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QOJ
| 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 |
|---|---|---|---|---|---|---|---|---|---|
| #305655 | #5208. Jumbled Trees | LaStataleBlue | TL | 2258ms | 12024kb | C++23 | 8.1kb | 2024-01-15 19:51:49 | 2024-01-15 19:51:50 |
Judging History
answer
#include<bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
template<typename T> T bpow(T x, size_t n) {
if(n == 0) return T(1);
else{auto t=bpow(x, n/2); t=t*t; return n%2 ? x*t : t;}
}
int m;
struct modular {
int r; typedef modular mo;
modular(): r(0) {}
modular(int64_t rr): r(rr%m){if(r<0)r+=m;}
mo inv() const {return bpow(*this, m - 2);}
mo operator-()const{return r ? m - r : 0;}
mo operator*(const mo &t)const{return (ll)r*t.r%m;}
mo operator/(const mo &t)const{return *this*t.inv();}
mo operator+=(const mo &t){
r += t.r; if(r >= m) r -= m; return *this;}
mo operator-=(const mo &t){
r -= t.r; if(r < 0) r += m; return *this;}
mo operator+(const mo &t)const{return mo(*this)+=t;}
mo operator-(const mo &t)const{return mo(*this)-=t;}
mo operator*=(const mo &t){return *this=*this*t;}
bool operator==(const mo &t)const{return r==t.r;}
bool operator>(const mo &t)const{return r>t.r;}
bool operator<=(const double &t)const{return r<=int(t);}
bool operator>(const double &t)const{return r>int(t);}
};
modular fabs(modular x){return x.r;}
typedef modular T; //oppure modular<mod>
typedef vector<T> vd;
const double eps = 1e-12;
vi col; //globale per ricavare il sottospazio
int solveLinear(vector<vd>& A, vd& b, vd& x) {
int n = sz(A), m = sz(x), rank = 0, br, bc;
if (n) assert(sz(A[0]) == m);
col.resize(m); iota(all(col), 0);
rep(i,0,n) {
T v, bv = 0;
rep(r,i,n) rep(c,i,m)
if ((v = fabs(A[r][c])) > bv)
br = r, bc = c, bv = v;
if (bv <= eps) {
rep(j,i,n) if (fabs(b[j]) > eps) return -1;
break;
}
swap(A[i], A[br]); swap(b[i], b[br]);
swap(col[i], col[bc]);
rep(j,0,n) swap(A[j][i], A[j][bc]);
bv = T(1)/A[i][i];
rep(j,i+1,n) {
T fac = A[j][i] * bv;
b[j] -= fac * b[i];
rep(k,i+1,m) A[j][k] -= fac*A[i][k];
}
rank++;
}
x.assign(m, T(0));
for (int i = rank; i--;) {
b[i] = b[i]/A[i][i];
x[col[i]] = b[i];
rep(j,0,i) {
b[j] -= A[j][i] * b[i];
}
}
return rank; // (multiple solutions if rank < m)
}
void solve(){
int n,e;
cin>>n>>e>>m;
vd b,x;
vector<vd> A;
vector<array<int,4>> edges(e);
vector ok(e,false),st(e,false);
vd curr(e);
vector grafo(n+1,vector<array<int,3>>());
for(int i=0;i<e;i++){
int u,v,x;
cin>>u>>v>>x;
b.push_back(x);
edges[i]={u,v,(int)grafo[u].size(),(int)grafo[v].size()};
grafo[u].push_back({v,false,i});
grafo[v].push_back({u,false,i});
}
auto set = [&](int id,bool val){
auto [u,v,ind1,ind2] = edges[id];
assert(grafo[u][ind1][2]==id);
assert(grafo[v][ind2][2]==id);
grafo[u][ind1][1]=val;
grafo[v][ind2][1]=val;
curr[id].r=val;
};
vector vis=vector(n,false);
auto dfs = [&](auto &dfs,int nodo)->void{
vis[nodo]=true;
for(auto [to,act,id] : grafo[nodo]){
if(!vis[to]){
st[id]=true;
set(id,true);
dfs(dfs,to);
}
}
};
dfs(dfs,1);
vector<int> cycle;
auto findcycle = [&](auto &findcycle,int nodo,int last,int st)->bool{
if(nodo==st)return true;
bool res=false;
for(auto [to,act,id] : grafo[nodo]){
if(act && to!=last){
if(findcycle(findcycle,to,nodo,st)){
cycle.push_back(id);
res=true;
}
}
}
return res;
};
for(int i=0;i<e;i++){
if(!st[i]){
//cout<<"processo "<<i<<"\n";
cycle.clear();
auto [u,v] = tie(edges[i][0],edges[i][1]);
findcycle(findcycle,u,-1,v);
set(i,true);
for(auto j : cycle){
//cout<<j<<" ";
if(ok[j])continue;
ok[j]=true;
set(j,false);
A.push_back(curr);
set(j,true);
