[考试总结]noip模拟14

咕掉了好长时间，现在终于回来了。。

这次考试炸裂得很完蛋，直接分数上天。

\(T1\) 本来想打一个记忆化搜索，然而老是通过不了样例，然后就挂了，只剩下了垃圾的 \(30pts\) 部分分数。

然而到现在记忆化还是调不出来。。。。

好废啊。

然后 \(T2,T3\) 也只能是暴力收场，垃得一批。

T1:

这个题目就是一个显然的 \(dp\) （只是 \(dp\) 显然，而不是 \(dp\) 方程显然）。。。

然后我们开始疯狂地推 \(dp\) 式子。。。

然后推不出来。。。

你推不出来不会加元吗？？？？？？？？？

这就是推 \(dp\) 方程的真谛

唉

但是我想不出来还有什么状态怎么办呢

那就考虑那些不连续的东西。

虽然他们无法直接转移，但是我们可以离散化

我们将值离散化，然后我们就可以将 \(dp\) 的第二维设置作为值。

我们再来分析问题的实质：

\(\huge{\text{实际上就是要求}min(A_{1\rightarrow i}>B_{i+1})}\)

然后就有了嘛。

然后线段树优化

我从一开始就垃了，巨佬们都想出了线段树优化，而我只能打打暴力维持一下生活这样子

#include<bits/stdc++.h>
using std::cout; using std::endl;
#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 = 0x7f7f7f,mod = 998244353;
#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 da[maxn],db[maxn],pre_a[maxn],pre_b[maxn];
	int n,a[maxn],b[maxn];
	int ans = -inf;
	int lisan[maxn],zhi = 0;
	int tot;
	class xin_segment
	{
		private:
			#define ls(fa) (fa << 1)
			#define rs(fa) (fa << 1 | 1)
			#define up(fa) t[fa].s = std::max(t[ls(fa)].s,t[rs(fa)].s)
			inline void down(int fa,int l,int r)
			{
				if(!t[fa].debt) return ;
				t[ls(fa)].debt += t[fa].debt; t[rs(fa)].debt += t[fa].debt;
				t[ls(fa)].s += t[fa].debt; t[rs(fa)].s += t[fa].debt;
				t[fa].debt = 0;
			}
		public:
			class xin_tree{public:int s,debt;}t[maxn];
			void insert(int fa,int l,int r,int pos,int val)
			{
				if(pos > r or pos < l ) return ;
				if(l == r){t[fa].s = std::max(t[fa].s,val); return ;}
				register int mid = l + r >> 1;
				down(fa,l,r);
				insert(ls(fa),l,mid,pos,val); insert(rs(fa),mid+1,r,pos,val);
				up(fa);
			}
			void update(int fa,int l,int r,int ql,int qr,int val)
			{
				if(qr < l or ql > r) return ;
				if(qr >= r and ql <= l)
				{
					t[fa].s += val; t[fa].debt += val;
					return ;
				}
				register int mid = l + r >> 1;
				down(fa,l,r);
				update(ls(fa),l,mid,ql,qr,val); update(rs(fa),mid+1,r,ql,qr,val);
				up(fa);
			}
			int query(int fa,int l,int r,int ql,int qr)
			{
				if(qr < l or ql > r) return -inf;
				if(qr >= r and ql <= l) return t[fa].s;
				register int mid = l + r >> 1,ret = 0;
				down(fa,l,r);
				ret = std::max(ret,query(ls(fa),l,mid,ql,qr));
				ret = std::max(ret,query(rs(fa),mid+1,r,ql,qr));
				return ret;
			}
	}t;

	inline short main()
	{
	#ifndef ONLINE_JUDGE
		openfile();
	#endif
		n = get<signed>();
		try(i,1,n) pre_a[i] = da[i] = get<signed>(),pre_b[i] = db[i] = get<signed>(),lisan[++zhi] = da[i],lisan[++zhi] = db[i];
		std::sort(lisan+1,lisan+zhi+1);
		int len = std::unique(lisan+1,lisan+zhi+1) - lisan - 1;
		try(i,1,n)
		{
			a[i] = std::lower_bound(lisan+1,lisan+len+1,pre_a[i]) - lisan;
			b[i] = std::lower_bound(lisan+1,lisan+len+1,pre_b[i]) - lisan;
//			cout<<a[i]<<' '<<b[i]<<endl;
		}
		try(i,1,n)
		{
			if(a[i] <= b[i])
			{
				register int temp = t.query(1,1,len,b[i]+1,len) + 1;
				ans = std::max(ans,temp);
				t.insert(1,1,len,a[i],temp);
			}
			else
			{
				register int temp = t.query(1,1,len,a[i]+1,len) + 1;
				ans = std::max(ans,temp);
				int zhuan = temp;
				temp = t.query(1,1,len,b[i]+1,a[i]) + 1;
				ans = std::max(ans,temp);
				t.update(1,1,len,b[i]+1,a[i],1);
				t.insert(1,1,len,a[i],zhuan);
			}
		}
		cout<<ans<<endl;
		return 0;
	}
}
signed main() {return xin::main();}

