pku2985 The k-th Largest Group

 

题意：初始化状态为N个含单一元素的集合，动态合并任意两个集合，查询第ith大的集合的大小

分析：以虚二叉树做辅助结构找出第ith大的集合的大小

 

#include  < iostream >
#include  < algorithm >
using   namespace  std;

#define  MAXN 200001

int  v[MAXN],N,M,pnt[MAXN],son[ 3 * MAXN];
// v[i]第i只猫所在组的猫的数量，范围在1～N之间；son[u]表示以结点u为根的子树的结点数

void  insert( int  num, int  k){
     int  l = 1 ,r = N,m,u = 1 ;
     while (l < r){
        m = (l + r) / 2 ;
        son[u] += k;
         if (num <= m){
            r = m;
            u = u * 2 ;
        }
         else {
            l = m + 1 ;
            u = u * 2 + 1 ;
        }
    }
    son[u] += k;
}

int  find( int  ith){
     int  l = 1 ,r = N,u = 1 ,m;
     while (l < r){
        m = (l + r) / 2 ;
         if (son[ 2 * u + 1 ] >= ith){
            l = m + 1 ;
            u = u * 2 + 1 ;
        }
         else {
            ith -= son[ 2 * u + 1 ];
            r = m;
            u = u * 2 ;
        }
    }
     return  l;
}



void  init(){
     int  i;
     for (i = 1 ;i <= N;i ++ ){
        pnt[i] = i;
        v[i] = 1 ;
        insert(v[i], 1 );
    }
}

int  fs( int  i){
     if (pnt[i] == i)
         return  i;
    pnt[i] = fs(pnt[i]);
     return  pnt[i];
}



int  main(){
     int  q,a,b,x,y,ith;
     while (scanf( " %d%d " , & N, & M) != EOF){
        init();
         while (M -- ){
            scanf( " %d " , & q);
             if (q == 0 ){
                scanf( " %d%d " , & a, & b);
                x = fs(a);
                y = fs(b);
                 if (x != y){
                    pnt[x] = y;                    
                    insert(v[x], - 1 );
                    insert(v[y], - 1 );
                    v[y] += v[x];
                    insert(v[y], 1 );
                }
            }
             else {
                scanf( " %d " , & ith);
                printf( " %d\n " ,find(ith));
            }
        }
    }
     return   0 ;
}