The 3rd Universal Cup. Stage 8: Cangqian

题解：

https://files.cnblogs.com/files/clrs97/ZJCPC24_Tutorial.pdf

 

Code：

A. Bingo

#include <bits/stdc++.h>
using namespace std;
string n;
int m;
typedef long long ll;
ll sum[1000005];
int pw[1000005];
bool all[1000005];
int sol[1000020];
void solv() {cin >> n >> m;int am = 0 ;for(int i = 0;i < n.size();i++) am = (10LL * am + n[i] - '0') % m;int ans = m - am;sum[n.size()] = 0;for(int i = 0;i < n.size();i++) {sum[i] = 1LL * ('9' - n[i]) * pw[n.size() - i - 1] ;}all[n.size()] = 1;for(int i = n.size() - 1;i >= 0;i--) {all[i] = all[i + 1] && (n[i] == '9') ;}for(int i = n.size() - 1;i >= 0;i--) sum[i] += sum[i + 1];string b; int d = m;while(d) {b += ((d % 10) + '0') ;d /= 10;}reverse(b.begin() , b.end()) ;vector<int> rm(b.size() + 1) ;for(int i = b.size() - 1;i >= 0;i--) {rm[i] = (b[i] - '0') * pw[b.size() - i - 1] + rm[i + 1] ;}for(int i = 0;i < n.size() && i + b.size() - 1 < n.size();i++) { //matchfor(int j = 0 ; j <= b.size();j++) {/// here mat , diff on n[i + j]if(i + j >= n.size()) break ;if(j == b.size()) {if(!all[i + j]) ans = min(ans , 1) ;break;}if(b[j] > n[i + j]) {/// // printf("in %d %d : %d %d %d\n",i,j,(ll)(b[j] - n[i + j] - 1) * pw[n.size() - (i + j) - 1] , sum[i + j + 1] , 1LL * rm[j + 1] * pw[n.size() - (i+b.size())]) ;ans = min((ll)ans , 1 + (ll)(b[j] - n[i + j] - 1) * pw[n.size() - (i + j) - 1] + sum[i + j + 1] + 1LL * rm[j + 1] * pw[n.size() - (i+b.size())]);}if(j == b.size() || i + j >= n.size() || b[j] != n[i + j]) break;}}int L = (int)n.size() - 1;// printf("L %d\n",L) ;for(int i = 0;i < n.size() + 15;i++) sol[i] = 0;for(int i = 0;i < n.size();i++) sol[n.size() - i - 1] = n[i] - '0' ;sol[0] += ans ;for(int i = 0;i <= L;i++) {sol[i + 1] += sol[i] / 10;sol[i] %= 10;if(sol[i + 1]) L = max(L , i + 1) ;}for(int i = L;i >= 0;i--) cout << sol[i] ; cout << '\n';return ;
}
int main() {// freopen("in.txt","r",stdin);// freopen("out2.txt","w",stdout) ;ios::sync_with_stdio(false) ; cin.tie(0) ; cout.tie(0) ;int t;cin >> t;pw[0] = 1;for(int i = 1;i <= 100000;i++) {pw[i] = min(1000000000LL , pw[i - 1] * 10LL) ;}while(t--) solv() ;
}

 

B. Simulated Universe

#include<bits/stdc++.h>
using namespace std;const int N=8e3+1e2+7;int T,n;int f[2][N];int main()
{ios::sync_with_stdio(false);cin.tie(0);cin>>T;while(T--){cin>>n;for(int i=0;i<=n;i++)f[0][i]=-1e9;f[0][0]=0;int now=0,last=1;int ans=0;for(int i=1;i<=n;i++){swap(now,last);for(int j=0;j<=i+1;j++)f[now][j]=-1e9;string ty;cin>>ty;if(ty=="B"){ans+=2;for(int j=0;j<=i;j++){if(f[last][j]<0)continue;f[now][j+1]=max(f[now][j],f[last][j]);if(f[last][j])f[now][j]=max(f[now][j],f[last][j]-1);}}else{int a,b;cin>>a>>b;for(int j=0;j<=i;j++){if(f[last][j]<0)continue;f[now][max(j-a,0)]=max(f[now][max(j-a,0)],f[last][j]);f[now][j]=max(f[now][j],f[last][j]+b);}}}for(int i=0;i<=n;i++)if(f[now][i]>=0){ans-=i;break;}cout<<ans<<"\n";}
}
/*
1
3 6
1 2 3
4 5 6
6 9 9
8 12 13
10 15 17
12 18 21
*/

