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ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#812891 | #9782. NonZero PrefSuf Sums | ucup-team135# | AC ✓ | 573ms | 31024kb | C++20 | 6.0kb | 2024-12-13 19:16:38 | 2024-12-13 19:16:39 |
Judging History
answer
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <queue>
#include <ctime>
#include <cassert>
#include <complex>
#include <string>
#include <cstring>
#include <chrono>
#include <random>
#include <bitset>
#include <fstream>
#include <array>
#include <functional>
#include <stack>
#include <memory>
using namespace std;
#define int long long
int p;
int po(int a,int b) {if(b==0) return 1; if(b==1) return a; if(b%2==0) {int u=po(a,b/2);return (u*1LL*u)%p;} else {int u=po(a,b-1);return (a*1LL*u)%p;}}
int inv(int x) {return po(x,p-2);}
mt19937 rnd;
#define app push_back
#define all(x) (x).begin(),(x).end()
#ifdef LOCAL
#define debug(...) [](auto...a){ ((cout << a << ' '), ...) << endl;}(#__VA_ARGS__, ":", __VA_ARGS__)
#define debugv(v) do {cout<< #v <<" : {"; for(int izxc=0;izxc<v.size();++izxc) {cout << v[izxc];if(izxc+1!=v.size()) cout << ","; }cout <<"}"<< endl;} while(0)
#else
#define debug(...)
#define debugv(v)
#endif
#define lob(a,x) lower_bound(all(a),x)
#define upb(a,x) upper_bound(all(a),x)
const int maxn=1005;
int fact[maxn];int invf[maxn];
int n,m;
int C(int a,int b,int c)
{
int ans=fact[a+b+c];ans*=invf[a];ans%=p;ans*=invf[b];ans%=p;ans*=invf[c];ans%=p;
return ans;
}
const int maxs=1e4+1005;
int dps[2*maxs];int dps2[2*maxs];
bool check(vector<int> v)
{
int s=accumulate(all(v),0LL);
if(s==0) {return false;}
int non0=0;for(int x:v) if(x) non0++;
if(non0<=1) {return false;}
int d=0;
for(int x:v) d=__gcd(d,x);
d=abs(d);
for(int &x:v) {x/=d;}
vector<int> vp,vm;
for(int x:v) if(x>0) vp.app(x);
for(int x:v) if(x<0) vm.app(x);
if(count(all(vp),1)==vp.size()) return true;
if(count(all(vm),-1)==vm.size()) return true;
sort(all(v));
vector<int> pr(v.size()+1);
do
{
for(int i=0;i<v.size();++i) {pr[i+1]=pr[i]+v[i];}
bool ok=1;
for(int i=1;i<v.size();++i)
{
if(pr[i]==0 || pr[i]==s)
{
ok=0;
}
}
if(ok) return true;
}while(next_permutation(all(v)));
debugv(v);
return false;
}
bool real(vector<int> v)
{
int s=accumulate(all(v),0LL);
if(s==0) {return false;}
int non0=0;for(int x:v) if(x) non0++;
if(non0<=1) {return false;}
sort(all(v));
vector<int> pr(v.size()+1);
do
{
for(int i=0;i<v.size();++i) {pr[i+1]=pr[i]+v[i];}
bool ok=1;
for(int i=1;i<v.size();++i)
{
if(pr[i]==0 || pr[i]==s)
{
ok=0;
}
}
if(ok) return true;
}while(next_permutation(all(v)));
return false;
}
vector<vector<int> > go(int n,int m)
{
if(n==0) {return {{}};}
vector<vector<int> > was=go(n-1,m);
vector<vector<int> > have;
for(vector<int> h:was)
{
for(int x=-m;x<=m;++x)
{
vector<int> h1=h;
h1.app(x);
if(!is_sorted(all(h1))) continue;
have.app(h1);
}
}
return have;
}
vector<vector<int> > go2(int n,int m)
{
if(n==0) {return {{}};}
vector<vector<int> > was=go2(n-1,m);
vector<vector<int> > have;
for(vector<int> h:was)
{
for(int x=-m;x<=m;++x)
{
vector<int> h1=h;
h1.app(x);
have.app(h1);
}
}
return have;
}
int stupid(int n,int m)
{
vector<vector<int> > h=go2(n,m);
debug(h.size());
int ans=0;int cnt=0;
for(auto v:h)
{
if(!real(v) && accumulate(all(v),0LL)) {++cnt;debugv(v);}
ans+=real(v);
}
debug(cnt);
return ans;
}
const int maxn1=105;
int dp1[3*maxn1][maxn1][maxn1];
int32_t main()
{
ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
/*vector<vector<int> > aa=go(10,4);vector<vector<int> > aas;
for(auto hh:aa) {sort(all(hh));aas.app(hh);}
sort(all(aas));aas.erase(unique(all(aas)),aas.end());
for(auto v:aas) {check(v);}
debug("okk");*/
cin>>n>>m>>p;
//debug(stupid(n,m));
fact[0]=1;for(int i=1;i<maxn;++i) {fact[i]=(fact[i-1]*i)%p;}
