[BZOJ 2462 BeiJing2011矩阵模板]矩阵Hash

[BZOJ 2462 BeiJing2011矩阵模板]矩阵Hash

分类：

Hash

1. 题目链接

[BZOJ 2462 BeiJing2011矩阵模板]

2. 题意描述

给定一个M行N列的01矩阵，以及Q个A行B列的01矩阵，你需要求出这Q个矩阵哪些在

原矩阵中出现过。

所谓01矩阵，就是矩阵中所有元素不是0就是1。

对于100%的数据，N,M<=1000,A,B<=100

3. 解题思路

矩阵Hash的模板题。

矩阵Hash的原理是对每行进行列哈希，相当于求出每行的列前缀的Hash值。然后再对之前的列Hash后的矩阵施加行哈希，得到矩阵的前缀Hash值,即Hash[i][j]表示从矩阵最左上角到点(i,j)的Hash值。

查询子矩阵的Hash值，就是进行四个矩阵分别乘以对应的权值后进行差分。

4. 实现代码

#include <bits/stdc++.h>
using namespace std;

typedef long long LL;
typedef long double LB;
typedef unsigned int uint;
typedef unsigned long long ULL;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef pair<LB, LB> PLB;
typedef vector<int> VI;

const int INF = 0x3f3f3f3f;
const LL INFL = 0x3f3f3f3f3f3f3f3fLL;
const long double PI = acos(-1.0);
const long double eps = 1e-4;
template<typename T> inline void umax(T &a, T b) { a = max(a, b); }
template<typename T> inline void umin(T &a, T b) { a = min(a, b); }
template <typename T> inline bool scan_d (T &ret) {
char c; int sgn;
if (c = getchar(), c == EOF) return 0; //EOF
while (c != '-' && (c < '0' || c > '9') ) if((c = getchar()) == EOF) return 0;
sgn = (c == '-') ? -1 : 1;
ret = (c == '-') ? 0 : (c - '0');
while (c = getchar(), c >= '0' && c <= '9') ret = ret * 10 + (c - '0');
ret *= sgn;
return 1;
}
//template<typename T, typename ...R> inline bool scan_d (T &ret, R& ...r) { scan_d(ret); scan_d(r...); }
template<typename T> void print(T x) {
static char s[33], *s1; s1 = s;
if (!x) *s1++ = '0';
if (x < 0) putchar('-'), x = -x;
while(x) *s1++ = (x % 10 + '0'), x /= 10;
while(s1-- != s) putchar(*s1);
}
inline void print(char ch) { putchar(ch); }
inline void print(const char s[]) { printf("%s", s); }
inline void print(char s[]) { printf("%s", s); }
inline void println() { putchar('\n'); }
template<typename T> inline void println(T f) { print(f); println(); }
//template<typename T, typename ...R> void print (T f, R ...r) { print(f); putchar(' '); print (r...); }
//template<typename T, typename ...R> void println(T f, R ...r) { print(f); putchar(' '); print (r...); println(); }
template<typename T> T randIntv(T a, T b) { return rand() % (b - a + 1) + a; } /*[a, b]*/

void debug() { cout << endl; }
//template<typename T, typename ...R> void debug (T f, R ...r) { cout << "[" << f << "]"; debug (r...); }

const int MAXN = 1005;
const int MAXA = 105;

const int HASH_SIZE = 1000007;

struct HNode {
ULL hv; int nxt;
//    int x, y;
} hd[HASH_SIZE];
int head[HASH_SIZE], tot;

void HInit() {
tot = 0;
memset(head, -1, sizeof(head));
}

bool HQuery(ULL hv) {
int u = hv % HASH_SIZE;
for(int i = head[u]; ~i; i = hd[i].nxt) {
if(hd[i].hv == hv) return true;
}
return false;
}

void HInsert(ULL hv) {
int u = hv % HASH_SIZE;
hd[tot].hv = hv;
hd[tot].nxt = head[u];
head[u] = tot ++;
}

int N, M, A, B, Q;
char S[MAXN][MAXN], T[MAXA][MAXA];

const ULL SEED[2] = {131, 13331};
ULL Hash[MAXN][MAXN], qz[MAXN][2];

ULL getHashV(int x, int y, int nn, int mm) {
assert(x - nn + 1 >= 0);
assert(y - mm + 1 >= 0);
return Hash[x][y] + Hash[x - nn][y - mm] * qz[mm][0] * qz[nn][1]
- Hash[x - nn][y] * qz[nn][1] - Hash[x][y - mm] * qz[mm][0];
}

int main() {
#ifdef ___LOCAL_WONZY___
freopen ("input.txt", "r", stdin);
//    freopen ("ans2.txt", "w+", stdout);
#endif // ___LOCAL_WONZY___
qz[0][0] = qz[0][1] = 1;
for(int i = 1; i < MAXN; ++i) {
qz[i][0] = qz[i - 1][0] * SEED[0];
qz[i][1] = qz[i - 1][1] * SEED[1];
}
while(~scanf("%d %d %d %d", &N, &M, &A, &B)) {
for(int i = 1; i <= N; ++i) scanf("%s", S[i] + 1);
for(int i = 0; i <= N; ++i) Hash[i][0] = 0;
for(int j = 0; j <= M; ++j) Hash[0][j] = 0;
for(int i = 1; i <= N; ++i) {
for(int j = 1; j <= M; ++j) {
Hash[i][j] = Hash[i][j - 1] * SEED[0] + S[i][j] - '0';
}
}
for(int i = 1; i <= N; ++i) {
for(int j = 1; j <= M; ++j) {
Hash[i][j] = Hash[i - 1][j] * SEED[1] + Hash[i][j];
}
}
HInit();
for(int i = A; i <= N; ++i) {
for(int j = B; j <= M; ++j) {
ULL hv = getHashV(i, j, A, B);
if(HQuery(hv) == false) HInsert(hv);
}
}
scanf("%d", &Q);
while(Q --) {
for(int i = 1; i <= A; ++i) scanf("%s", T[i] + 1);
ULL hv = 0;
for(int i = 1; i <= A; ++i) {
ULL temp = 0;
for(int j = 1; j <= B; ++j) {
temp = temp * SEED[0] + T[i][j] - '0';
}
hv = hv * SEED[1] + temp;
}
printf("%d\n", HQuery(hv) > 0 ? 1 : 0);
}
}
#ifdef ___LOCAL_WONZY___
cout << "Time elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC * 1000 << " ms." << endl;
#endif // ___LOCAL_WONZY___
return 0;
}