[CSP-S模拟测试58]题解

以后题解还是单独放吧。

A.Divisors

根号筛求所有数的因子，扫一遍去重统计即可。

#include<cstdio>
#include<iostream>
#include<cstring>
#include<vector>
#include<map>
using namespace std;
const int N=205;
int a[N],m,n;
map<int,int> bu;
vector<int> res,app;
int ans[N];
int main()
{
	//freopen("dt.in","r",stdin);
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++)
	{
		scanf("%d",&a[i]);
		for(int j=1;1LL*j*j<=a[i];j++)
		{
			if(a[i]%j)continue;
			if(j*j==a[i])res.push_back(j);
			else res.push_back(j),res.push_back(a[i]/j);
		}
	}
	int sz=res.size();
	for(int i=0;i<sz;i++)
	{
		if(res[i]>n)continue;
		if(bu.find(res[i])==bu.end())app.push_back(res[i]);
		bu[res[i]]++;
	}
	sz=app.size();
	for(int i=0;i<sz;i++)
		ans[bu[app[i]]]++;
	ans[0]=n-sz;
	for(int i=0;i<=m;i++)
		printf("%d
",ans[i]);
	return 0;
}

B.Market

离线询问。把询问和商店都按时间排序，维护一个指针把所有能被当前计划购买的商品都放进来跑一次背包。

注意到话费很大而价值很小，那么把价值作为dp数组下标，后缀取min保证单调后二分查找最优解即可。

#include<cstdio>
#include<iostream>
#include<cstring>
#include<algorithm>
using namespace std;
int read()
{
	int x=0,f=1;char ch=getchar();
	while(!isdigit(ch)){if(ch=='-')f=-1;ch=getchar();}
	while(isdigit(ch))x=x*10+ch-'0',ch=getchar();
	return x*f;
}
const int inf=0x3f3f3f3f;
int n,m,f[100005],ans[100005];
struct shop
{
	int c,v,t;
	friend bool operator < (shop a,shop b)
	{
		return a.t<b.t;
	}
}s[305];
struct plan
{
	int t,num,id;
	friend bool operator < (plan a,plan b)
	{
		return a.t<b.t;
	}
}p[100005];
void show()
{
	for(int i=1;i<=n*300;i++)
		cout<<f[i]<<endl;
}
int main()
{
	/*freopen("dt.in","r",stdin);
	freopen("my.out","w",stdout);*/
	n=read();m=read();
	for(int i=1;i<=n;i++)
		s[i].c=read(),s[i].v=read(),s[i].t=read();
	for(int i=1;i<=m;i++)
		p[i].t=read(),p[i].num=read(),p[i].id=i;
	sort(s+1,s+n+1);sort(p+1,p+m+1);
	memset(f,0x3f,sizeof(f));
	f[0]=0;
	int j=1;
	for(int i=1;i<=m;i++)
	{
		while(j<=n&&s[j].t<=p[i].t)
		{
			for(int k=n*300;k>=s[j].v;k--)
				f[k]=min(f[k],f[k-s[j].v]+s[j].c);
			for(int k=n*300;k;k--)
				f[k]=min(f[k],f[k+1]);
			j++;
		}
		//ow();
		//cout<<p[i].id<<' '<<p[i].num<<endl;
		ans[p[i].id]=upper_bound(f+1,f+n*300+1,p[i].num)-f-1;

	}
	for(int i=1;i<=m;i++)
		printf("%d
",ans[i]);
	return 0;
}

C.Dash Speed

直接从边考虑似乎不可做，那么换一个角度思考，从可行的速度入手，不断往当前集合中加边，最终边集的直径就是答案。

这种做法与某次考试的T2十分类似。

以速度为下标建立一棵线段树，并把符合区间限制的边插入(方式类似于前向星，或者直接vector也行)。

之后就可以通过$O(n log n)$的线段树分治一次性得到所有答案。到达一个线段树区间时，将存在这里的边所连接的点集合并。具体合并方式就是像之前那道题一样，讨论6种情况来确定新联通块端点。

由于分治需要回溯，回溯需要撤销影响，所以并查集的结构不能中途发生不可逆改变，即不能路径压缩。那么这里就需要另外一种合并方式——按秩合并。

之后用栈记录一下改变的信息，回溯时弹栈撤销即可。

#include<cstdio>
#include<iostream>
#include<cstring>
#include<vector>
#include<cmath>
#define re register
using namespace std;
namespace IO{
    #define BUF_SIZE 100000
    #define OUT_SIZE 100000
    #define ll long long
    //fread->read

