2016 ICPC 沈阳

A - Thickest Burger

a+b+max(a,b)

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;

int main(){
	//freopen("in.txt","r",stdin);
	int n,a,b;
	while(~scanf("%d",&n)){
		for(int i=1;i<=n;i++){
			scanf("%d%d",&a,&b);
			printf("%d\n",a+b+max(a,b));
		}
	}
	return 0;
}

B - Relative atomic mass

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
char s[100];
int main(){
	//freopen("in.txt","r",stdin);
	int t;
	scanf("%d",&t);
	while(t--){
		scanf("%s",s);
		int ans=0;
		int len=strlen(s);
		for(int i=0;i<len;i++) {
			if(s[i]=='H') ans+=1;
			else if(s[i]=='O') ans+=16;
			else ans+=12;
		}
		printf("%d\n",ans);
	}
	return 0;
}

C - Recursive sequence

将$n^4$,$n$带着一起转移。

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
const ll P = 2147493647;
const int N = 7;
ll n,a,b;
struct matrix {
	ll a[N][N];
	int row,col;
	matrix():row(N),col(N){memset(a,0,sizeof a);}
	ll* operator [](int x){return a[x];}
	matrix operator * (matrix x){
		matrix tmp;
		for(int i=0;i<N;i++)
			for(int j=0;j<N;j++){
				tmp[i][j]=0;
				for(int k=0;k<N;k++)
					tmp[i][j]=(tmp[i][j]+a[i][k]*x[k][j]%P)%P;
			}
		return tmp;
	}
	void operator *= (matrix x){*this = *this * x;}

	matrix operator ^ (ll x){
		matrix ret;
		for(int i=0;i<N;i++) ret[i][i]=1;
		matrix tmp=*this;
		for(;x;x>>=1,tmp*=tmp){if(x&1)ret *= tmp;}
		return ret;
	}
};



int main(){
	//freopen("in.txt","r",stdin);
	int T;
	cin>>T;
	while(T--){
		cin>>n>>a>>b;
		a%=P;b%=P;
		if(n==1){
			printf("%lld\n",a);
			continue;
		}
		if(n==2){
			printf("%lld\n",b);
			continue;
		}
		matrix base;
		base[0][1]=2;
		base[0][0]=base[0][2]=base[1][0]=1;
		base[2][2]=base[3][3]=base[4][4]=base[5][5]=base[6][6]=1;
		base[2][6]=base[3][6]=base[4][6]=base[5][6]=1;
		base[2][3]=4;base[2][4]=6;base[2][5]=4;
		base[3][4]=base[3][5]=3;
		base[4][5]=2;
		base=base^(n-2);
		ll res = base[0][0]*b%P+base[0][1]*a%P+81ll*base[0][2]%P+27ll*base[0][3]%P+9ll*base[0][4]%P+3ll*base[0][5]%P+base[0][6];
		res %= P;
		cout<<res<<endl;
	}
	return 0;
}

E - Counting Cliques

#include<iostream>
#include<string.h>
#include<vector>
using namespace std;
int s,u,v,ans;
int g[111][111];
int data[111];
vector<int>e[1111];
int dfs(int id,int size)
{
	if(size==s)
	{
		ans++;
		return 0;
	}
	for(int i=0;i<e[id].size();i++)
	{
		int ep=e[id][i];
		bool flag=true;
		for(int j=1;j<size;j++)
			if(!g[ep][data[j]])
			{
				flag=false;
				break;
			}
		if(flag)
		{
			data[++size]=ep;
			dfs(ep,size);
			data[size--]=0;
		}
	}
}
int main()
{
	int t;
	cin>>t;
	while(t--)
	{
		int n,m;
		cin>>n>>m>>s;
		memset(g,0,sizeof(g));
		for(int i=1;i<=n;i++)
			e[i].clear();
		for(int i=1;i<=m;i++)
		{
			cin>>u>>v;
			if(u>v)
				swap(u,v);
			e[u].push_back(v);
			g[u][v]=g[v][u]=1;
		}
		ans=0;
		for(int i=1;i<=n;i++)
		{
			int size=1;
			data[1]=i;
			dfs(i,1);
		}
		cout<<ans<<endl;
	}
    return 0;
}

G - Do not pour out

积分+二分答案。

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
const double eps = 1e-10;
const double pi = 4.0*atan(1.0);

int dcmp(double x){
	if(x<-eps) return -1;
	if(x>eps) return 1;
	return 0;
}

double d;

double calc(double x){
	return pi*cos(x)-x*cos(x)+sin(x)-1.0/3.0*sin(x)*sin(x)*sin(x);
}

double f(double x){
	double ax=acos(2.0*tan(x)-1.0);
	double ret=calc(ax)-calc(pi);
	return ret/tan(x);
}

int main(){
	//freopen("in.txt","r",stdin);
	int T;
	cin>>T;
	while(T--){
		scanf("%lf",&d);
		if(dcmp(d)<=0){
			puts("0.00000");
			continue;
		}
		if(dcmp(d-1)>=0){
			double theta=atan(2-d);
			double res=pi/cos(theta);
			printf("%.5lf\n",res);
		} else {
			double l=0.0,r=pi/4.0,ansk;
			while(dcmp(l-r)<=0){
				double mid = (l+r)/2.0;
				double sx=f(mid);
				if(dcmp(sx-d*pi)<=0){
					l=mid+eps;
					ansk=mid;
				} else {
					r=mid-eps;
				}
			}
			double ax=acos(2.0*tan(ansk)-1.0-eps);
			double sx=pi-ax+sin(ax)*cos(ax);
			double res=sx/sin(ansk);
			printf("%.5lf\n",res);
		}
	}
	return 0;
}

H - Guessing the Dice Roll

建立AC自动机fail节点接建立方程组，高斯消元。
坑。