Binary application

1.Take a single 1.

i&-i   The value returned is the number from the last forward to the first 1.

int work(int x){int num=0;for(;x;x-=x&-x) num++;return num;}

e.g.:luogu 1582Water reverse

#include<bits/stdc++.h>
using namespace std;
int n,k,ans;
inline int read(){
    int x=0,f=1;char ch=getchar();
    while(!isdigit(ch)){if(ch=='-')f=-1;ch=getchar();}
    while(isdigit(ch)){x=(x<<1)+(x<<3)+(ch^48);ch=getchar();}
    return x*f;}
inline int sudo(int i){int ans=0;for(;i;i-=i&(-i)) ans++;return ans;}
int main(){
    n=read();k=read();
    while(sudo(n)>k) ans+=n&(-n),n+=n&(-n);
    printf("%d\n",ans);return 0;}

 2.State compression: using binary numbers to represent sets.

UVa 11825 

#include<bits/stdc++.h>
using namespace std;
inline int read(){
    int x=0,f=1;char ch=getchar();
    while(!isdigit(ch)){if(ch=='-')f=-1;ch=getchar();}
    while(isdigit(ch)){x=(x<<1)+(x<<3)+(ch^48);ch=getchar();}
    return x*f;}
const int N=18;
int p[N],s[N],cover[1<<N],f[1<<N];
int kase,n;

int main(){
    while(scanf("%d",&n)!=EOF&&n){
        memset(p,0,sizeof p);
        memset(s,0,sizeof s);
        memset(cover,0,sizeof cover);
        memset(f,0,sizeof f);
        for(int i=0;i<n;i++){
            int m,x;
            scanf("%d",&m);
            p[i]=1<<i;
            while(m--){scanf("%d",&x);p[i]|=(1<<x);}}
            
        int ALL=(1<<n)-1;//Representative for all numbers//sRepresentative number, cover[s] stands for PI under I.
        for(int s=0;s<=(1<<n)-1;s++){//All possible collections
            cover[s]=0;
            for(int i=0;i<n;i++)
            if(s&(1<<i)) cover[s]|=p[i];}
        
        for(int s=1;s<=(1<<n)-1;s++){
            f[s]=0;
            for(int s0=s;s0;s0=(s0-1)&s)
            // s0-1Looking down, bitwise and finding subset
            if(cover[s0]==ALL) f[s]=max(f[s],f[s^s0]+1);
            //State transfer, exclusive or exclusion of the situation.
        }
        printf("Case %d: %d\n",++kase,f[ALL]);
    }return 0;
}

 

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