    bool IOerror=0;
    inline char nc(){
        static char buf[BUF_SIZE],*p1=buf+BUF_SIZE,*pend=buf+BUF_SIZE;
        if (p1==pend){
            p1=buf; pend=buf+fread(buf,1,BUF_SIZE,stdin);
            if (pend==p1){IOerror=1;return -1;}
            //{printf("IO error!
");system("pause");for (;;);exit(0);}
        }
        return *p1++;
    }
    inline bool blank(char ch){return ch==' '||ch=='
'||ch=='
'||ch=='	';}
    inline void read(int &x){
        bool sign=0; char ch=nc(); x=0;
        for (;blank(ch);ch=nc());
        if (IOerror)return;
        if (ch=='-')sign=1,ch=nc();
        for (;ch>='0'&&ch<='9';ch=nc())x=x*10+ch-'0';
        if (sign)x=-x;
    }
    inline void read(ll &x){
        bool sign=0; char ch=nc(); x=0;
        for (;blank(ch);ch=nc());
        if (IOerror)return;
        if (ch=='-')sign=1,ch=nc();
        for (;ch>='0'&&ch<='9';ch=nc())x=x*10+ch-'0';
        if (sign)x=-x;
    }
    inline void read(double &x){
        bool sign=0; char ch=nc(); x=0;
        for (;blank(ch);ch=nc());
        if (IOerror)return;
        if (ch=='-')sign=1,ch=nc();
        for (;ch>='0'&&ch<='9';ch=nc())x=x*10+ch-'0';
        if (ch=='.'){
            double tmp=1; ch=nc();
            for (;ch>='0'&&ch<='9';ch=nc())tmp/=10.0,x+=tmp*(ch-'0');
        }
        if (sign)x=-x;
    }
    inline void read(char *s){
        char ch=nc();
        for (;blank(ch);ch=nc());
        if (IOerror)return;
        for (;!blank(ch)&&!IOerror;ch=nc())*s++=ch;
        *s=0;
    }
    inline void read(char &c){
        for (c=nc();blank(c);c=nc());
        if (IOerror){c=-1;return;}
    }
    //fwrite->write
    struct Ostream_fwrite{
        char *buf,*p1,*pend;
        Ostream_fwrite(){buf=new char[BUF_SIZE];p1=buf;pend=buf+BUF_SIZE;}
        void out(char ch){
            if (p1==pend){
                fwrite(buf,1,BUF_SIZE,stdout);p1=buf;
            }
            *p1++=ch;
        }
        void print(int x){
            static char s[15],*s1;s1=s;
            if (!x)*s1++='0';if (x<0)out('-'),x=-x;
            while(x)*s1++=x%10+'0',x/=10;
            while(s1--!=s)out(*s1);
        }
        void println(int x){
            static char s[15],*s1;s1=s;
            if (!x)*s1++='0';if (x<0)out('-'),x=-x;
            while(x)*s1++=x%10+'0',x/=10;
            while(s1--!=s)out(*s1); out('
');
        }
        void print(ll x){
            static char s[25],*s1;s1=s;
            if (!x)*s1++='0';if (x<0)out('-'),x=-x;
            while(x)*s1++=x%10+'0',x/=10;
            while(s1--!=s)out(*s1);
        }
        void println(ll x){
            static char s[25],*s1;s1=s;
            if (!x)*s1++='0';if (x<0)out('-'),x=-x;
            while(x)*s1++=x%10+'0',x/=10;
            while(s1--!=s)out(*s1); out('
');
        }
        void print(double x,int y){
            static ll mul[]={1,10,100,1000,10000,100000,1000000,10000000,100000000,
                1000000000,10000000000LL,100000000000LL,1000000000000LL,10000000000000LL,
                100000000000000LL,1000000000000000LL,10000000000000000LL,100000000000000000LL};
            if (x<-1e-12)out('-'),x=-x;x*=mul[y];
            ll x1=(ll)floor(x); if (x-floor(x)>=0.5)++x1;
            ll x2=x1/mul[y],x3=x1-x2*mul[y]; print(x2);
            if (y>0){out('.'); for (size_t i=1;i<y&&x3*mul[i]<mul[y];out('0'),++i); print(x3);}
        }
        void println(double x,int y){print(x,y);out('
');}
        void print(char *s){while (*s)out(*s++);}
        void println(char *s){while (*s)out(*s++);out('
');}
        void flush(){if (p1!=buf){fwrite(buf,1,p1-buf,stdout);p1=buf;}}
        ~Ostream_fwrite(){flush();}
    }Ostream;
    inline void print(int x){Ostream.print(x);}
    inline void println(int x){Ostream.println(x);}
    inline void print(char x){Ostream.out(x);}
    inline void println(char x){Ostream.out(x);Ostream.out('
');}
    inline void print(ll x){Ostream.print(x);}
    inline void println(ll x){Ostream.println(x);}
    inline void print(double x,int y){Ostream.print(x,y);}
    inline void println(double x,int y){Ostream.println(x,y);}
    inline void print(char *s){Ostream.print(s);}
    inline void println(char *s){Ostream.println(s);}
    inline void println(){Ostream.out('
');}
    inline void flush(){Ostream.flush();}
    #undef ll
    #undef OUT_SIZE
    #undef BUF_SIZE
};
const int N=1e5+5;
int n,m;
int to[N<<4],head[N<<4],nxt[N<<4],tot,fr[N<<4];
int fa[N],size[N],son[N],Top[N],dep[N],ans[N];
vector<int> g[N];
#define ls(k) (k)<<1
#define rs(k) (k)<<1|1
struct Stack
{
    int x,y,op,nd1,nd2;
}s[N<<4];
int top;
void ins(int k,int l,int r,int L,int R,int x,int y)
{
    if(L<=l&&R>=r)
    {
        to[++tot]=y;fr[tot]=x;
        nxt[tot]=head[k];head[k]=tot;
        return ;
    }
    int mid=l+r>>1;
    if(L<=mid)ins(ls(k),l,mid,L,R,x,y);
    if(R>mid)ins(rs(k),mid+1,r,L,R,x,y);
}
void dfs1(int x,int f)
{
    size[x]=1;fa[x]=f;
    int sz=g[x].size();
    for(int i=0;i<sz;i++)
    {
        int y=g[x][i];
        if(y==f)continue;
        dep[y]=dep[x]+1;
        dfs1(y,x);
        size[x]+=size[y];
        if(size[y]>size[son[x]])son[x]=y;
    }
    return ;
}
void dfs2(int x,int f)
{
    Top[x]=f;
    if(!son[x])return ;
    dfs2(son[x],f);
    int sz=g[x].size();
    for(int i=0;i<sz;i++)
    {
        int y=g[x][i];
        if(!Top[y])dfs2(y,y);
    }
}

