10.15 上午 考试

今天的题也很水啊，然而我并没有AK，中间还停了电，唠了会磕

T1

直接模拟

#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <cmath>
#define ll long long
#define dis(x,y) (dep[x]+dep[y]-2*dep[LCA(x,y)])
#define mem(a,b) memset(a,b,sizeof(a))
using namespace std;
inline int read()
{
    char q=getchar();int ans=0;
    while(q<'0'||q>'9')q=getchar();
    while(q>='0'&&q<='9'){ans=ans*10+q-'0';q=getchar();}
    return ans;
}
const int LEN=106;

int n;

char s[LEN];
int len;

void read_line()
{
    len=0;
    char tt=getchar();
    while(tt!='
')
    {
        if(tt>='0'&&tt<='9')
        {
            s[++len]='0';
            while(tt>='0'&&tt<='9')
                tt=getchar();
            continue;
        }
        s[++len]=tt;
        tt=getchar();
    }
}

int pr[156],nx[150];

inline void del(int x)
{
    pr[nx[x]]=pr[x];
    nx[pr[x]]=nx[x];
}

int is_fu(char x)
{
    if(x=='+'||x=='-'||x=='*'||x=='/')
        return 1;
    return 0;
}

int check()
{
    /*printf("
");
    for(int i=1;i<=len;++i)
        printf("%c ",s[i]);
    printf("
");*/
    for(int i=1;i<=len;++i)
        pr[i]=i-1,nx[i]=i+1;
    nx[0]=1;pr[len+1]=len;
    int ff=1;
    while(ff)
    {
        ff=0;
        for(int i=nx[0];i<=len;i=nx[i])
            if(s[i]=='0')
            {
                while(pr[i]>0&&s[pr[i]]==' ')
                    ff=1,del(pr[i]);
                while(nx[i]<=len&&s[nx[i]]==' ')
                    ff=1,del(nx[i]);
                while(pr[i]>0&&s[pr[i]]=='('&&nx[i]<=len&&s[nx[i]]==')')
                    ff=1,del(pr[i]),del(nx[i]);
                while(nx[i]<=len&&is_fu(s[nx[i]])&&nx[nx[i]]<=len&&s[nx[nx[i]]]=='0')
                    ff=1,del(nx[nx[i]]),del(nx[i]);
            }
    }
    int tt=0,all=0;
    //printf("
");
    for(int i=nx[0];i<=len;i=nx[i])
    {
        ++all;
        //printf("%c ",s[i]);
        if(s[i]=='0')
            ++tt;
    }
    //printf("tt=%d
",tt);
    if(all==1&&tt==1)
        return 1;
    return 0;
}

int main(){

    //freopen("T1.in","r",stdin);

    n=read();
    for(int i=1;i<=n;++i)
    {
        read_line();
        if(check())
            printf("Yes
");
        else
            printf("No
");
    }
}

T2

hash表+拓扑序

#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <cmath>
#define ull unsigned long long
#define ll long long
#define mem(a,b) memset(a,b,sizeof(a))
using namespace std;
const int N=100006;
const int LEN=76;
const int P1=76543;
const int P2=151651;
const int MOD=1000003;
const int mod=1e9+7;

struct son
{
    int v,next;
}a1[N*5];
int first[MOD],e;
void addbian(int u,int v)
{
    a1[e].v=v;
    a1[e].next=first[u];
    first[u]=e++;
}

struct son1
{
    int next,order;
    ull ha1,ha2;
};
struct HASH
{
    son1 a3[N*5];
    int first[MOD],e,temp;
    void clear()
    {
        mem(a3,0);
        mem(first,-1);
        e=0;
    }
    int checkifin(ull x1,ull x2)
    {
        temp=x1%MOD;
        for(int i=first[temp];i!=-1;i=a3[i].next)
            if(a3[i].ha1==x1&&a3[i].ha2==x2)
                return a3[i].order;
        return -1;
    }
    void add(ull x1,ull x2,int order)
    {
        temp=x1%MOD;
        a3[e].order=order;
        a3[e].ha1=x1;
        a3[e].ha2=x2;
        a3[e].next=first[temp];
        first[temp]=e++;
    }
}H;

int m,con;
char s1[LEN],s2[LEN];
int ind[N];
int len1,len2;

int get1()
{
    int t1,ans;
    ull x1=0,x2=0;
    len1=strlen(s1);
    for(int i=0;i<len1;++i)
    {
        x1=(x1+s1[i])*P1;
        x2=(x2+s1[i])*P2;
    }
    t1=H.checkifin(x1,x2);
    if(t1==-1)
    {
        ans=++con;
        H.add(x1,x2,con);
    }
    else
        ans=t1;
    return ans;
}

int get2()
{
    int t1,ans;
    ull x1=0,x2=0;
    len2=strlen(s2);
    for(int i=0;i<len2;++i)
    {
        x1=(x1+s2[i])*P1;
        x2=(x2+s2[i])*P2;
    }
    t1=H.checkifin(x1,x2);
    if(t1==-1)
    {
        ans=++con;
        H.add(x1,x2,con);
    }
    else
        ans=t1;
    return ans;
}