 

C. Challenge NPC

#include <bits/stdc++.h>
using namespace std;
typedef pair<int,int> pii ;
vector<pii> Ed;
int main() {ios::sync_with_stdio(false) ; cin.tie(0) ;int k ; cin >> k;int n = k + 2;for(int i = 1;i <= n;i++) {for(int j = 1;j < i;j++) {Ed.push_back({j*2 , i*2 - 1});Ed.push_back({j*2 - 1 , i *2});}}cout << n*2 << ' ' << Ed.size() <<' ' << 2 << '\n' ;for(int i = 1;i <= n*2;i++) {cout << (i&1) + 1 <<' ' ;}cout << '\n';for(auto [x,y] : Ed) cout << x <<' ' << y << '\n';return 0;
}

 

D. Puzzle: Easy as Scrabble

#include<bits/stdc++.h>
using namespace std;
using ll=long long;
const int N=300005,P=998244353;
#define NO {puts("NO"); exit(0);}
int dx[]={0,0,1,-1},dy[]={1,-1,0,0}; 
auto solve(){int n,m;cin>>n>>m;vector<string> a(n+2);for(auto &s:a) cin>>s;vector f(n+2,vector<array<char,4>>(m+1));vector inq(n+2,vector<bool>(m+2));for(int i=1;i<=n;i++){if(a[i][0]!='.')f[i][1][0]=a[i][0];if(a[i][m+1]!='.')f[i][m][1]=a[i][m+1];}for(int j=1;j<=m;j++){if(a[0][j]!='.')f[1][j][2]=a[0][j];if(a[n+1][j]!='.')f[n][j][3]=a[n+1][j];}auto check=[&](int x,int y){static int vis[256];static int time;int num=0; ++time;for(auto c:f[x][y]){if(!isalpha(c)) continue;if(a[x][y]!='x') a[x][y]=c;if(vis[c]!=time){vis[c]=time;num++;}}if(num>1) return true;return num==1&&a[x][y]=='x';};queue<pair<int,int>> qu;for(int i=1;i<=n;i++){for(int j=1;j<=m;j++){if(check(i,j)){qu.push({i,j});inq[i][j]=true;}}}while(qu.size()){auto [x,y]=qu.front(); qu.pop();inq[x][y]=false;a[x][y]='x';for(int i=0;i<4;i++){if(!isalpha(f[x][y][i])) continue;int nx=x+dx[i],ny=y+dy[i];if(nx<=0||ny<=0||nx>n||ny>m) NO;f[nx][ny][i]=f[x][y][i];if(a[nx][ny]!='x') a[nx][ny]=f[x][y][i];if(!inq[nx][ny]&&check(nx,ny)){inq[nx][ny]=true;qu.push({nx,ny});}}f[x][y]={0,0,0,0};}puts("YES");for(int i=1;i<=n;i++){for(int j=1;j<=m;j++){if(a[i][j]=='x') a[i][j]='.';putchar(a[i][j]);}puts("");}
}
int main(){ios::sync_with_stdio(false);cin.tie(0);int t=1;// cin>>t;while(t--){solve();// cout<<solve()<<'\n';// cout<<(solve()?"Yes":"No")<<'\n';}return 0;
}/* Generated by powerful Codeforces Tool(cf tool)* Author: sleep__* Time: 2024-04-04 14:25:05
**/

 

