Set Operation
Description
You are given N sets, the i-th set (represent by S(i)) have C(i) element (Here "set" isn't entirely the same as the "set" defined in mathematics, and a set may contain two same element). Every element in a set is represented by a positive number from 1 to 10000. Now there are some queries need to answer. A query is to determine whether two given elements i and j belong to at least one set at the same time. In another word, you should determine if there exist a number k (1 <= k <= N) such that element i belongs to S(k) and element j also belong to S(k).
Input
First line of input contains an integer N (1 <= N <= 1000), which represents the amount of sets. Then follow N lines. Each starts with a number C(i) (1 <= C(i) <= 10000), and then C(i) numbers, which are separated with a space, follow to give the element in the set (these C(i) numbers needn't be different from each other). The N + 2 line contains a number Q (1 <= Q <= 200000), representing the number of queries. Then follow Q lines. Each contains a pair of number i and j (1 <= i, j <= 10000, and i may equal to j), which describe the elements need to be answer.
Output
For each query, in a single line, if there exist such a number k, print "Yes"; otherwise print "No".
Sample Input 3 3 1 2 3 3 1 2 5 1 10 4 1 3 1 5 3 5 1 10 Sample Output Yes Yes No No Hint
The input may be large, and the I/O functions (cin/cout) of C++ language may be a little too slow for this problem.
Source
POJ Monthly,Minkerui
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思路:
开一个a[32][10001]的数组就能保存所有信息了,并且能优化时间了。充分利用一个int能保存32个信息,把矩阵的每列都看做一个二进制数,但是这个数太大,所以需要分n/32+1个数来保存。每次操作时只要对相应的列进行&操作就够了。既节省了空间,有优化了时间,确实蛮经典的。
代码:
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <string>
#include <map>
#include <stack>
#include <vector>
#include <set>
#include <queue>
//#pragma comment (linker,"/STACK:102400000,102400000")
#define maxn 10005
#define mod 1000000000
#define INF 0x3f3f3f3f
using namespace std;
int n,m,ans,q,flag;
int a[32][maxn];
int main()
{
int i,j,t,x,y,u,v;
while(~scanf("%d",&n))
{
memset(a,0,sizeof(a));
for(i=0;i<n;i++)
{
scanf("%d",&m);
x=i/32;
t=i%32;
for(j=0;j<m;j++)
{
scanf("%d",&u);
y=u;
a[x][y]|=(1<<t);
}
}
m=n/32;
scanf("%d",&q);
for(i=1;i<=q;i++)
{
scanf("%d%d",&u,&v);
flag=0;
for(j=0;j<=m;j++)
{
if(a[j][u]&a[j][v])
{
flag=1;
break ;
}
}
if(flag) printf("Yes\n");
else printf("No\n");
}
}
return 0;
}