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[][],s[][];
int read(){
    int x=,f=;char ch=getchar();
    while(ch<''||ch>''){if(ch=='-')f=-;ch=getchar();}
    while(ch>=''&&ch<=''){x=x*+ch-'';ch=getchar();}
    return x*f;
}
int main(){
    freopen("game.in","r",stdin);
    freopen("game.out","w",stdout);
    n=read();
    for(int i=;i<=n;i++)
        for(int j=;j<i;j++){
            scanf("%lf",&p[i][j]);
            s[i][j]=1.0-p[i][j];
        }
    if(n==){
        ans=;
        printf("%.2lf",ans);
        return ;
    }
    if(n==){
        double ans1=p[][];
        double ans2=s[][]*;
        ans=ans1+ans2;
        printf("%.2lf",ans);
    }
    if(n==){
        double ans1=p[][]*p[][]*;
        double ans2=p[][]*s[][]*;
        double ans3=s[][]*p[][]*;
        double ans4=s[][]*s[][]*;
        ans=ans1+ans2+ans3+ans4;
        ans1=p[][]*;ans2=s[][]*;
        ans3=p[][]*;ans4=s[][]*;
        ans=max(ans,max(ans1+ans2,ans3+ans4));
        printf("%.2lf",ans);
    }
}

30暴力

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

100

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

50分暴力

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

100

/*
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[][];
int x1[],y1[],x2[],y2[],v[];
int read(){
    int x=,f=;char ch=getchar();
    while(ch<''||ch>''){if(ch=='-')f=-;ch=getchar();}
    while(ch>=''&&ch<=''){x=x*+ch-'';ch=getchar();}
    return x*f;
}
bool judge1(){
    for(int k=;k<=n;k++){
        int maxn=;
        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+){
        if(judge1()){
            ans++;
            ans%=mod;
        }
        return ;
    }
    for(int i=;i<=m;i++){
        int cx=now/w+;
        int cy=now%w;
        if(cy==)    cy=w,cx-=;
        map1[cx][cy]=i;
        sove1(now+);
        map1[cx][cy]=;
    }
}
long long fastpow(long long a,long long b){
    long long s=;
    for(;b;b>>=){
        if(b&)    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=;i<=n;i++){
        x1[i]=read();y1[i]=read();
        x2[i]=read();y2[i]=read();
        v[i]=read();
    }
    if(h<=&&w<=&&n<=&&m<=){
        sove1();
        printf("%I64d\n",ans);
        return ;
    }
    else if(n==){
        int p=w*h;
        ans=fastpow(m,p);
        printf("%I64d\n",ans);
    }
    else if(n==){
        int sum=w*h;
        int sx=x2[]-x1[]+;
        int zy=y2[]-y1[]+;
        int sumn=sx*zy;
        long long ans1=fastpow(m,sum-sx*zy);
        long long ans2=(fastpow(v[],sumn)-fastpow(v[]-,sumn)+mod)%mod;
        ans=ans1*ans2%mod;
        printf("%I64d\n",ans);
    }
}
/*
3 3 3 1
1 1 2 3 3
*/

50分暴力

#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+;
int T,h,w,m,n;
int xs[],ys[],xp,yp,vs[],vp,ts[];
int rc[][],mv[][],as[][];
void mins(int&a,int b){if(a>b)a=b;}
int pw(int a,int n){
    int v=;
    for(;n;n>>=,a=i64(a)*a%P)if(n&)v=i64(v)*a%P;
    return v;
}
int main(){

    freopen("grid.in","r",stdin);
    freopen("grid.out","w",stdout);
    int ans=;
    scanf("%d%d%d%d",&h,&w,&m,&n);
    xp=yp=vp=;xs[xp++]=;
    xs[xp++]=h+;ys[yp++]=;
    ys[yp++]=w+;vs[vp++]=m;
    for(int i=;i<n;++i){
        for(int j=;j<;++j)    scanf("%d",rc[i]+j);
        xs[xp++]=rc[i][];
        xs[xp++]=rc[i][]+;
        ys[yp++]=rc[i][];
        ys[yp++]=rc[i][]+;
        vs[vp++]=rc[i][];
        vs[vp++]=rc[i][]-;
    }
    sort(xs,xs+xp);
    xp=unique(xs,xs+xp)-xs-;
    sort(ys,ys+yp);
    yp=unique(ys,ys+yp)-ys-;
    sort(vs,vs+vp);
    vp=unique(vs,vs+vp)-vs;
    for(int i=;i<xp;++i)
        for(int j=;j<yp;++j)
            as[i][j]=(xs[i+]-xs[i])*(ys[j+]-ys[j]);
    for(int t=;t<n;++t){
        rc[t][]=std::lower_bound(xs,xs+xp,rc[t][])-xs;
        rc[t][]=std::lower_bound(xs,xs+xp,rc[t][]+)-xs;
        rc[t][]=std::lower_bound(ys,ys+yp,rc[t][])-ys;
        rc[t][]=std::lower_bound(ys,ys+yp,rc[t][]+)-ys;
        rc[t][]=std::lower_bound(vs,vs+vp,rc[t][])-vs;
    }/*离散化*/
    for(int S=;S<(<<n);++S){
        for(int i=;i<xp;++i)
            for(int j=;j<yp;++j)
                mv[i][j]=vp-;
        int s=;
        for(int t=;t<n;++t){
            int v=rc[t][];
            if(S>>t&)    s=-s,--v;
            for(int i=rc[t][];i<rc[t][];++i)
                for(int j=rc[t][];j<rc[t][];++j)
                    mins(mv[i][j],v);
        }
        for(int i=;i<vp;++i)    ts[i]=;
        for(int i=;i<xp;++i)
            for(int j=;j<yp;++j)
                ts[mv[i][j]]+=as[i][j];
        for(int i=;i<vp;++i)    s=i64(s)*pw(vs[i],ts[i])%P;
        ans=(ans+s)%P;
    }
    printf("%d\n",(ans+P)%P);
    return ;
}

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