2018.11.5 PION模拟赛

期望：30 + 40 + 50 = 120

实际：30 + 50 + 40 = 120

‘’

思路：最重要的是发现

是完全没有用的，然后这个题目就可以转成DP来做。

/*
期望的分：30 
*/
#include<cstdio>
#include<cstring>
#include<iostream> 
#include<algorithm>
using namespace std;
int n;
double ans;
double p[1010][1010],s[1010][1010];
int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
int main(){
    freopen("game.in","r",stdin);
    freopen("game.out","w",stdout);
    n=read();
    for(int i=1;i<=n;i++)
        for(int j=0;j<i;j++){
            scanf("%lf",&p[i][j]);
            s[i][j]=1.0-p[i][j];
        }
    if(n==0){
        ans=0;
        printf("%.2lf",ans);
        return 0;
    }
    if(n==1){
        double ans1=p[1][0];
        double ans2=s[1][0]*0;
        ans=ans1+ans2;
        printf("%.2lf",ans);
    }
    if(n==2){
        double ans1=p[1][0]*p[2][1]*2;
        double ans2=p[1][0]*s[2][1]*1;
        double ans3=s[1][0]*p[2][0]*1;
        double ans4=s[1][0]*s[2][0]*0; 
        ans=ans1+ans2+ans3+ans4;
        ans1=p[2][0]*1;ans2=s[2][0]*0;
        ans3=p[1][0]*1;ans4=s[1][0]*0;
        ans=max(ans,max(ans1+ans2,ans3+ans4));
        printf("%.2lf",ans);
    }
}

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
int n;
double p[1010][1010],f[1010][1010];
int main(){
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
        for(int j=0;j<i;j++)
            scanf("%lf",&p[i][j]);
    f[0][0]=1;
    for(int i=0;i<n;i++)
        for(int j=0;j<=i;j++){
            f[i+1][j+1]+=f[i][j]*p[i+1][j];
            f[i+1][j]+=f[i][j]*(1-p[i+1][j]);
        }
    double ans=0;
    for(int j=0;j<=n;j++)    ans+=j*f[n][j];
    printf("%.2lf\n",ans);
}

 

 

 

/*
期望的分：40 
*/
#include<cstdio>
#include<cstring>
#include<iostream> 
#include<algorithm>
using namespace std;
int n,x,sum,ans=0x7f7f7f7f;
int v[50],f[10000000];
int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
int cmp(int a,int b){
    return a>b;
}
void dfs(int now,int tot){
    if(tot<0)    return ;
    if(now==n+1){
        ans=min(ans,tot);
        return ;
    }
    dfs(now+1,tot-v[now]);
    dfs(now+1,tot);
}
int main(){
    freopen("cake.in","r",stdin);
    freopen("cake.out","w",stdout);
    n=read();x=read();
    for(int i=1;i<=n;i++){
        v[i]=read();
        sum+=v[i];
    }
    if(sum<=x){ printf("%d\n",x-sum);return 0; }
    if(n<20){
        sort(v+1,v+1+n,cmp);
        dfs(1,x);
        cout<<ans;
    }
    else{
        for(int i=1;i<=n;i++)
            for(int j=x;j>=v[i];j--)
                f[j]=max(f[j],f[j-v[i]]+v[i]);
        cout<<x-f[x];
    }
}

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
int n,x,O,tot;
int a[45],c[2][1100000];
int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
void dfs(int l,int r,int sum){
    c[O][++tot]=sum;
    for(int i=l;i<=r;i++)
        if(sum+a[i]<=x)
            dfs(i+1,r,sum+a[i]);
}
int build(int l,int r,int o){
    O=o;tot=0;
    dfs(l,r,0);
    return tot;
}
int main(){
    scanf("%d%d",&n,&x);
    for(int i=1;i<=n;i++)    a[i]=read();
    int A=build(1,n/2,0);
    int B=build(n/2+1,n,1);
    sort(c[0]+1,c[0]+A+1);
    sort(c[1]+1,c[1]+B+1);
    int now=B,ans=0;
    for(int i=1;i<=A;i++){
        while(c[0][i]+c[1][now]>x&&now)    now--;
        if(now==0)    break;
        ans=max(ans,c[0][i]+c[1][now]);
    }
    printf("%d\n",x-ans);
}

 