int lca(int x,int y)
{
    while(Top[x]!=Top[y])
    {
        if(dep[Top[x]]<dep[Top[y]])swap(x,y);
        x=fa[Top[x]];
        //cout<<x<<' '<<y<<endl;
    }
    return dep[x]<dep[y]?x:y;
}
int dis(int x,int y)
{
    return dep[x]+dep[y]-(dep[lca(x,y)]<<1);
}

namespace U
{
    int fa[N],node[N][3],rk[N];
    void ini()
    {
        for(int i=1;i<=n;i++)
            fa[i]=node[i][0]=node[i][1]=i;
    }
    int findf(int x)
    {
        return fa[x]==x?x:findf(fa[x]);
    }
    void merge(int xx,int yy,int &d)
    {
        int x=findf(xx),y=findf(yy),nd1,nd2,maxd=-1,nowd=dis(node[x][0],node[x][1]);
        if(nowd>maxd)maxd=nowd,nd1=node[x][0],nd2=node[x][1];
        nowd=dis(node[y][0],node[y][1]);
        if(nowd>maxd)maxd=nowd,nd1=node[y][0],nd2=node[y][1];
        for(re int i=0;i<2;i++)
            for(re int j=0;j<2;j++)
            {
                nowd=dis(node[x][i],node[y][j]);
                if(nowd>maxd)maxd=nowd,nd1=node[x][i],nd2=node[y][j];
            }
        d=max(d,maxd);
        if(rk[x]<rk[y])swap(x,y);
        s[++top]=(Stack){x,y,0,node[x][0],node[x][1]};
        if(rk[x]==rk[y])++rk[x],s[top].op=1;
        fa[y]=x;node[x][0]=nd1;node[x][1]=nd2;
    }
}
void cancel(int k)
{
    while(top>k)
    {
        U::rk[s[top].x]-=s[top].op;
        U::fa[s[top].y]=s[top].y;
        U::node[s[top].x][0]=s[top].nd1;
        U::node[s[top].x][1]=s[top].nd2;
        top--;
    }
}
void work(int k,int l,int r,int sum)
{
    int pos=top;
    for(re int i=head[k];i;i=nxt[i])
        U::merge(fr[i],to[i],sum);
    if(l==r)
    {
        ans[l]=sum;
        cancel(pos);
        return ;
    }
    int mid=l+r>>1;
    work(ls(k),l,mid,sum);
    work(rs(k),mid+1,r,sum);
    cancel(pos);
}
int main()
{
    //freopen("speed2.in","r",stdin);
    IO::read(n);IO::read(m);
    for(re int i=1;i<n;i++)
    {
        int x,y,l,r;
        IO::read(x);IO::read(y);
        IO::read(l);IO::read(r);
        g[x].push_back(y);
        g[y].push_back(x);
        ins(1,1,n,l,r,x,y);
    }
    dep[1]=1;
    dfs1(1,0);dfs2(1,1);
    /*for(int i=1;i<=n;i++)
        cout<<i<<' '<<size[i]<<' '<<son[i]<<' '<<Top[i]<<endl;*/
    U::ini();
    work(1,1,n,0);
    while(m--)
    {
        int q;
        IO::read(q);
        IO::println(ans[q]);
    }
    return 0;
}