【poj3690】Constellations 哈希

传送门

题目分析

考虑将大矩阵的每个1*q矩阵哈希值求出，然后让小矩阵的第一行在大矩阵中找，如果找到，并且能匹配所有行则出现过。否则没出现过。

在初始化1*q矩阵时可以进行优化：假设该行为123456，要求1*5的矩阵哈希值，可以先暴力求出1~5，为 $1 * H^4 + 2 * H^3 + 3 * H^2 + 4 * H + 5$，现在要删除1添加6：变为$2 * H^4 + 3 * H^3 + 4 * H^2 + 5 * H + 6$，也就是先减去1的哈希值乘以$H^{len - 1}$，然后乘以H，加上6的哈希值。代码如下:

  for(int i = ; i <= n; i++){
      for(int k = ; k <= q; k++)
          fixedHash[i][] = fixedHash[i][] * H + getVal(matrix[i][k]);
      for(int j = ; j <= m - q + ; j++)
          fixedHash[i][j] = (fixedHash[i][j - ] - getVal(matrix[i][j - ]) * poww[q - ]) * H + getVal(matrix[i][j + q - ]);
  }

code

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<string>
#include<algorithm>
using namespace std;

const int N = ;
typedef unsigned long long ull;
const ull H = ;
ull fixedHash[N][N], hash[], poww[];
int n, m, T, p, q, k;
char matrix[N][N], small[][];

inline int getVal(char x){
    return x == '*' ?  : ;
}

inline bool check(int x, int y){
    for(int k = x + ; k <= x + p - ; k++)
        if(fixedHash[k][y] != hash[k - x + ])
            return false;
    return true;
}

int main(){
    freopen("h.in", "r", stdin);
    poww[] = ;
    for(int i = ; i <= ; i++) poww[i] = poww[i - ] * H;
    while(scanf("%d%d%d%d%d", &n, &m, &T, &p, &q), n + m + T + p + q){
        memset(matrix, , sizeof matrix);
        for(int i = ; i <= n; i++) scanf("%s", matrix[i] + );
        memset(fixedHash, , sizeof fixedHash);
        for(int i = ; i <= n; i++){
            for(int k = ; k <= q; k++)
                fixedHash[i][] = fixedHash[i][] * H + getVal(matrix[i][k]);
            for(int j = ; j <= m - q + ; j++)
                fixedHash[i][j] = (fixedHash[i][j - ] - getVal(matrix[i][j - ]) * poww[q - ]) * H + getVal(matrix[i][j + q - ]);
        }
        int cnt = ;
        for(int i = ; i <= T; i++){
            memset(small, , sizeof small);
            for(int j = ; j <= p; j++)
                scanf("%s", small[j] + );
            memset(hash, , sizeof hash);
            for(int j = ; j <= p; j++)
                for(int k = ; k <= q; k++)
                    hash[j] = hash[j] * H + getVal(small[j][k]);
            bool flag = true;
            for(int j = ; j <= n - p + ; j++){
                for(int k = ; k <= m - q + ; k++){
                    if(fixedHash[j][k] == hash[])
                        if(check(j, k)){
                            cnt++;
                            flag = false;
                            break;
                        }
                }
                if(!flag) break;
            }
        }
        printf("Case %d: %d\n", ++k, cnt);
    }
}