/*
期望得分：50 
*/
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define mod 1000000007
using namespace std;
long long ans;
int h,w,m,n;
int map1[4][4];
int x1[11],y1[11],x2[11],y2[11],v[11];
int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f; 
}
bool judge1(){
    for(int k=1;k<=n;k++){
        int maxn=0; 
        for(int i=x1[k];i<=x2[k];i++)
            for(int j=y1[k];j<=y2[k];j++)
                maxn=max(maxn,map1[i][j]);
        if(maxn!=v[k])    return false;
    }
    return true;
}
void sove1(int now){
    if(now==w*h+1){
        if(judge1()){
            ans++;
            ans%=mod;
        }    
        return ;
    }
    for(int i=1;i<=m;i++){
        int cx=now/w+1;
        int cy=now%w;
        if(cy==0)    cy=w,cx-=1;
        map1[cx][cy]=i;
        sove1(now+1);
        map1[cx][cy]=0;
    }
}
long long fastpow(long long a,long long b){
    long long s=1;
    for(;b;b>>=1){
        if(b&1)    s=s*a%mod;
        a=a*a%mod;
    }
    return s;
}
int main(){
    freopen("grid.in","r",stdin);
    freopen("grid.out","w",stdout);
    h=read();w=read();m=read();n=read();
    for(int i=1;i<=n;i++){
        x1[i]=read();y1[i]=read();
        x2[i]=read();y2[i]=read();
        v[i]=read();
    }
    if(h<=3&&w<=3&&n<=3&&m<=3){
        sove1(1);
        printf("%I64d\n",ans);
        return 0;
    }
    else if(n==0){
        int p=w*h;
        ans=fastpow(m,p);
        printf("%I64d\n",ans);
    }
    else if(n==1){
        int sum=w*h;
        int sx=x2[1]-x1[1]+1;
        int zy=y2[1]-y1[1]+1;
        int sumn=sx*zy;
        long long ans1=fastpow(m,sum-sx*zy);
        long long ans2=(fastpow(v[1],sumn)-fastpow(v[1]-1,sumn)+mod)%mod;
        ans=ans1*ans2%mod;
        printf("%I64d\n",ans);
    }
}
/*
3 3 3 1
1 1 2 3 3
*/

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <string>
#include <cmath>
#include <algorithm>
#include <iostream>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <vector>
using namespace std;
typedef long long i64;
const int P=1e9+7;
int T,h,w,m,n;
int xs[33],ys[33],xp,yp,vs[33],vp,ts[33];
int rc[33][5],mv[33][33],as[33][33];
void mins(int&a,int b){if(a>b)a=b;}
int pw(int a,int n){
    int v=1;
    for(;n;n>>=1,a=i64(a)*a%P)if(n&1)v=i64(v)*a%P;
    return v;
}
int main(){
    
    freopen("grid.in","r",stdin);
    freopen("grid.out","w",stdout);
    int ans=0;
    scanf("%d%d%d%d",&h,&w,&m,&n);
    xp=yp=vp=0;xs[xp++]=1;
    xs[xp++]=h+1;ys[yp++]=1;
    ys[yp++]=w+1;vs[vp++]=m;
    for(int i=0;i<n;++i){
        for(int j=0;j<5;++j)    scanf("%d",rc[i]+j);
        xs[xp++]=rc[i][0];
        xs[xp++]=rc[i][2]+1;
        ys[yp++]=rc[i][1];
        ys[yp++]=rc[i][3]+1;
        vs[vp++]=rc[i][4];
        vs[vp++]=rc[i][4]-1;
    }
    sort(xs,xs+xp);
    xp=unique(xs,xs+xp)-xs-1;
    sort(ys,ys+yp);
    yp=unique(ys,ys+yp)-ys-1;
    sort(vs,vs+vp);
    vp=unique(vs,vs+vp)-vs;
    for(int i=0;i<xp;++i)
        for(int j=0;j<yp;++j)
            as[i][j]=(xs[i+1]-xs[i])*(ys[j+1]-ys[j]);
    for(int t=0;t<n;++t){
        rc[t][0]=std::lower_bound(xs,xs+xp,rc[t][0])-xs;
        rc[t][2]=std::lower_bound(xs,xs+xp,rc[t][2]+1)-xs;
        rc[t][1]=std::lower_bound(ys,ys+yp,rc[t][1])-ys;
        rc[t][3]=std::lower_bound(ys,ys+yp,rc[t][3]+1)-ys;
        rc[t][4]=std::lower_bound(vs,vs+vp,rc[t][4])-vs;
    }/*离散化*/
    for(int S=0;S<(1<<n);++S){
        for(int i=0;i<xp;++i)
            for(int j=0;j<yp;++j)
                mv[i][j]=vp-1;
        int s=1;
        for(int t=0;t<n;++t){
            int v=rc[t][4];
            if(S>>t&1)    s=-s,--v;
            for(int i=rc[t][0];i<rc[t][2];++i)
                for(int j=rc[t][1];j<rc[t][3];++j)
                    mins(mv[i][j],v);
        }
        for(int i=0;i<vp;++i)    ts[i]=0;
        for(int i=0;i<xp;++i)
            for(int j=0;j<yp;++j)
                ts[mv[i][j]]+=as[i][j];
        for(int i=0;i<vp;++i)    s=i64(s)*pw(vs[i],ts[i])%P;
        ans=(ans+s)%P;
    }
    printf("%d\n",(ans+P)%P);
    return 0;
}