}
//cout<<"cicle \n";
set(i,false);
}
}
A.push_back(curr);
vector<int> opz;
for(int i=0;i<e;i++){
if(!st[i]){
assert(curr[i].r==0);
opz.push_back(i);
}
}
if(opz.size()>1)
for(int x=0;x<(int)opz.size();x++){
int i = opz[x];
int j = opz[(x+1)%((int)opz.size())];
//cout<<i<<" "<<j<<"\n";
int rimi,rimj;
cycle.clear();
int u = edges[i][0];
int v = edges[i][1];
findcycle(findcycle,u,-1,v);
set(i,true);
rimi = cycle[rand()%cycle.size()];
set(rimi,false);
cycle.clear();
u = edges[j][0];
v = edges[j][1];
findcycle(findcycle,u,-1,v);
set(j,true);
rimj = cycle[rand()%cycle.size()];
set(rimj,false);
A.push_back(curr);
set(rimj,true);
set(j,false);
set(rimi,true);
set(i,false);
}
if(opz.size()>2)
for(int x=0;x<(int)opz.size();x++){
int i = opz[x];
int j = opz[(x+2)%((int)opz.size())];
//cout<<i<<" "<<j<<"\n";
int rimi,rimj;
cycle.clear();
int u = edges[i][0];
int v = edges[i][1];
findcycle(findcycle,u,-1,v);
set(i,true);
rimi = cycle[rand()%cycle.size()];
set(rimi,false);
cycle.clear();
u = edges[j][0];
v = edges[j][1];
findcycle(findcycle,u,-1,v);
set(j,true);
rimj = cycle[rand()%cycle.size()];
set(rimj,false);
A.push_back(curr);
set(rimj,true);
set(j,false);
set(rimi,true);
set(i,false);
}
/*
while((int)A.size()<min(2*e,e+((int)opz.size())/2)){
vector<int> opz;
for(int i=0;i<e;i++){
if(!st[i]){
assert(curr[i].r==0);
opz.push_back(i);
}
}
if(opz.size()<=1)break;
int i = opz[rand()%opz.size()];
int j = i;
while(j==i)j = opz[rand()%opz.size()];
int rimi,rimj;
cycle.clear();
int u = edges[i][0];
int v = edges[i][1];
findcycle(findcycle,u,-1,v);
set(i,true);
rimi = cycle[rand()%cycle.size()];
set(rimi,false);
cycle.clear();
u = edges[j][0];
v = edges[j][1];
findcycle(findcycle,u,-1,v);
set(j,true);
rimj = cycle[rand()%cycle.size()];
set(rimj,false);
A.push_back(curr);
set(rimj,true);
set(j,false);
set(rimi,true);
set(i,false);
}
*/
vector tmp = vector(e,vd(A.size()));
for(int i=0;i<(int)A.size();i++){
for(int j=0;j<(int)A[i].size();j++){
tmp[j][i]=A[i][j];
}
}
swap(A,tmp);
x.resize(A[0].size());
if(solveLinear(A,b,x)==-1){
cout<<"-1\n";
}else{
cout<<x.size()<<"\n";
for(int i=0;i<(int)x.size();i++){
cout<<x[i].r<<" ";
for(int j=0;j<(int)tmp[i].size();j++)if(tmp[i][j]==1){
cout<<j+1<<" ";
}
cout<<"\n";
}
}
}
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
int t=1;
//cin>>t;
for(int i=1;i<=t;i++)solve();
return 0;
}
详细
Test #1:
score: 100
Accepted
time: 1ms
memory: 3480kb
input:
3 3 101 1 2 30 2 3 40 3 1 50
output:
3 30 2 3 20 1 3 10 1 2
result:
ok Participant found an answer (3 trees) and jury found an answer (5 trees)
Test #2:
score: 0
Accepted
time: 1ms
memory: 3516kb
input:
2 2 37 1 2 8 1 2 15
output:
2 15 2 8 1
result:
ok Participant found an answer (2 trees) and jury found an answer (3 trees)
Test #3:
score: 0
Accepted
time: 0ms
memory: 3472kb
input:
5 4 5 1 3 1 2 3 2 2 5 3 4 1 4
output:
-1
result:
ok Both jury and participant did not find an answer
Test #4:
score: 0
Accepted
time: 1ms
memory: 3516kb
input:
10 15 997 4 3 459 9 7 94 9 8 767 10 2 877 5 8 258 3 4 166 8 5 621 8 10 619 9 1 316 10 5 516 3 10 125 1 7 961 3 6 500 4 10 976 3 4 842
output:
-1
result:
ok Both jury and participant did not find an answer
Test #5:
score: 0
Accepted
time: 1ms
memory: 3544kb
input:
20 30 9973 1 10 696 3 8 2905 12 7 6609 20 10 1962 11 9 8430 19 2 412 6 3 6936 19 7 9113 14 15 5635 15 7 1770 13 10 3182 3 16 2625 17 1 7387 11 5 3700 9 15 1048 2 3 7717 12 10 8625 7 13 8141 5 14 2245 6 4 2819 18 19 8709 18 5 6191 17 10 7606 9 20 8626 17 4 8848 4 13 1073 10 8 2277 14 2 7714 11 8 5318...
