越狱

盒子与球

斯特林第二类数（用dp求）*盒子的阶乘

int dp[11][11]; //n>=k
int A(int x){
	int res=1;
	fer(i,2,x+1)res*=i;
	return res;
}
signed main(){
	IOS;
	dp[2][1]=dp[2][2]=dp[1][1]=1;
	fer(i,3,11){
		dp[i][1]=1;
		fer(j,2,i){
			dp[i][j]=j*dp[i-1][j]+dp[i-1][j-1];
		}
		dp[i][i]=1;
	}
	int n,r;cin>>n>>r;
	cout<<dp[n][r]*A(r);
	
	return 0;
}

矩阵乘法

const int N=1e3+1,mod=1e9+7;
int a[N][N],b[N][N],res[N][N];
signed main(){
	IOS;
	int l,m,n; cin>>l>>m>>n;
	fer(i,0,l){
		fer(j,0,m)cin>>a[i][j];
	}
	fer(i,0,m){
		fer(j,0,n){
			cin>>b[i][j];
		}
	}
	//result l*n
	 fer(i,0,l){
	 	fer(j,0,n){
	 		fer(k,0,m){
	 			res[i][j]+=a[i][k]*b[k][j];
			 }
		 }
	 }
	 fer(i,0,l){
	 	fer(j,0,n){
	 		cout<<res[i][j]<<" ";
		 }
		 cout<<endl;
	 }
	return 0;
}

找朋友

最小的：1、1、1、1、……、n-m+1
最大的：n/m平均分，n%m平均分到每个小组里
res=$C_x^2$

int C(int x,int k){
	int res=1;
	for(int i=x;i>x-k;i--){
		res*=i;
	}
	fer(i,2,k+1)res/=i;
	return res;
}
signed main(){
	IOS;
	int n,m;cin>>n>>m;
	int res1=0,res2=0;
	int x=n/m;
	int y=n%m;
	//y个 C_{x+1}^2,(m-y)个C_x^2 
	res1=y*C(x+1,2)+(m-y)*C(x,2);
	res2=C(n-m+1,2);
	cout<<res1<<" "<<res2;
	return 0;
}

点餐

signed main(){
	IOS;
	int a;cin>>a;
	int b[3];
	fer(i,0,3)cin>>b[i];
	if(b[0]+b[1]+b[2]<=2*a)cout<<"YES";
	else cout<<"NO";
	return 0;
}