int dui[N*10],he,en;
ll num[N];

ll work()
{
    ll ans=0;
    mem(num,0);
    he=1;en=0;
    for(int i=1;i<=con;++i)
        if(!ind[i])
        {
            num[i]=1;
            dui[++en]=i;
        }
    int now,temp;
    while(en>=he)
    {
        now=dui[he++];
        for(int i=first[now];i!=-1;i=a1[i].next)
        {
            temp=a1[i].v;
            --ind[temp];
            num[temp]+=num[now];num[temp]%=mod;
            if(!ind[temp])
                dui[++en]=temp;
        }
        if(first[now]==-1)
            ans+=num[now],ans%=mod;
    }
    return ans%mod;
}

int main(){

    //freopen("T2.in","r",stdin);

    H.clear();
    mem(first,-1);

    scanf("%d",&m);
    int t1,t2;
    for(int i=1;i<=m;++i)
    {
        scanf("%s%s",s1,s2);
        t1=get1();t2=get2();
        //printf("i=%d t1=%d t2=%d
",i,t1,t2);
        addbian(t1,t2);
        ++ind[t2];
    }
    cout<<work();
}

T3

$ f_i $ 为从(0,0)到第i个被淹的路口且不经过前面被淹的路口的方案数

$$ f_i=C_{x_i+y_i}^{x_i} - sum_{x_ j<=x_i,y_ j<=y_i}C_{x_ i-x_ j+y_i-y_ j}^{x_i-x_ j}f_ j $$

#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <cmath>
#define ull unsigned long long
#define ll long long
#define mem(a,b) memset(a,b,sizeof(a))
using namespace std;
const int N=100006;
const int LEN=76;
const int P1=76543;
const int P2=151651;
const int MOD=1000003;
const int mod=1e9+7;

struct son
{
    int v,next;
}a1[N*5];
int first[MOD],e;
void addbian(int u,int v)
{
    a1[e].v=v;
    a1[e].next=first[u];
    first[u]=e++;
}

struct son1
{
    int next,order;
    ull ha1,ha2;
};
struct HASH
{
    son1 a3[N*5];
    int first[MOD],e,temp;
    void clear()
    {
        mem(a3,0);
        mem(first,-1);
        e=0;
    }
    int checkifin(ull x1,ull x2)
    {
        temp=x1%MOD;
        for(int i=first[temp];i!=-1;i=a3[i].next)
            if(a3[i].ha1==x1&&a3[i].ha2==x2)
                return a3[i].order;
        return -1;
    }
    void add(ull x1,ull x2,int order)
    {
        temp=x1%MOD;
        a3[e].order=order;
        a3[e].ha1=x1;
        a3[e].ha2=x2;
        a3[e].next=first[temp];
        first[temp]=e++;
    }
}H;

int m,con;
char s1[LEN],s2[LEN];
int ind[N];
int len1,len2;

int get1()
{
    int t1,ans;
    ull x1=0,x2=0;
    len1=strlen(s1);
    for(int i=0;i<len1;++i)
    {
        x1=(x1+s1[i])*P1;
        x2=(x2+s1[i])*P2;
    }
    t1=H.checkifin(x1,x2);
    if(t1==-1)
    {
        ans=++con;
        H.add(x1,x2,con);
    }
    else
        ans=t1;
    return ans;
}

int get2()
{
    int t1,ans;
    ull x1=0,x2=0;
    len2=strlen(s2);
    for(int i=0;i<len2;++i)
    {
        x1=(x1+s2[i])*P1;
        x2=(x2+s2[i])*P2;
    }
    t1=H.checkifin(x1,x2);
    if(t1==-1)
    {
        ans=++con;
        H.add(x1,x2,con);
    }
    else
        ans=t1;
    return ans;
}

int dui[N*10],he,en;
ll num[N];

ll work()
{
    ll ans=0;
    mem(num,0);
    he=1;en=0;
    for(int i=1;i<=con;++i)
        if(!ind[i])
        {
            num[i]=1;
            dui[++en]=i;
        }
    int now,temp;
    while(en>=he)
    {
        now=dui[he++];
        for(int i=first[now];i!=-1;i=a1[i].next)
        {
            temp=a1[i].v;
            --ind[temp];
            num[temp]+=num[now];num[temp]%=mod;
            if(!ind[temp])
                dui[++en]=temp;
        }
        if(first[now]==-1)
            ans+=num[now],ans%=mod;
    }
    return ans%mod;
}

int main(){

    //freopen("T2.in","r",stdin);

    H.clear();
    mem(first,-1);

    scanf("%d",&m);
    int t1,t2;
    for(int i=1;i<=m;++i)
    {
        scanf("%s%s",s1,s2);
        t1=get1();t2=get2();
        //printf("i=%d t1=%d t2=%d
",i,t1,t2);
        addbian(t1,t2);
        ++ind[t2];
    }
    cout<<work();
}