output:
42 8759 1 2 3 5 6 7 8 9 10 11 12 14 16 19 20 21 24 25 26 749 1 2 3 4 5 6 7 8 9 10 11 12 14 16 19 20 21 25 26 5258 1 2 3 4 6 7 8 9 10 11 12 14 16 19 20 21 24 25 26 7032 1 2 3 4 5 6 7 8 9 10 11 12 16 19 20 21 24 25 26 1520 1 2 3 4 5 6 7 8 9 10 11 12 14 16 20 21 24 25 26 5821 1 2 3 4 5 6 7 8 10 11...
result:
ok Participant found an answer (42 trees) and jury found an answer (59 trees)
Test #6:
score: 0
Accepted
time: 2ms
memory: 3600kb
input:
50 80 99991 6 5 67664 39 4 74944 11 9 13035 13 48 81979 40 20 57943 20 31 72081 1 6 39307 48 39 3550 28 48 41071 18 28 42935 37 32 7538 37 29 3815 50 37 88043 38 41 7283 40 26 66278 37 34 60696 47 19 80875 4 26 67 20 32 91858 39 24 83485 45 25 12241 48 46 61691 37 44 47541 39 40 70034 37 42 25006 27...
output:
-1
result:
ok Both jury and participant did not find an answer
Test #7:
score: 0
Accepted
time: 10ms
memory: 3776kb
input:
100 150 999983 84 10 999545 69 48 930138 48 13 303468 36 6 668122 91 84 115623 62 71 59711 12 37 749281 86 49 281976 26 46 624831 91 8 450475 92 55 460900 50 63 513056 72 2 477622 26 96 11359 31 82 953946 6 71 406339 24 7 177090 70 4 67359 31 39 795565 47 32 407459 26 35 760698 22 37 508175 8 93 612...
output:
-1
result:
ok Both jury and participant did not find an answer
Test #8:
score: 0
Accepted
time: 30ms
memory: 3936kb
input:
200 250 9999991 170 185 3242943 70 17 6083198 137 55 4000889 15 171 1113989 108 65 7988488 192 37 8812990 53 143 8707264 80 180 2504807 55 163 2706048 67 64 6210980 87 165 7693967 155 122 8550804 56 99 7228534 114 138 7047731 190 196 6684929 86 197 8866886 38 195 6717874 112 133 7257617 160 104 3210...
output:
-1
result:
ok Both jury and participant did not find an answer
Test #9:
score: 0
Accepted
time: 325ms
memory: 5704kb
input:
500 600 99999989 265 416 47066772 354 266 16969437 195 415 7917612 354 136 43128175 163 191 58723996 144 84 65835385 157 45 94124747 232 441 17509499 70 397 64101208 223 387 7043647 320 47 84970673 100 2 87310855 87 131 75042257 101 391 27645446 79 26 68547739 390 185 92142961 257 15 80922292 276 48...
output:
-1
result:
ok Both jury and participant did not find an answer
Test #10:
score: 0
Accepted
time: 822ms
memory: 7776kb
input:
500 700 99999989 250 2 71289880 454 447 70661327 328 253 57519343 11 201 67456781 294 99 23392419 215 322 61059212 411 389 69899684 488 429 89579827 437 79 60564061 413 380 34922641 477 372 14858185 156 44 3101349 88 8 52225146 115 26 8582010 171 237 33206748 237 495 31192017 146 32 62712576 209 352...
output:
-1
result:
ok Both jury and participant did not find an answer
Test #11:
score: 0
Accepted
time: 1421ms
memory: 9628kb
input:
500 800 99999989 258 304 1237432 159 152 6684056 8 47 64155938 436 265 83092505 204 302 3892712 142 302 77925167 37 15 20298972 202 395 35856655 284 260 96812598 365 172 48834835 196 101 64871741 174 45 37729972 302 206 90932677 305 275 27712443 443 157 81820535 16 248 22708463 461 479 64749118 105 ...
output:
-1
result:
ok Both jury and participant did not find an answer
Test #12:
score: 0
Accepted
time: 2258ms
memory: 12024kb
input:
500 900 99999989 122 188 44796717 73 121 56798468 334 358 95823235 485 453 96779071 209 391 45946094 332 168 91056077 481 483 81268636 148 393 25213027 107 214 99281713 493 46 61525618 472 355 74320568 258 482 99615552 159 393 20311839 411 121 5207095 20 131 65269699 45 339 51772607 195 292 64556504...
output:
-1
result:
ok Both jury and participant did not find an answer
Test #13:
score: -100
Time Limit Exceeded
input:
500 1000 99999989 75 20 25003980 292 19 89418683 353 246 74910681 183 201 97535184 254 421 50614221 15 396 86624029 82 13 67776336 86 70 62843451 279 3 55801636 29 425 30024776 176 243 16631048 498 363 77415492 55 305 80862521 213 110 30693079 432 358 99667002 201 30 44433122 97 203 16284993 118 490...