E. Team Arrangement

#include<cstdio>
#include<algorithm>
using namespace std;
typedef unsigned long long ull;
const int N=65,inf=~0U>>1;
int n,i,w[N],num[N],ans;ull in[N],out[N];
struct E{int l,r;}e[N];
inline bool cmp(const E&a,const E&b){return a.r<b.r;}
inline void solve(int m){int sum=0;ull S=0;for(int i=1;i<=m;i++){S^=in[i];int now=num[i];sum+=now*w[i];now*=i;while(now--){if(!S)return;S-=S&-S;}S^=S&out[i];}if(sum>ans)ans=sum;
}
void dfs(int x,int m){if(x>m)return;num[x]=0;dfs(x+1,m);for(int i=1;;i++){m-=x;num[x]=i;if(!m)solve(x);if(m<=0)break;dfs(x+1,m);}
}
int main(){scanf("%d",&n);for(i=0;i<n;i++)scanf("%d%d",&e[i].l,&e[i].r);sort(e,e+n,cmp);for(i=0;i<n;i++){in[e[i].l]^=1ULL<<i;out[e[i].r]^=1ULL<<i;}for(i=1;i<=n;i++)scanf("%d",&w[i]);ans=-inf;dfs(1,n);if(ans==-inf)puts("impossible");else printf("%d",ans);
}

 

F. Stage: Agausscrab

#include<bits/stdc++.h>
using namespace std;const int N=1e3+1e2+7;int n;string s[N];int a[N];int main()
{ios::sync_with_stdio(false);cin.tie(0);cin>>n;for(int i=1;i<=n;i++)cin>>s[i]>>a[i];string ans;for(int i=1;i<=n;i++){int r=0;for(int j=1;j<=n;j++)if(a[j]>a[i])r++;r+=1;for(int j=1;j<=r;j++)if(s[i].size())s[i].pop_back();ans+=s[i];}ans[0]=ans[0]-'a'+'A';cout<<"Stage: "<<ans<<"\n";
}

 

G. Crawling on a Tree

#include<cstdio>
#include<algorithm>
#include<cstdlib>
using namespace std;
typedef long long ll;
const int N=10005,M=10005;
int n,m,i,lim[N],g[N],v[N<<1],w[N<<1],wt[N<<1],nxt[N<<1],ed;
int wf[N],wk[N],need[N],sz[N],heavy[N];
ll ans[M];
struct E{ll s,d[M];int l,r;void clr(){s=l=0;r=m;for(int i=0;i<=m;i++)d[i]=0;}
}f[15];
inline void add(int x,int y,int z,int k){v[++ed]=y;w[ed]=z;wt[ed]=k;nxt[ed]=g[x];g[x]=ed;
}
inline void merge(const E&A,const E&B,E&C){int l=A.l+B.l,r=min(A.r+B.r,m);static ll d[M];int i=A.l+1,j=B.l+1,k=l+1;while(k<=r&&i<=A.r&&j<=B.r)d[k++]=A.d[i]<B.d[j]?A.d[i++]:B.d[j++];while(k<=r&&i<=A.r)d[k++]=A.d[i++];while(k<=r&&j<=B.r)d[k++]=B.d[j++];C.s=A.s+B.s;C.l=l;C.r=r;for(int i=l+1;i<=r;i++)C.d[i]=d[i];
}
void dfs(int x,int y){need[x]=lim[x];sz[x]=1;for(int i=g[x];i;i=nxt[i]){int u=v[i];if(u==y)continue;wf[u]=w[i];wk[u]=wt[i];dfs(u,x);sz[x]+=sz[u];if(sz[u]>sz[heavy[x]])heavy[x]=u;need[x]=max(need[x],need[u]);}
}
void go(int x,int y,int o){int u=heavy[x];if(u){go(u,x,o);f[o+1].clr();merge(f[o],f[o+1],f[o]);}else f[o].clr();for(int i=g[x];i;i=nxt[i]){int u=v[i];if(u==y||u==heavy[x])continue;go(u,x,o+1);merge(f[o],f[o+1],f[o]);}int L=need[x],R=wk[x],W=wf[x];int A=max(f[o].l,L*2-R),B=min(f[o].r,R);if(A>B){for(int i=1;i<=m;i++)puts("-1");exit(0);}for(int i=f[o].l+1;i<=A;i++)f[o].s+=f[o].d[i];f[o].l=A;f[o].r=B;f[o].s+=1LL*(max(L,A)*2-A)*W;for(int i=A+1;i<=B&&i<=L;i++)f[o].d[i]-=W;for(int i=max(A,L)+1;i<=B;i++)f[o].d[i]+=W;
}
int main(){scanf("%d%d",&n,&m);for(i=1;i<n;i++){int x,y,z,k;scanf("%d%d%d%d",&x,&y,&z,&k);add(x,y,z,k);add(y,x,z,k);}for(i=2;i<=n;i++)scanf("%d",&lim[i]);wk[1]=m*2;dfs(1,0);go(1,0,0);for(i=1;i<=m;i++)ans[i]=-1;ll sum=f[0].s;for(i=f[0].l;i<=m;i++){if(i>=need[1])ans[i]=sum;if(i<m)sum+=f[0].d[i+1];}for(i=1;i<=m;i++)printf("%lld\n",ans[i]);
}