for(int i=0;i<maxn;++i) {invf[i]=inv(fact[i]);}
int al=po(2*m+1,n);
int bad=2*n*m;bad%=p;
dps[maxs]=1;
for(int i=0;i<n;++i)
{
fill(dps2,dps2+2*maxs,0);
for(int j=-m;j<=m;++j)
{
for(int s1=0;s1<2*maxs;++s1)
{
if(dps[s1])
{
dps2[s1+j]+=dps[s1];if(dps2[s1+j]>=p) dps2[s1+j]-=p;
}
}
}
copy(dps2,dps2+2*maxs,dps);
}
bad+=dps[maxs];bad%=p;
debug(bad);
dp1[0][0][0]=1;
debug("regrf");
for(int mx=1;mx<=m;++mx)
{
for(int s=0;s<3*maxn1-mx;++s)
{
for(int n=0;n<maxn1;++n)
{
dp1[s][mx][n]+=dp1[s][mx-1][n];if(dp1[s][mx][n]>=p) dp1[s][mx][n]-=p;
}
}
for(int s=3*maxn1-mx;s>=0;--s)
{
for(int cnt=1;cnt*mx+s<3*maxn1;++cnt) {
for(int n=0;n<maxn1;++n)
{
dp1[s+cnt*mx][mx][n+cnt]+=(dp1[s][mx][n]*invf[cnt]);dp1[s+cnt*mx][mx][n+cnt]%=p;
}
}
}
}
debug(dp1[1][1][1]);
debug("rgef");
int bad1=0;
for(int np=0;np<=n;++np)
{
for(int s=1;s<np;++s)
{
for(int n0=0;n0<n-np;++n0) {
int nm=n-n0-np;
for(int mx=max(1LL,s-1);mx<=m;++mx)
{
int o=((2*(m/mx)*1LL*(dp1[np-s][mx][nm]-dp1[np-s][mx-1][nm]))%p);
o*=fact[n];o%=p;
o*=invf[np];o%=p;
o*=invf[n0];o%=p;
bad+=o;bad%=p;
bad1+=o;bad1%=p;
}
}
}
}
debug(bad1);
cout<<((al-bad)%p+p)%p;
return 0;
}
詳細信息
Test #1:
score: 100
Accepted
time: 17ms
memory: 5744kb
input:
2 1 998244353
output:
2
result:
ok single line: '2'
Test #2:
score: 0
Accepted
time: 165ms
memory: 17412kb
input:
69 42 696969697
output:
378553557
result:
ok single line: '378553557'
Test #3:
score: 0
Accepted
time: 14ms
memory: 6072kb
input:
2 1 998244353
output:
2
result:
ok single line: '2'
Test #4:
score: 0
Accepted
time: 174ms
memory: 17060kb
input:
69 42 696969697
output:
378553557
result:
ok single line: '378553557'
Test #5:
score: 0
Accepted
time: 239ms
memory: 24816kb
input:
61 75 677323601
output:
34613998
result:
ok single line: '34613998'
Test #6:
score: 0
Accepted
time: 57ms
memory: 10708kb
input:
13 14 670577333
output:
41465431
result:
ok single line: '41465431'
Test #7:
score: 0
Accepted
time: 42ms
memory: 7024kb
input:
14 6 987686347
output:
37536510
result:
ok single line: '37536510'
Test #8:
score: 0
Accepted
time: 43ms
memory: 8512kb
input:
15 12 196428923
output:
29322522
result:
ok single line: '29322522'
Test #9:
score: 0
Accepted
time: 48ms
memory: 7276kb
input:
68 7 786815587
output:
149281835
result:
ok single line: '149281835'
Test #10:
score: 0
Accepted
time: 25ms
memory: 5892kb
input:
3 2 503002109
output:
82
result:
ok single line: '82'
Test #11:
score: 0
Accepted
time: 38ms
memory: 6568kb
input:
13 5 756093197
output:
415698676
result:
ok single line: '415698676'
Test #12:
score: 0
Accepted
time: 30ms
memory: 7812kb
input:
2 3 646574611
output:
30
result:
ok single line: '30'
Test #13:
score: 0
Accepted
time: 162ms
memory: 22800kb
input:
39 68 120037189
output:
43217507
result:
ok single line: '43217507'
Test #14:
score: 0
Accepted
time: 27ms
memory: 7888kb
input:
13 4 423132517
output:
360231790
result:
ok single line: '360231790'
Test #15:
score: 0
Accepted
time: 31ms
memory: 6076kb
input:
14 3 309713387
output:
94215386
result:
ok single line: '94215386'
Test #16:
score: 0
Accepted
time: 136ms
memory: 25112kb
input:
24 77 886983941
output:
211636479
result:
ok single line: '211636479'
Test #17:
score: 0
Accepted
time: 30ms
memory: 6048kb
input:
3 3 504388063
output:
270
result:
ok single line: '270'
Test #18:
score: 0
Accepted
time: 17ms
memory: 5880kb
input:
3 1 936205423
output:
8
result:
ok single line: '8'
Test #19:
score: 0
Accepted
time: 26ms
memory: 6304kb
input:
3 3 295983139
output:
270
result:
ok single line: '270'
Test #20:
score: 0
Accepted
time: 49ms
memory: 9268kb
input:
10 15 446169107
output:
149884328
result:
ok single line: '149884328'
Test #21:
score: 0
Accepted
time: 67ms
memory: 9860kb
input:
37 18 833753929
output:
592917251
result:
ok single line: '592917251'
Test #22:
score: 0
Accepted
time: 27ms
memory: 6004kb
input:
11 3 998773403
output:
860630017
result:
ok single line: '860630017'
Test #23:
score: 0
Accepted
time: 102ms
memory: 27104kb
input:
14 85 688036639
output:
347188409
result:
ok single line: '347188409'
Test #24:
score: 0
Accepted
time: 30ms
memory: 6064kb
input:
3 3 844621907
output:
270
result:
ok single line: '270'
Test #25:
score: 0
Accepted
time: 30ms
memory: 8344kb
input:
3 4 204335891
output:
620
result:
ok single line: '620'
Test #26:
score: 0
Accepted
time: 45ms
memory: 7344kb
input:
7 8 113007667
output:
58946097
result:
ok single line: '58946097'
Test #27:
score: 0
Accepted
time: 17ms
memory: 5856kb
input:
4 1 637268377
output:
22
result:
ok single line: '22'
Test #28:
score: 0
Accepted
time: 52ms
memory: 8816kb
input:
11 14 391637237
output:
303270280
result:
ok single line: '303270280'
Test #29:
score: 0
Accepted
time: 25ms
memory: 5964kb
input:
3 2 208286231
output:
82
result:
ok single line: '82'
Test #30:
score: 0
Accepted
time: 41ms
memory: 8132kb
input:
2 11 662696483
output:
462
result:
ok single line: '462'
Test #31:
score: 0
Accepted
time: 90ms
memory: 19464kb
input:
19 55 974135299
output:
887460557
result:
ok single line: '887460557'
Test #32:
score: 0
Accepted
time: 45ms
memory: 7500kb
input:
6 8 417027509
output:
23351024
result:
ok single line: '23351024'
Test #33:
score: 0
Accepted
time: 54ms
memory: 8440kb
input:
8 13 624006587
output:
353008442
result:
ok single line: '353008442'
Test #34:
score: 0
Accepted
time: 42ms
memory: 7828kb
input:
10 10 740294671
output:
79436611
result:
ok single line: '79436611'
Test #35:
score: 0
Accepted
time: 50ms
memory: 9400kb
input:
11 10 394088657
output:
161476458
result:
ok single line: '161476458'
Test #36:
score: 0
Accepted
time: 66ms
memory: 12168kb
input:
9 27 562853573
output:
135252259
result:
ok single line: '135252259'
Test #37:
score: 0
Accepted
time: 30ms
memory: 6032kb
input:
8 3 829129009
output:
5349034
result:
ok single line: '5349034'
Test #38:
score: 0
Accepted
time: 143ms
memory: 17812kb
input:
51 49 924010279
output:
815049368
result:
ok single line: '815049368'
Test #39:
score: 0
Accepted
time: 25ms
memory: 5876kb
input:
12 2 308466749
output:
223013998
result:
ok single line: '223013998'
Test #40:
score: 0
Accepted
time: 34ms
memory: 7976kb
input:
7 4 567557693
output:
4502296
result:
ok single line: '4502296'
Test #41:
score: 0
Accepted
time: 174ms
memory: 29272kb
input:
36 93 943780729
output:
13599465
result:
ok single line: '13599465'
Test #42:
score: 0
Accepted
time: 17ms
memory: 5792kb
input:
2 1 828681127
output:
2
result:
ok single line: '2'
Test #43:
score: 0
Accepted
time: 30ms
memory: 6348kb
input:
3 3 534160729
output:
270
result:
ok single line: '270'
Test #44:
score: 0
Accepted
time: 48ms
memory: 8248kb
input:
7 12 920925433
output:
453086694
result:
ok single line: '453086694'
Test #45:
score: 0
Accepted
time: 25ms
memory: 7536kb
input:
3 2 440546987
output:
82
result:
ok single line: '82'
Test #46:
score: 0
Accepted
time: 73ms
memory: 7592kb
input:
90 9 291269963
output:
72560304
result:
ok single line: '72560304'
Test #47:
score: 0
Accepted
time: 58ms
memory: 7804kb
input:
38 10 867575113
output:
165530481
result:
ok single line: '165530481'
Test #48:
score: 0
Accepted
time: 102ms
memory: 15008kb
input:
48 37 152663531
output:
135425620
result:
ok single line: '135425620'
Test #49:
score: 0
Accepted
time: 59ms
memory: 9112kb
input:
15 15 991731803
output:
102703562
result:
ok single line: '102703562'
Test #50:
score: 0
Accepted
time: 573ms
memory: 31024kb
input:
100 100 696969697
output:
313377809
result:
ok single line: '313377809'
Extra Test:
score: 0
Extra Test Passed