NOIP2018国庆雅礼集训day1 题解

因为我不想用电脑来画图，所以本篇题解大部分都手写。
T1 养花 flower
T2 折射 refract
T3 画作 paint =BZOJ2638 黑白染色

//T1 flower

#include<cstdio>
#include<cstring>
#include<cmath>
using namespace std;

const int maxn=100010,maxm=1100,maxk=100000;
int n,m,len,q,l[maxm],r[maxm],pos[maxn],a[maxn],f[maxm][maxn],b[maxn],ans;

int read()
{
	int x=0;
	char c=getchar();
	while (c<48||c>57)
		c=getchar();
	while (c>=48&&c<=57)
		x=(x<<1)+(x<<3)+(c^48),c=getchar();
	return x;
}

int max(int a,int b)
{
	if (a>b)
		return a;
	return b;
}

int min(int a,int b)
{
	if (a<b)
		return a;
	return b;
}

int main()
{
	freopen("flower.in","r",stdin);
	freopen("flower.out","w",stdout);
	int i,j,k,L,R,ql,qr;
	n=read(),q=read();
	len=1000;
	m=n/len;
	if (m*len<n)
		m++;
	for (i=1;i<=m;i++)
	{
		l[i]=r[i-1]+1;
		r[i]=i*len;
	}
	r[m]=n;
	for (i=1;i<=n;i++)
	{
		a[i]=read();
		pos[i]=(i-1)/len+1;
	}
	for (i=1;i<=m;i++)
	{
		memset(b,0,sizeof(b));
		for (j=l[i];j<=r[i];j++)
			b[a[j]]=a[j];
		for (j=1;j<=maxk;j++)
			b[j]=max(b[j],b[j-1]);
		for (j=1;j<=maxk;j++)
			for (k=0;k<=maxk;k+=j)
				f[i][j]=max(f[i][j],b[min(maxk,j+k-1)]-k);
	}
	while (q--)
	{
		L=read(),R=read(),k=read();
		ql=pos[L],qr=pos[R];
		ans=0;
		if (ql+1>=qr)
		{
			for (i=L;i<=R;i++)
				ans=max(ans,a[i]%k);
		}
		else
		{
			for (i=L;i<=r[ql];i++)
				ans=max(ans,a[i]%k);
			for (i=l[qr];i<=R;i++)
				ans=max(ans,a[i]%k);
			for (i=ql+1;i<=qr-1;i++)
				ans=max(ans,f[i][k]);
		}
		printf("%d
",ans);
	}
	return 0;
}

//T2 refract

#include<cstdio>
#include<algorithm>
using namespace std;

const int maxn=6010,mod=1000000007;
int n,f[2][maxn],ans;
struct node
{
	int x,y;
	bool operator <(const node &b)const
	{
		return x<b.x;
	}
}a[maxn];

int inc(int a,int b)
{
	a+=b;
	if (a>=mod)
		return a-mod;
	return a;
}

int read()
{
	int x=0,f=1;
	char c=getchar();
	while (c<48||c>57)
		f=c=='-'?-1:1,c=getchar();
	while (c>=48&&c<=57)
		x=(x<<1)+(x<<3)+(c^48),c=getchar();
	return x*f;
}

int main()
{
	freopen("refract.in","r",stdin);
	freopen("refract.out","w",stdout);
	int i,j;
	n=read();
	for (i=1;i<=n;i++)
		a[i]=(node){read(),read()};
	sort(a+1,a+n+1);
	for (i=1;i<=n;i++)
	{
		f[0][i]=f[1][i]=1;
		for (j=i-1;j>=1;j--)
		{
			if (a[i].y>a[j].y)
				f[0][i]=inc(f[0][i],f[1][j]);
			else
				f[1][j]=inc(f[1][j],f[0][i]);
		}
	}
	ans=mod-n;
	for (i=1;i<=n;i++)
		ans=inc(ans,inc(f[0][i],f[1][i]));
	printf("%d
",ans);
	fclose(stdin);
	fclose(stdout);
	return 0;
}

//T3 paint

#include<cstdio>
#include<cstring>
using namespace std;

const int maxn=55,inf=0x3f3f3f3f;
int n,m,mx[4]={0,1,0,-1},my[4]={1,0,-1,0},dis[maxn*maxn],id[maxn][maxn],q[maxn*maxn*2],l,r,cnt,ix[maxn*maxn],iy[maxn*maxn],ans;
char ch[maxn];
bool mp[maxn][maxn],vis[maxn*maxn];

int max(int a,int b)
{
	if (a>b)
		return a;
	return b;
}

int min(int a,int b)
{
	if (a<b)
		return a;
	return b;
}

int bfs(int u)
{
	int i,v,x,y,tx,ty;
	l=maxn*maxn,r=l-1;
	q[++r]=u;
	vis[u]=1;
	memset(dis,0x3f,sizeof(dis));
	memset(vis,0,sizeof(vis));
	dis[u]=1;
	while (l<=r)
	{
		u=q[l++];
		x=ix[u],y=iy[u];
		for (i=0;i<=3;i++)
		{
			tx=x+mx[i],ty=y+my[i];
			v=id[tx][ty];
			if (tx<1||tx>n||ty<1||ty>m||vis[v])
				continue;
			if (mp[tx][ty]==mp[x][y])
			{
				dis[v]=dis[u];
				q[--l]=v;
				vis[v]=1;
			}
			else
			{
				dis[v]=dis[u]+1;
				q[++r]=v;
				vis[v]=1;
			}
			if (mp[tx][ty]&&dis[v]>=ans)
				return inf;
		}
	}
	int tmp=0;
	for (i=1;i<=cnt;i++)
		if (mp[ix[i]][iy[i]])
			tmp=max(tmp,dis[i]);
	return tmp;
}

int main()
{
	freopen("paint.in","r",stdin);
	freopen("paint.out","w",stdout);
	int i,j;
	scanf("%d%d",&n,&m);
	for (i=1;i<=n;i++)
	{
		scanf("%s",ch+1);
		for (j=1;j<=m;j++)
		{
			mp[i][j]=(ch[j]-48);
			id[i][j]=++cnt;
			ix[cnt]=i,iy[cnt]=j;
		}
	}
	ans=inf;
	for (i=1;i<=n;i++)
		for (j=1;j<=m;j++)
			ans=min(ans,bfs(id[i][j]));
	printf("%d
",ans);
	fclose(stdin);
	fclose(stdout);
	return 0;
}