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matrix_bool.cc
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181 lines (173 loc) · 4.13 KB
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//
// Boolean matrix
//
// Description:
// This admits very fast operations for boolean matrices.
//
// Algorithm:
// Block matrix decomposition technique:
// For a matrix A of size n x n, we split A as the block matrix
// each block is of size n/W x n/W. Here, computation of each
// W x W block is performed by bit operations;
//
// Complexity: (in practice)
// 50--60 times faster than the naive implementation.
//
#include <iostream>
#include <vector>
#include <cstdio>
#include <algorithm>
#include <functional>
#include <ctime>
using namespace std;
namespace bitmatrix {
typedef unsigned long long ull;
struct mat {
int n, m;
vector<vector<ull>> x;
mat(int m, int n) : m(m), n(n), x(1+m/8, vector<ull>(1+n/8)) { }
bool get(int i, int j) const {
return x[i/8][j/8] & (1ull << (8*(i%8)+(j%8)));
}
void set(int i, int j, int b) {
if (b) x[i/8][j/8] |= (1ull << (8*(i%8)+(j%8)));
else x[i/8][j/8] &= ~(1ull << (8*(i%8)+(j%8)));
}
};
ostream &operator<<(ostream &os, const mat &A) {
for (int i = 0; i < A.m; ++i) {
for (int j = 0; j < A.n; ++j)
os << A.get(i, j);
os << endl;
}
return os;
}
mat eye(int n) {
mat I(n, n);
for (int i = 0; i < I.x.size(); ++i)
I.x[i][i] = 0x8040201008040201;
return I;
}
mat add(mat A, const mat &B) {
for (int i = 0; i < A.x.size(); ++i)
for (int j = 0; j < A.x[0].size(); ++j)
A.x[i][j] |= B.x[i][j];
return A;
}
void disp(ull a) {
for (int i = 0; i < 8; ++i) {
for (int j = 0; j < 8; ++j) {
printf("%d", !!(a & 1));
a >>= 1;
}
printf("\n");
}
}
ull mul(ull a, ull b) { // C[i][j] |= A[i][k] & B[k][j]
const ull u = 0xff, v = 0x101010101010101;
ull c = 0;
for (;a && b; a >>= 1, b >>= 8)
c |= (((a & v) * u) & ((b & u) * v));
return c;
}
mat mul(mat A, mat B) {
mat C(A.n, B.m);
for (int i = 0; i < A.x.size(); ++i)
for (int k = 0; k < B.x.size(); ++k)
for (int j = 0; j < B.x[0].size(); ++j)
C.x[i][j] |= mul(A.x[i][k], B.x[k][j]);
return C;
}
mat pow(mat A, int k) {
mat X = eye(A.n);
for (; k > 0; k >>= 1) {
if (k & 1) X = mul(X, A);
A = mul(A, A);
}
return X;
}
ull transpose(ull a) {
ull t = (a ^ (a >> 7)) & 0x00aa00aa00aa00aa;
a = a ^ t ^ (t << 7);
t = (a ^ (a >> 14)) & 0x0000cccc0000cccc;
a = a ^ t ^ (t << 14);
t = (a ^ (a >> 28)) & 0x00000000f0f0f0f0;
a = a ^ t ^ (t << 28);
return a;
}
mat transpose(mat A) {
mat B(A.m, A.n);
for (int i = 0; i < A.x.size(); ++i)
for (int j = 0; j <= A.x[0].size(); ++j)
B.x[j][i] = transpose(A.x[i][j]);
return B;
}
}
namespace vector_bool {
typedef vector<bool> vec;
typedef vector<vec> mat;
mat eye(int n) {
mat I(n, vec(n));
for (int i = 0; i < n; ++i)
I[i][i] = 1;
return I;
}
mat add(mat A, const mat &B) {
for (int i = 0; i < A.size(); ++i)
for (int j = 0; j < A[0].size(); ++j)
A[i][j] = (A[i][j] | B[i][j]);
return A;
}
mat mul(mat A, const mat &B) {
for (int i = 0; i < A.size(); ++i) {
vec x(A[0].size());
for (int k = 0; k < B.size(); ++k)
for (int j = 0; j < B[0].size(); ++j)
x[j] = (x[j] | (A[i][k] & B[k][j]));
A[i].swap(x);
}
return A;
}
mat pow(mat A, int k) {
mat X = eye(A.size());
for (; k > 0; k >>= 1) {
if (k & 1) X = mul(X, A);
A = mul(A, A);
}
return X;
}
}
int main() {
for (int n = 1; n < 10000; n *= 2) {
printf("%d\t", n);
{
using namespace bitmatrix;
mat A(n, n);
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
A.set(i, j, rand() % 2);
}
}
double _time = clock();
A = pow(add(A, eye(n)), n); // (A + I)^n is a transitive closure
_time = clock() - _time;
printf("%f\t", _time / CLOCKS_PER_SEC);
}
printf("\n");
continue;
{
using namespace vector_bool;
mat A(n, vec(n));
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
A[i][j] = rand() % 2;
}
A[i][i] = 1;
}
double _time = clock();
A = pow(add(A, eye(n)), n); // (A + I)^n is a transitive closure
_time = clock() - _time;
printf("%f\n", _time / CLOCKS_PER_SEC);
}
}
}