 

H. Permutation

#include <bits/stdc++.h>
using namespace std;
int n;
const double C = (sqrt(5) - 1) / 2;
int f[1000005];
int d[1000005];
int qry(int l,int r) {cout << "? " << l <<' ' << r << '\n' ;fflush(stdout) ;int x ; cin >> x;return x;
}
void solv() {cin >> n;int l = 1 , r = n;int lst_pos = -1;while(l < r) {int c = d[r - l + 1];// printf("C %d %d %d\n",l,r,c) ;if(lst_pos == -1) lst_pos = qry(l , r);if(r - l == 1) {if(lst_pos == l) l = r;else r = l;break ;}if(l + c - 1 >= lst_pos) {int x = qry(l , l + c - 1);if(x == lst_pos) r = l + c - 1;else {l = l + c;lst_pos = -1;}}else {int x = qry(r - c + 1 , r);if(x == lst_pos) l = r - c + 1;else {r = r - c;lst_pos = -1;}}}cout << "! " << l << '\n' ;fflush(stdout) ;return ;
}
int main() {// ios::sync_with_stdio(false) ; cin.tie(0) ;int t;cin >> t;f[1] = f[2] = 0;for(int i = 3;i <= 1000000;i++) {int mxc = (int)(C * i); f[i] = 1e9;for(int j = max(mxc - 10 , (i + 1)/2) ; j <= min(i - 1 , mxc + 10) ; j++) {if(max(f[j] + 1 , f[i - j] + 2) < f[i]) {f[i] = max(f[j] + 1 , f[i - j] + 2) ;d[i] = j;}}// if(f[i] > ceil(1.5 * log2(i)) - 1) {//     printf("%d %d %lf\n",i,f[i],ceil(1.5 * log2(i)) - 1);// }}// printf("%d\n",f[1000000]) ;?while(t--) solv() ;
}

 

I. Piggy Sort

#include<bits/stdc++.h>
using namespace std;#define int long longconst int N=2e3+1e2+7;int T,n,m;int x[N][N],sx[N];map<int,int> vis[N];int use[N];int av[N],bv[N],fd,ans[N];void dfs(int t)
{if(t==n+1){vector<int> id(n);iota(id.begin(),id.end(),1);sort(id.begin(),id.end(),[&](const int &a,const int &b){if(av[a]*bv[b]!=av[b]*bv[a])return av[a]*bv[b]<av[b]*bv[a];return a<b;});fd=1;for(int i=0;i<n;i++)ans[id[i]]=i+1;for(int i=1;i<=n;i++)cout<<ans[i]<<" \n"[i==n];return;}for(int i=1;i<=n;i++){if(use[i])continue;int va=x[2][i]-x[1][t];int vb=sx[2]-sx[1];int ok=1;for(int j=3;j<=m;j++){if(va*(sx[j]-sx[1])%vb){ok=0;break;}int w=va*(sx[j]-sx[1])/vb+x[1][t];if(!vis[j].count(w)||!vis[j][w]){ok=0;break;}}if(ok){for(int j=1;j<=m;j++){int w=va*(sx[j]-sx[1])/vb+x[1][t];vis[j][w]--;}use[i]=1;av[t]=va,bv[t]=vb;dfs(t+1);use[i]=0;for(int j=1;j<=m;j++){int w=va*(sx[j]-sx[1])/vb;vis[j][w]++;}}}
}signed main()
{ios::sync_with_stdio(false);cin.tie(0);cin>>T;while(T--){cin>>n>>m;for(int i=1;i<=m;i++){vis[i].clear();sx[i]=0;for(int j=1;j<=n;j++)cin>>x[i][j],vis[i][x[i][j]]++,sx[i]+=x[i][j];}if(sx[1]==sx[2]){for(int i=1;i<=n;i++)cout<<i<<" \n"[i==n];continue;}fd=0;dfs(1);assert(fd);}
}
/*
1
3 6
1 2 3
4 5 6
6 9 9
8 12 13
10 15 17
12 18 21
*/

