 56 507 269 967 48 651 108 405 14 430 319 322 236 510 217 290 808 903 699 960 550 305 282 441 667 825 24 474 649 856 171 284 222 401 39 627 443 276 861 759 62 553 945 243 38 439 452 956 159 96 117 301 182 411 902 159 17...
output:
615424
result:
ok 1 number(s): "615424"
Test #23:
score: -100
Wrong Answer
time: 8ms
memory: 25108kb
input:
6000 1000 226 126 99 274 50 247 244 91 70 104 263 208 196 299 211 268 69 76 278 72 80 11 120 172 224 239 53 296 198 20 282 184 9 96 133 214 79 15 201 220 64 282 211 225 250 256 122 9 1 180 280 44 16 62 90 208 102 140 173 70 242 136 235 249 6 23 38 62 135 204 82 227 281 167 96 233 196 97 243 105 117 ...
output:
45301056
result:
wrong answer 1st numbers differ - expected: '45326920', found: '45301056'