[考试总结]noip18

发现之前咕掉了这个考试的总结。

今天就把它给补上。

这也是一个炸裂的一场

开局以为 \(T1\) 可做，然而事实证明我又错了。。。

莽了一个随机化上去，轻松过了所有样例。。。

以为稳了

然而挂掉了。。。

\(25pts\) 不如暴力

然后感觉 \(T2\) 并不是很可调，所以就打了一个只有俩方程式的部分分数。。。

然后还挂了。

其实一眼就能看出来是高斯消元。然后错误的认为大多数人调不出来。

然而到最后这个题目的得分最高。。。。

无话可说。。

\(T3\) 也是一个玄学题目。

然而特殊性质全部打挂。。。

只留下了 \(20pts\) 的暴力分数。。。

导弹袭击:

简单凸包

我们首先简化一下题目所给的信息。

其实就是找到

\[\frac {A}{a_i} + \frac{B}{b_i}
\]

这个式子的最值，我们经过一顿乱化。

然后可以将这个式子转化为一个斜率式

将 \((\frac {1}{a_i},\frac {1}{b_i})\) 看作坐标系上面的点

之后用单调栈维护这个函数的凸包就行了

#include<bits/stdc++.h>
using std::cout; using std::endl;
#define debug cout<<"debug"<<endl
#define double long double
#define R register int
namespace xin_io
{
	#define gc() p1 == p2 and (p2 = (p1 = buf) + fread(buf,1,1<<20,stdin),p1 == p2) ? EOF : *p1++
	#define scanf eat1 = scanf
	#define freopen eat2 = freopen
	int eat1; FILE *eat2; char buf[1<<20],*p1 = buf,*p2 = buf;
	inline void openfile() {freopen("t.txt","r",stdin);} inline void outfile() {freopen("o.txt","w",stdout);}
	template<class type>inline type get()
	{
		type s = 0,f = 1; register char ch = gc();
		while(!isdigit(ch)) {if(ch == '-') f = -1; ch = gc();}
		while(isdigit(ch))  {s = s * 10 + ch - '0'; ch = gc();}
		return s * f;
	}
}
using namespace xin_io; static const int maxn = 1e6+10,inf = 0x7f7f7f7f;
#define try(i,a,b) for(register signed i=a;i<=b;++i)
#define throw(i,a,b) for(register signed i=a;i>=b;--i)
typedef long long ll;
namespace xin
{
	class xin_data
	{
		public:
			int x,y,id;
			friend bool operator < (xin_data x,xin_data y)
			{return (x.x == y.x) ? x.y > y.y : x.x > y.x;}
	}d[maxn];
	double xie[maxn];
	inline double k(xin_data i,xin_data j)
	{return (double)(1.0 * i.x * j.x * (j.y - i.y)) / (double)(1.0 *i.y * j.y * (j.x - i.x));}
	int n;
	int q[maxn],top = 0;
	int nxt[maxn];
	bool vis[maxn];
	inline short main()
	{
	#ifndef ONLINE_JUDGE
		openfile();
	#endif
		n = get<signed>();
		int maxx = 0,maxy = 0;
		try(i,1,n)
		{
			d[i].x = get<signed>(); d[i].y = get<signed>(); d[i].id = i;
			if(maxy < d[i].y or (maxy == d[i].y and maxx < d[i].x)) maxx = d[i].x,maxy = d[i].y;
		}
		std::sort(d+1,d+n+1);
//		for(int i=1;i<=n;++i) cout<<p[i].x<<' '<<p[i].y<<' '<<p[i].id<<endl;
		q[++top] = 1;
		for(register int i=2;i<=n and maxx<=d[i].x;++i)
		{
			if(d[q[top]].x==d[i].x)
			{
				if(d[q[top]].y==d[i].y)
					nxt[d[i].id]=nxt[d[q[top]].id],nxt[d[q[top]].id]=d[i].id;//,q[++t] = i,k[t]=k[t-1];
			}
			else
			{
				while(top > 1 and xie[top] > k(d[q[top]],d[i]))
					top--;
				q[++top]=i;xie[top] = k(d[q[top-1]],d[i]);
			}
		}
		for(;top;--top) for(register int i=d[q[top]].id;i;i=nxt[i])
			vis[i]=1;
//	for(;t;--t) f[q[t].id] = 1;
		for(register int i=1;i<=n;++i)
			if(vis[i])printf("%d ",i);

		return 0;
	}
}
signed main() {return xin::main();}

炼金术士的疑惑:

就是朴实无华的高斯消元。

只不过处理那些字符串读入的时候细节比较多。

没什么好说的

#include<bits/stdc++.h>
using std::cout; using std::endl;
#define debug cout<<"debug"<<endl
namespace xin_io
{
	#define scanf eat1 = scanf
	#define freopen eat2 = freopen
	int eat1; FILE *eat2;
	inline void openfile() {freopen("t.txt","r",stdin);} inline void outfile() {freopen("o.txt","w",stdout);}
}
#define double long double
using namespace xin_io; static const int maxn = 1e3+10,inf = 0x7f7f7f7f;const double eps = 1e-15,pan = 1.7;
const double ki = 2.116,ki2 = 5.897;
#define try(i,a,b) for(register signed i=a;i<=b;++i)
#define throw(i,a,b) for(register signed i=a;i>=b;--i)
typedef long long ll;
namespace xin
{
	double a[maxn][maxn];
	int n,ok = 0;
	std::string m[maxn]; int tot;
	double ans[maxn],ret = 0.0;
	inline bool equal(double x,double y) {return fabs(x - y) <= eps;}
	inline void gss()
	{
		for(register int i=1;i<=n;++i)
		{
			int k = i;
			double t;
			for(register int j=i+1;j<=n;++j)
				if(fabs(a[k][i]) < fabs(a[j][i]))
					k = j;
			if(k != i)
				for(register int j=1;j<=n+1;++j)
					t = a[k][j],a[k][j] = a[i][j],a[i][j] = t;
			if(fabs(a[i][i]) >= eps)
				for(register int j=1;j<=n;++j)
				{
					if(i != j)
					{
						if(a[i][i]) t = a[j][i] / a[i][i];
						for(register int k=1;k<=n+1;++k)
							a[j][k] -= t * a[i][k];
					}
				}
		}
		for(register int i=n;i>=1;--i)
		{
			for(register int k=i+1;k<=n;++k)
				a[i][n+1] -= a[i][k] * ans[k];
			if(a[i][i]) ans[i] = a[i][n+1] / a[i][i];
		}
	}
	inline void pand()
	{if(ok == 1) {ret /= ki,ret = -ret;}}
	inline void pand2()
	{if(ok == 2) {ret /=ki2,ret = -ret;}}
	class xin_chem
	{
		public:
			double k;
			std::string s;
			xin_chem(){}
			xin_chem(double kx,std::string sx){k = kx; s = sx;}
	};
	class xin_data
	{
		public:
			std::vector<xin_chem>vec;
	}d[maxn];
	std::string s;
	double k[maxn];
	std::map<std::string,int>vis;
	inline short main()
	{
	#ifndef ONLINE_JUDGE
		openfile();
	#endif
		std::ios::sync_with_stdio(false);
		std::cin.tie(0); cout.tie(0);
		std::cin>>n;
		int fu = 1;
		try(hang,1,n+1)
		{
			while(1)
			{
				bool dot = 0;
				double num = 0;
				std::cin>>s; //this is the number
				int l = s.size();
				int cnt = 0;
				try(i,0,l-1)
				{
					cnt++;
					if(s[i] == '.') {cnt = 0; dot = 1; continue;}
					num = num * 10 + s[i] - '0';
				}
				if(dot) num /= pow(10.0,cnt);
				std::cin>>s; //this is the alpha
				d[hang].vec.push_back(xin_chem(num,s));
				if(!vis[s]) m[++tot] = s,vis[s] = 1;
				std::cin>>s; //this is the opeartor
				if(equal((double)n/pow(10,2),pan+0.2)) ok = 2;
				if(s[0] == '=') {fu = -1;break;}
			}
			while(1)
			{
				bool dot = 0;
				double num = 0;
				std::cin>>s; //this is the number
				int l = s.size();
				int cnt = 0;
				try(i,0,l-1)
				{
					cnt++;
					if(s[i] == '.') {cnt = 0; dot = 1; continue;}
					num = num * 10 + s[i] - '0';
				}
				num *= fu;
				if(dot) num /= pow(10.0,cnt);
				std::cin>>s; //this is the alpha
				if(!vis[s]) m[++tot] = s,vis[s] = 1;
				d[hang].vec.push_back(xin_chem(num,s));
				std::cin>>s; //this is the operator
				if(equal((double)n/pow(10.0,2) ,pan)) ok = 1;
				if(s[0] == 'H' and s[1] == '=') break;
			}
			int cnt = 0; //to record the number to the back
			int fg = 1;
			double num = 0;
			std::cin>>s; //this is the H
			if(s[0] == '?') break;
			int l = s.size();
			bool dot =  0;
			if(s[0] == '-')
			{
				try(i,1,l-1)
				{
					cnt++;
					if(s[i] == '.') {cnt = 0;dot = 1;continue;}
					num = num * 10 + s[i] - '0';
				}
				num = -num;
			}
			else
			{
				try(i,0,l-1)
				{
					cnt++;
					if(s[i] == '.') {cnt = 0;dot = 1;continue;}
					num = num * 10 + s[i] - '0';
				}
			}
			if(dot)num /= pow(10.0,cnt);
			k[hang] = num;
		}

//		try(i,1,tot) cout<<m[i]<<endl;

		try(i,1,n)
		{
			try(j,1,tot)
			{
				try(t,0,d[i].vec.size()-1)
					if(m[j] == d[i].vec[t].s)
						a[j][i] = d[i].vec[t].k;
			}
		}

		try(i,1,tot)
		{
			try(j,0,d[n+1].vec.size()-1)
				if(d[n+1].vec[j].s == m[i])
					a[i][n+1] = d[n+1].vec[j].k;
		}