 

J. Even or Odd Spanning Tree

#include<cstdio>
#include<algorithm>
using namespace std;
const int N=200005,K=18,M=500005,inf=~0U>>1;
int Case,n,m,cnt,i,j,x,y,z,tmp,f[N],g[N],v[N<<1],w[N<<1],nxt[N<<1],ed;
int d[N],fa[N][K],fe[N][K],fo[N][K];
long long mst,ans;int delta;bool on[M];
struct E{int x,y,z;}e[M];
inline bool cmp(const E&a,const E&b){return a.z<b.z;}
inline void umax(int&a,int b){a<b?(a=b):0;}
int F(int x){return f[x]==x?x:f[x]=F(f[x]);}
inline void add(int x,int y,int z){v[++ed]=y;w[ed]=z;nxt[ed]=g[x];g[x]=ed;}
void dfs(int x,int y){for(int i=1;i<K;i++){fa[x][i]=fa[fa[x][i-1]][i-1];fe[x][i]=max(fe[x][i-1],fe[fa[x][i-1]][i-1]);fo[x][i]=max(fo[x][i-1],fo[fa[x][i-1]][i-1]);}for(int i=g[x];i;i=nxt[i]){int u=v[i],z=w[i];if(u==y)continue;d[u]=d[x]+1;fa[u][0]=x;if(z&1){fe[u][0]=0;fo[u][0]=z;}else{fe[u][0]=z;fo[u][0]=0;}dfs(u,x);}
}
inline int ask(int x,int y,int w[][K]){if(x==y)return 0;if(d[x]<d[y])swap(x,y);int ret=0;for(int i=K-1;~i;i--)if(d[fa[x][i]]>=d[y]){umax(ret,w[x][i]);x=fa[x][i];}if(x==y)return ret;for(int i=K-1;~i;i--)if(fa[x][i]!=fa[y][i]){umax(ret,w[x][i]);umax(ret,w[y][i]);x=fa[x][i];y=fa[y][i];}umax(ret,w[x][0]);umax(ret,w[y][0]);return ret;
}
int main(){scanf("%d",&Case);while(Case--){scanf("%d%d",&n,&m);for(i=0;i<=n;i++){g[i]=d[i]=0;for(j=0;j<K;j++)fa[i][j]=fe[i][j]=fo[i][j]=0;}mst=cnt=ed=0;for(i=1;i<=m;i++){scanf("%d%d%d",&e[i].x,&e[i].y,&e[i].z);on[i]=0;}sort(e+1,e+m+1,cmp);for(i=1;i<=n;i++)f[i]=i;for(i=1;i<=m;i++){x=e[i].x,y=e[i].y,z=e[i].z;if(F(x)==F(y))continue;on[i]=1;f[f[x]]=f[y];mst+=z;cnt++;add(x,y,z),add(y,x,z);}if(cnt<n-1){puts("-1 -1");continue;}dfs(1,0);delta=inf;for(i=1;i<=m;i++){if(on[i])continue;z=e[i].z;tmp=ask(e[i].x,e[i].y,z&1?fe:fo);if(!tmp)continue;z-=tmp;if(delta>z)delta=z;}if(delta<inf)ans=mst+delta;else ans=-1;if(mst&1)swap(ans,mst);printf("%lld %lld\n",mst,ans);}
}
/*
3
2 1
1 2 5
3 1
1 3 1
4 4
1 2 1
1 3 1
1 4 1
2 4 2
*/

 

