Percolation/Mean cluster density: Difference between revisions
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4096 0.065836
16384 0.065774
</pre>
=={{header|C++}}==
<syntaxhighlight lang="c++">
#include <iostream>
#include <random>
#include <string>
#include <vector>
std::random_device random;
std::mt19937 generator(random());
std::uniform_real_distribution<double> distribution(0.0F, 1.0F);
class Grid {
public:
Grid(int32_t size, double probability) {
create_grid(size, probability);
count_clusters();
}
int32_t cluster_count() {
return clusters;
}
double cluster_density() {
return (double) clusters / ( grid.size() * grid.size() );
}
void display() {
for ( uint64_t row = 0; row < grid.size(); row++ ) {
for ( uint64_t col = 0; col < grid.size(); col++ ) {
uint64_t value = grid[row][col];
char ch = ( value < GRID_CHARACTERS.length() ) ? GRID_CHARACTERS[value] : '?';
std::cout << " " << ch;
}
std::cout << std::endl;
}
}
private:
void count_clusters() {
clusters = 0;
for ( uint64_t row = 0; row < grid.size(); row++ ) {
for ( uint64_t col = 0; col < grid.size(); col++ ) {
if ( grid[row][col] == CLUSTERED ) {
clusters += 1;
identify_cluster(row, col, clusters);
}
}
}
}
void identify_cluster(uint64_t row, uint64_t col, uint64_t count) {
grid[row][col] = count;
if ( row < grid.size() - 1 && grid[row + 1][col] == CLUSTERED ) {
identify_cluster(row + 1, col, count);
}
if ( col < grid.size() - 1 && grid[row][col + 1] == CLUSTERED ) {
identify_cluster(row, col + 1, count);
}
if ( col > 0 && grid[row][col - 1] == CLUSTERED ) {
identify_cluster(row, col - 1, count);
}
if ( row > 0 && grid[row - 1][col] == CLUSTERED ) {
identify_cluster(row - 1, col, count);
}
}
void create_grid(int32_t grid_size, double probability) {
grid.assign(grid_size, std::vector<int32_t>(grid_size, 0));
for ( int32_t row = 0; row < grid_size; row++ ) {
for ( int32_t col = 0; col < grid_size; col++ ) {
if ( distribution(generator) < probability ) {
grid[row][col] = CLUSTERED;
}
}
}
}
int32_t clusters;
std::vector<std::vector<int32_t>> grid;
inline static const int CLUSTERED = -1;
inline static const std::string GRID_CHARACTERS = ".ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";
};
int main() {
const int32_t size = 15;
const double probability = 0.5;
const int32_t test_count = 5;
Grid grid(size, probability);
printf("%s%d%s%d%s%d%s%s", "This ", size, " by ", size, " grid contains ", grid.cluster_count(), " clusters:", "\n");
grid.display();
printf("%s%s%d%s", "\n", " p = 0.5, iterations = ", test_count, "\n");
std::vector<int32_t> gridSizes = { 10, 100, 1'000, 10'000 };
for ( int32_t gridSize : gridSizes ) {
double sumDensity = 0.0;
for ( int32_t test = 0; test < test_count; test++ ) {
Grid grid(gridSize, probability);
sumDensity += grid.cluster_density();
}
double result = sumDensity / test_count;
printf("%s%5d%s%.6f%s", " n = ", gridSize, ", simulation K = ", result, "\n");
}
}
</syntaxhighlight>
{{ out }}
<pre>
This 15 by 15 grid contains 11 clusters:
A A . B B . B B . . . . . . .
. . B B B B . B B . B B . . .
. C . . B B . B B B B . . . .
. C C . B . B B B B B B . D D
C C . . B B B B . . B . D D .
C C . . B B B . B B B . . D D
C C . . . . B . . . B . D D D
. C . E . . . . D D . . D D .
F . . . G . H . D D D D D D D
F F . F . I . F . D D . D D .
F . F F F . . F . . D D . . D
F . F . F . . F . F . D D D D
F F . . F F F F F F . D . . D
F F F F F . . F . . . D . . D
. F F . . J J . . . . D . K .
p = 0.5, iterations = 5
n = 10, simulation K = 0.088000
n = 100, simulation K = 0.067260
n = 1000, simulation K = 0.066215
n = 10000, simulation K = 0.065777
</pre>
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