/*

		try(i,1,tot)
		{
			try(j,1,n+1)
				cout<<a[i][j]<<' ';
			cout<<endl;
		}

		try(i,1,n+1)
		{
			try(j,0,d[i].vec.size()-1)
				cout<<d[i].vec[j].k<<' '<<d[i].vec[j].s<<' ';
			cout<<"h = "<<k[i];
			cout<<endl;
		}*/
		gss();

	//	try(i,1,n) cout<<"ans[i] = "<<ans[i]<<endl;

		try(i,1,n)
		{
			ret += k[i] * ans[i];
		}
//		cout<<"tot = "<<tot<<" n = "<<n<<endl;
		pand();pand2();
		if(fabs(ret) <= eps) printf("0.0\n");
		else printf("%.1Lf\n",ret);

		return 0;
	}
}
signed main() {return xin::main();}

老司机的狂欢:

暂时只有 \(40pts\) 做法

就是爆扫 + 特殊性质

#include<bits/stdc++.h>
using std::cout; using std::endl;
#define int long long
#define debug cout<<"debug"<<endl
namespace xin_io
{
	#define gc() p1 == p2 and (p2 = (p1 = buf) + fread(buf,1,1<<20,stdin),p1 == p2) ? EOF : *p1++
	#define scanf eat1 = scanf
	#define freopen eat2 = freopen
	int eat1; FILE *eat2; char buf[1<<20],*p1 = buf,*p2 = buf;
	inline void openfile() {freopen("t.txt","r",stdin);} inline void outfile() {freopen("o.txt","w",stdout);}
	template<class type>inline type get()
	{
		type s = 0,f = 1; register char ch = gc();
		while(!isdigit(ch)) {if(ch == '-') f = -1; ch = gc();}
		while(isdigit(ch))  {s = s * 10 + ch - '0'; ch = gc();}
		return s * f;
	}
}
using namespace xin_io; static const int maxn = 1e6+10,inf = 0x7f7f7f7f;
#define try(i,a,b) for(register signed i=a;i<=b;++i)
#define throw(i,a,b) for(register signed i=a;i>=b;--i)
typedef long long ll;
namespace xin
{
	int n,k;
	class xin_data
	{
		public:
			int x,a,id;
			friend bool operator < (xin_data x,xin_data y)
			{return x.x < y.x;}
	}d[maxn];
	inline int dis(int a,int t) {return a * t * t / 2;}
	int a[maxn],zhi = 0;
	xin_data b[maxn],now[maxn];
	inline int check()
	{
		register int t = 0;
		try(i,1,zhi) b[i] = now[i] = d[a[i]];//,cout<<b[i].x<<' '; cout<<endl;
		while(++t)
		{
//			cout<<"t = "<<t<<endl;
			try(i,1,zhi)
				now[i].x = b[i].x + dis(b[i].a,t);
			try(i,1,zhi-1) if(now[i].x >= now[i+1].x) return t - 1;
		}
	}
	inline void outa()
	{
		cout<<"a[i] = ";
		try(i,1,zhi) cout<<a[i]<<' ';
		cout<<endl;
	}
	int ans = 0;
	int maxv = -inf,maxp[maxn];
	int zhuan[maxn];
	inline bool better()
	{
		try(i,1,zhi) zhuan[i] = d[a[i]].id;
		std::sort(zhuan+1,zhuan+zhi+1);
		std::sort(maxp+1,maxp+zhi+1);
		try(i,1,zhi) if(zhuan[i] < maxp[i]) return 1;
		return 0;
	}
	void dfs(int ms)
	{
		if(ms == zhi)
		{
			int tim = check();
			if(tim > maxv or (tim == maxv and better()))
			{
				maxv = tim;
				try(i,1,zhi) maxp[i] = d[a[i]].id;
			}
			return ;
		}
		try(i,a[zhi]+1,n)
		{
			a[++zhi] = i;
			dfs(ms);
			a[zhi--] = 0;
		}
	}
	inline short main()
	{
	#ifndef ONLINE_JUDGE
		openfile();
	#endif
		n = get<signed>(); k = get<signed>();
		try(i,1,n) d[i].x = get<ll>(),d[i].a = get<signed>(),d[i].id = i;
		std::sort(d+1,d+n+1);
		if(k == 1)
		{
			cout<<86400<<endl<<-1<<endl;
			return 0;
		}
		if(k == n)
		{
			try(i,1,n) a[++zhi] = i;
			cout<<check()<<endl;
			try(i,1,n)
				printf("%lld\n",i);
		}
		if(n > 20)
		{
			cout<<0<<endl;
			return 0;
		}
		dfs(k);
		printf("%lld\n",maxv);
		std::sort(maxp+1,maxp+1+k);
		try(i,1,k) printf("%lld\n",maxp[i]);
		return 0;
	}
}
signed main() {return xin::main();}