K. Sugar Sweet 3

#include <bits/stdc++.h>
using namespace std;
int A , B , C  , x;
int n ;
const int N = 605;
const int mod = 1e9 + 7;
int fpow(int a,int b) {int ans = 1;while(b) {if(b & 1) ans = 1LL * ans * a %mod;a = 1LL * a * a %mod; b>>= 1;}return ans;
}
int F[N][N];
// int Ga[N][N] , Gb[N][N], Gc[N][N];
// int dota[N][N] , dotb[N][N] , dotc[N][N];
int dot[N][N];
int Cata[N] ;
int d[N] ;
int t[N * 2] , rt[N * 2] ;
int lm ; ///多项式的项数
int mat[N][N] , rmat[N][N];
int C_(int a,int b) {return 1LL * t[a] * rt[b] % mod * rt[a - b] % mod;
}
int A_(int a,int b) {return 1LL * t[a] * rt[a - b] % mod;
}
vector<int> get_coe(int n , vector<int> w) { ///已知n个点值[1 to n]，求sum{ai * wi} 对应的 di的系数，i from 0 to n - 1for(int i = 1;i <= n;i++) {for(int j = 1;j <= n;j++) {mat[i][j] = fpow(i , j - 1) ; // MAT * A = Drmat[i][j] = (i == j) ;}}for(int i = 1;i <= n;i++) {int cur = -1;for(int j = i ;j <= n;j++) {if(mat[j][i]) {cur = j ; break ;}}for(int j = 1;j <= n;j++) {swap(mat[cur][j] , mat[i][j]) ; swap(rmat[cur][j] , rmat[i][j]) ;}int r = fpow(mat[i][i] , mod - 2);for(int j = 1;j <= n;j++) {if(i == j) continue ;int f = (mod - 1LL * mat[j][i] * r %mod) % mod;for(int k = 1;k <= n;k++) {mat[j][k] = (mat[j][k] + 1LL * mat[i][k] * f) % mod ; rmat[j][k] = (rmat[j][k] + 1LL * rmat[i][k] * f) % mod;}}for(int j = 1;j <= n;j++) {mat[i][j] = 1LL * mat[i][j] * r % mod;rmat[i][j] = 1LL * rmat[i][j] * r % mod;}}// for(int i = 1;i <= n;i++ , printf("\n")) for(int j = 1;j <= n;j++) printf("%d ",rmat[i][j]) ;///A = Rmat * Dvector<int> coe(n) ;for(int i = 0;i < n;i++) {for(int j = 0;j < n;j++) {coe[j] = (coe[j] + 1LL * w[i] * rmat[i + 1][j + 1]) % mod;}}return coe;
}int main() {cin >> A >> B >> C >> x;n = A + B + C;if(n & 1) {cout << 0 ; return 0;}if(A > n/2 || B > n/2 || C > n/2) {cout << 0 ; return 0;}t[0] = rt[0] = 1;for(int i = 1;i <= n + 1;i++) t[i] = 1LL * t[i - 1] * i % mod , rt[i] = fpow(t[i] , mod - 2) ;Cata[0] = 1;for(int i = 1;i <= n/2;i++) Cata[i] = 1LL * C_(i*2 , i) * fpow(i + 1 , mod - 2) % mod;//// F[i][j]表示i个主元分j段的方案数，Fi(x)作为其egfF[0][0] = 1;lm = n / 2 + 1;for(int i = 1;i <= n/2;i++) {for(int j = 1;j <= i;j++) {for(int k = 1;k <= i;k++) { ///最后一段包含的主元个数F[i][j] = (F[i][j] + 1LL * F[i - k][j - 1] * Cata[k - 1]) % mod;}// printf("%d %d : %d\n",i,j,F[i][j]) ;}}for(int i = 0;i <= n/2;i++) {for(int j = 0;j <= i;j++) F[i][j] = 1LL * F[i][j] * rt[j] % mod ; ///变成egffor(int j = 1;j <= lm;j++) {dot[i][j] = 0;for(int k = i;k >= 0;k--) dot[i][j] = (1LL * dot[i][j] * j + F[i][k]) % mod;///dot 代表点值}}vector<int> w(n/2 + 1) ;for(int i = 0;i <= n/2;i++) w[i] = 1LL * fpow(i , x) * t[i] % mod;vector<int> coe = get_coe(n/2 + 1 , w) ; /// coe.len = n/2 + 1int ans = 0;for(int a = 0;a <= n/2 && a <= A;a++) {for(int b = 0;b + a <= n / 2 && b <= B;b++) {int c = n / 2 - a - b;if(c > C) continue ;/// F[a] * F[b] * F[c]for(int i = 1;i <= lm;i++) d[i] = 1LL * dot[a][i] * dot[b][i] % mod * dot[c][i] % mod;// for(int i = 1;i <= lm;i++) printf("%d ",3LL * d[i] % mod) ; printf("\n") ;int sol = 0;for(int i = 1;i <= lm;i++) sol = (sol + 1LL * d[i] * coe[i - 1]) % mod;int sol2 = 0;for(int ab = 0;ab <= A - a && ab <= b; ab++){int ac = (A - a - ab) ;int bc = (c - ac) ;int ba = (B - b - bc) ;int ca = (a - ba) ;int cb = (C - c - ca) ;if(ac < 0 || bc < 0 || ba < 0 || ca < 0 || cb < 0) continue ;sol2 = (sol2 + 1LL * C_(a , ba) * C_(b , ab) % mod * C_(c , ac)) % mod;}// printf("%d %d %d : %d %d\n",a,b,c,sol,sol2);ans = (ans + 1LL * sol * sol2) % mod;}}cout << ans << '\n';
}