T2:

还没改出来，现在只能拿个 \(40pts\) 暴力分。。。

#include<bits/stdc++.h>
using std::cout; using std::endl;
#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,mod = 998244353;
#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;
int n,m;
class xin_edge{public:int ver,next;}edge[maxn];
int head[maxn],zhi = 0;
inline void add(int x,int y) {edge[++zhi].ver = y; edge[zhi].next = head[x]; head[x] = zhi;}
int c[maxn];
int d[maxn];
namespace subtask1
{
	bool vis[maxn],col[maxn];
	void dfs1(int x,int f)
	{
		d[x] = d[f] + 1;
		for(register int i=head[x];i;i=edge[i].next)
		{
			register int y = edge[i].ver;
			dfs1(y,x);
		}
	}
	int q[maxn],zhi = 0;
	inline int query(int pos,int len)
	{
		int ans = 0;
		if(!len) return 1;
		memset(vis,0,sizeof(bool) * (n + 1)); memset(col,0,sizeof(bool) * (n + 1));
		q[++zhi] = pos; vis[pos] = col[c[pos]] = 1; ans = 1;
		while(zhi)
		{
			register int x = q[zhi--];
			for(register int i=head[x];i;i=edge[i].next)
			{
				register int y = edge[i].ver;
				if(d[y] - d[pos] > len) continue;
				if(!vis[y])
				{
					vis[y] = 1;
					if(!col[c[y]]) col[c[y]] = 1,ans++;
					q[++zhi] = y;
				}
			}
		}
		return ans;
	}
	inline short main()
	{
		try(i,1,n) c[i] = get<signed>();
		try(i,2,n)
		{
			register int x = get<signed>();
			add(x,i);
		}
		dfs1(1,0);
		try(que,1,m)
		{
			register int x = get<signed>(),len = get<signed>();
			printf("%d\n",query(x,len));
		}
		return 0;
	}
}
signed main()
{
#ifndef ONLINE_JUDGE
	openfile();
#endif
	n = get<signed>(); m = get<signed>();
	subtask1::main();
	return 0;
}

垃圾的我在考场上莫队还打垃了。

T3:

暴力极度好想，就是暴力搜索，然后就愉快有 \(50pts\)

#include<bits/stdc++.h>
using std::cout; using std::endl;
#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,mod = 998244353;
#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
{
	std::string s;
	int len,l;
	bool ok = 0;
	std::vector<char> a; int zhi = 0,ans = 0;
	std::map<std::vector<char>,int>vis;
	void dfs(int ms,int pos)
	{
		if(a.size() == ms)
		{
			if(!vis[a]) vis[a] = 1,ans++;
			return ;
		}
		for(register int i=pos+1;i<l;++i)
		{
			a.push_back(s[i]);
			dfs(ms,i);
			a.pop_back();
		}
	}
	inline short main()
	{
	#ifndef ONLINE_JUDGE
		openfile();
	#endif
		std::cin>>s>>len;
		l = s.size();
		for(register int i=1;i<l;++i)
			if(s[i] != s[i-1]) ok = 1;
		if(!ok){cout<<1<<endl;return 0;}
		dfs(len,-1);
		cout<<ans<<endl;
		return 0;
	}
}
signed main() {return xin::main();}

老 \(STL\) 人了

然后考虑正解。。

这就是一道luogu上绿色的模板题嘛 ---赵sir

我又垃了。

好吧，方程就是：

\[f_{i,j} = f_{i-1,j} + f_{i,j-1} - f{p-1,j-1}
\]

表示处理前 \(i\) 个位置，然后长度为 \(j\),\(p\) 就是这个字母上一个出现的位置。

然后就有了：

#include<bits/stdc++.h>
using std::cout; using std::endl;
#define debug cout<<"debug"<<endl
#define int long long
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 = 3e3+10,inf = 0x7f7f7f7f,mod = 998244353;
#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 f[maxn][maxn];
	char s[maxn];
	int l,len;
	int p[maxn];
	int dfs(int i,int j)
	{
		if(i < j) return 0;
		if(f[i][j]) return f[i][j];
		if(!i or !j) return 1;
		if(p[i]) f[i][j] = (dfs(i-1,j) + dfs(i-1,j-1) - dfs(p[i]-1,j-1) + mod) % mod;
		else f[i][j] = (dfs(i-1,j) + dfs(i-1,j-1)) % mod;
		return f[i][j] % mod;
	}
	inline void do_prework()
	{
		try(i,1,l)
			try(j,i+1,l)
				if(s[j] == s[i])
					{p[j] = i;break;}
	}
	inline short main()
	{
	#ifndef ONLINE_JUDGE
		openfile();
	#endif
		scanf("%s%lld",s+1,&len); l = strlen(s+1);
		try(i,0,len) f[i][i] = 1;
		do_prework();
		f[l][len] = dfs(l,len) % mod;
		cout<<f[l][len] % mod<<endl;
		return 0;
	}
}
signed main() {return xin::main();}