NOIP 2016 愤怒的小鸟 题解

一道状压dp题，但是竟然可以搜索搜过！！(儒雅随和)。

代码(爆搜)

#include<bits/stdc++.h>
using namespace std;
const double eps=1e-8;
int T,n,m,ans;
double x[25],y[25],a[25],b[25];
bool book[25];
bool cheak(double a,double b){
    return (fabs(a-b)<eps);
}
int clu(){
    int tmp=0;
    for(int i=1;i<=n;++i){
        if(book[i]) tmp++;
    }
    return tmp;
}
void dfs(int c,int k){
    if(k+clu()>=ans) return;
    if(c>n){
        ans=k+clu();
        return;
    }
    bool flag=false;
    for(int i=1;i<=k;++i){
        if(cheak(a[i]*x[c]*x[c]+b[i]*x[c],y[c])){
            flag=true;
            dfs(c+1,k);
            break;
        }
    }
    if(!flag){
        for(int i=1;i<=n;++i){
            if(!cheak(x[i],x[c])&&book[i]){
                double a1=(x[i]*y[c]-y[i]*x[c])/(x[c]*x[i]*(x[c]-x[i]));
                double b1=(y[c]-x[c]*x[c]*a1)/x[c];
                if(a1<0){
                    a[k+1]=a1;
                    b[k+1]=b1;
                    book[i]=0;
                    dfs(c+1,k+1);
                    book[i]=1;
                }
            }
        }
        book[c]=1;
        dfs(c+1,k);
        book[c]=0;
    }
     
}
int main(){
    scanf("%d",&T);
    while(T--){
        scanf("%d %d",&n,&m);
        for(int i=1;i<=n;++i){
            scanf("%lf %lf",&x[i],&y[i]);
        }
        memset(book,0,sizeof(book));
        ans=n;
        if(m==1) ans=n/3+2;
        else if(m==2) ans=(2*n)/3+1;
        dfs(1,0);
        printf("%d
",ans);
    }
} 

状压dp

#include<bits/stdc++.h>
using namespace std;
const double eps=1e-8;
int dp[262144],st[200],num;
double x[25],y[25];
int t,n,m;
bool cheak(double a,double b){
    return fabs(a-b)<eps;
}
void init(){
    memset(dp,0x3f,sizeof(dp));
    memset(st,0,sizeof(st));
    num=0;
    dp[0]=0;
    for(int i=1;i<=n;++i){
        for(int j=i+1;j<=n;++j){
            if(!cheak(x[i],x[j])){
                double a1=(x[i]*y[j]-y[i]*x[j])/(x[i]*x[j]*(x[j]-x[i]));
                double b1=(y[j]-a1*x[j]*x[j])/x[j];
                if(a1<0){
                    ++num;
                    for(int k=1;k<=n;++k){
                        if(cheak(a1*x[k]*x[k]+b1*x[k],y[k])){
                            st[num]|=(1<<(k-1));
                        }
                    }
                }
            }
        }
    }
}
void solve(){
    init();
    for(int s=0;s<(1<<n);++s){
        for(int i=1;i<=num;++i) dp[s|st[i]]=min(dp[s|st[i]],dp[s]+1);
        for(int i=1;i<=n;++i) dp[s|(1<<(i-1))]=min(dp[s|1<<(i-1)],dp[s]+1);
    }
}
int main(){
    scanf("%d",&t);
    while(t--){
        scanf("%d %d",&n,&m);
        for(int i=1;i<=n;++i){
            scanf("%lf %lf",&x[i],&y[i]);
        }
        solve();
        printf("%d
",dp[(1<<n)-1]);
    }
    return 0;
}