 

L. Challenge Matrix Multiplication

#include <bits/stdc++.h>
using namespace std;
const int N = 1e6 + 5;
typedef pair<int,int> pii;
int to[N] , fir[N] , nxt[N] ;
bool ok[N];
int cc = 0;
int nc , nodes[N];
void adde(int u,int v) {++cc;to[cc] = v;nxt[cc] = fir[u];fir[u] = cc;
}int in[N] , out[N] ;
int n ,m ;int ans[N];bool vis[N];
pii fr[N] ;
int cnt = 0;
int qu[N] , l , r;
void bfs(int u) {l = 1 , r = 0;qu[++r] = u;vis[u] = 1;while(l <= r) {int u = qu[l++];cnt++;for(int i = fir[u] ; i ; i = nxt[i]) {if(!vis[to[i]]) {qu[++r] = to[i] ;vis[to[i]] = 1;}}}return ;
}
int main() {ios::sync_with_stdio(false) ; cin.tie(0); cout.tie(0);clock_t cl = clock() ;cin >>n>>m; //printf("??? %d %d\n",n,m);for(int i = 1;i <= m;i++) {int u , v;cin >> u >> v;in[v]++ ; out[u]++;adde(u , v);}for(int i = 1;i <= n;i++) ans[i] = 1;int all = m;clock_t sum0 = 0 , sum1 = 0;while(all) {// clock_t a = clock();for(int i = 1;i <= n;i++) {if(in[i] < out[i]) {memset(vis,0,sizeof(vis)) ;vis[i] = 1;int lst;for(int j = i ; j <= n;j++) {if(!vis[j]) continue ;if(in[j] > out[j]) {lst = j ; break ;}for(int x = fir[j] ; x ; x = nxt[x]) {if(!vis[to[x]] && !ok[x]) {vis[to[x]] = 1;fr[to[x]] = {j , x};}}}int u = lst ;nc = 0;while(u) {nodes[nc++] = u;if(u != i) in[u]--;if(u != lst) out[u]--;if(u == i) break ;ok[fr[u].second] = 1;u = fr[u].first ;all--;}break ;}}// sum0 += (clock() - a);// a = clock() ;cnt = 0;memset(vis,0,sizeof(vis));for(int i = 0;i < nc;i++) {bfs(nodes[i]) ;ans[nodes[i]] = cnt;}// static int gg = 0;// sum1 += (clock() - a) ;// printf("i-th round %d %d\n",++gg , nc) ;}// cerr << (double)(clock() - cl) / CLOCKS_PER_SEC <<' ' << (double)sum0 / CLOCKS_PER_SEC <<' ' << (double)sum1 / CLOCKS_PER_SEC << '\n';// return 0;for(int i = 1;i <= n;i++) cout << ans[i] <<' ' ;cout << '\n';
}

 

M. Triangles

#include<bits/stdc++.h>
using namespace std;
int main()
{ios_base::sync_with_stdio(false);long long n,a,b;cin>>n>>a>>b;long long ans=0;for(long long r=1;r<=n;r++){ans+=r*(r+1);if(r*2>n)ans-=(r*2-n)*(r*2-n+1)/2;}for(long long i=1;i<=b;i++){ans-=(a-b+1);ans-=max(min(a+1-i,n-a)-(b-i),0ll);}cout<<ans<<endl;return 0;
}