Getting Started with Linear Basis

Recommended blog: https://www.cnblogs.com/vb4896/p/6149022.html

　　　　　 https://blog.csdn.net/qaq__qaq/article/details/53812883

I don't think this is very easy to understand. It took a day and a half to understand a little bit and write a blog.

 

First of all, we need to clarify what kind of problems this linear basis can solve, such as dynamically adding elements, solving set XOR maximum

There is an increase operation here, add an element to the inside, sweep down from the highest bit, when the sweep reaches 1, and the position in the linear base is 0, add this element to the linear base, otherwise use this element to XOR Numbers in Linear Basis

int val[maxn][40];
void insert(int b[], int x){
    for(int i = 30; i >= 0; i--){
        if (x>>i&1){
            if (!b[i]) {b[i] = x; break;}
            else x ^= b[i];
        }
    }
}

 merge

void unit(int x,int y){
    // brute force x into y
    for(int i=30;i>=0;--i)
        if(val[x][i]) insert (val[y],val[x][i]);
}

 Inquire

Query whether an element is in the collectionx

maximum value

Sweep from high to low

int cal(int p){
    int years = 0;
    for(int i = 30; i >= 0; i--){
        if ((ans^val[i]) > ans) {
            ans ^ = val [i];
        }
    }
    return ans;
}

 minimum

int query(){
    for(int i = 0; i <= 30; i++){
        if (val[i]) return val[i];
    }
    return 0;
}