P2922 [USACO08DEC]秘密消息Secret Message

Posted 2020-11-01 whymhe

题目描述

Bessie is leading the cows in an attempt to escape! To do this, the cows are sending secret binary messages to each other.

Ever the clever counterspy, Farmer John has intercepted the first b_i (1 <= b_i <= 10,000) bits of each of M (1 <= M <= 50,000) of these secret binary messages.

He has compiled a list of N (1 <= N <= 50,000) partial codewords that he thinks the cows are using. Sadly, he only knows the first c_j (1 <= c_j <= 10,000) bits of codeword j.

For each codeword j, he wants to know how many of the intercepted messages match that codeword (i.e., for codeword j, how many times does a message and the codeword have the same initial bits). Your job is to compute this number.

The total number of bits in the input (i.e., the sum of the b_i and the c_j) will not exceed 500,000.

Memory Limit: 32MB

POINTS: 270

贝茜正在领导奶牛们逃跑．为了联络，奶牛们互相发送秘密信息．

信息是二进制的，共有M(1≤M≤50000)条．反间谍能力很强的约翰已经部分拦截了这些信息，知道了第i条二进制信息的前bi(l《bi≤10000)位．他同时知道，奶牛使用N(1≤N≤50000)条密码．但是，他仅仅了解第J条密码的前cj(1≤cj≤10000)位．

对于每条密码J，他想知道有多少截得的信息能够和它匹配．也就是说，有多少信息和这条密码有着相同的前缀．当然，这个前缀长度必须等于密码和那条信息长度的较小者．

在输入文件中，位的总数（即∑Bi+∑Ci）不会超过500000.

输入输出格式

输入格式：

 

* Line 1: Two integers: M and N

* Lines 2..M+1: Line i+1 describes intercepted code i with an integer b_i followed by b_i space-separated 0‘s and 1‘s

* Lines M+2..M+N+1: Line M+j+1 describes codeword j with an integer c_j followed by c_j space-separated 0‘s and 1‘s

 

输出格式：

 

* Lines 1..M: Line j: The number of messages that the jth codeword could match.

 

输入输出样例

输入样例#1： 复制

4 5 
3 0 1 0 
1 1 
3 1 0 0 
3 1 1 0 
1 0 
1 1 
2 0 1 
5 0 1 0 0 1 
2 1 1 

输出样例#1： 复制

1 
3 
1 
1 
2 

说明

Four messages; five codewords.

The intercepted messages start with 010, 1, 100, and 110.

The possible codewords start with 0, 1, 01, 01001, and 11.

0 matches only 010: 1 match

1 matches 1, 100, and 110: 3 matches

01 matches only 010: 1 match

01001 matches 010: 1 match

11 matches 1 and 110: 2 matches

 

 

//01 Trie

//记录经过该路径的信息条数cnt（不在这儿结束，不与该路径相同）,以及在这儿结束的信息条数sum（与该路径相同的信息条数） 
//那么，在query的时候，
//ans+=沿线路径各点的sum 
//如果密码能匹配成功，就让ans+=root->cnt
//也就是加上与该密码前缀相同的信息条数
//如果密码不能匹配成功 
//就直接返回ans就可以了 

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

const int N=5e5+5;

int n,m,len;
struct TREE
{
    int num;
    int cnt,sum;
    TREE *son[2];
}tree[N];

typedef TREE* Tree;
Tree Root,now_node,null;

inline int read()
{
    char c=getchar();int num=0;
    for(;!isdigit(c);c=getchar());
    for(;isdigit(c);c=getchar())
        num=num*10+c-‘0‘;
    return num;
}

void init()
{
    Root=now_node=null=tree;
    null->son[1]=null->son[0]=null;
}

inline Tree new_node(int num)
{
    ++now_node;
    now_node->num=num;
    now_node->son[0]=now_node->son[1]=null;
    return now_node;
}

void insert(Tree root)        //插入信息 
{
    for(int i=1,a;i<=len;++i)
    {
        a=read();
        if(root->son[a]==null)
            root->son[a]=new_node(a);
        root=root->son[a];
        ++(root->cnt);        //经过该路径的信息条数+1 
    }
    --(root->cnt);        //减去完全一样的 
    ++(root->sum);        //该条信息+1 
}

int query(Tree root)
{
    int ans=0;
    bool ok=1;
    for(int i=1,a;i<=len;++i)
    {
        a=read();
        if(ok==0||root->son[a]==null)    //不要提前return，因为密码还没读完 
        {
            ok=0;
            continue;
        }
        root=root->son[a];
        ans+=root->sum;        //加上比密码短的信息条数，他们完全包含在密码里或者与密码相同 
    }
    if(ok)    //密码匹配成功 
        return ans+root->cnt;        //加上与密码前缀相同的信息条数 
    return ans;
}

int main()
{
//    freopen("testdata.in","r",stdin);
//    freopen("233.out","w",stdout);
    init();
    m=read(),n=read();
    for(int i=1;i<=m;++i)
    {
        len=read();
        insert(Root);
    }
    for(int i=1;i<=n;++i)
    {
        len=read();
        printf("%d\n",query(Root));
    }
    return 0;
}