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Pascal's triangle/Puzzle: Difference between revisions
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=={{header|Java}}==
Generate 11 equations and 11 unknowns. Reuse code from Cramer's Rule.
<lang java>
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
public class PascalsTrianglePuzzle {
public static void main(String[] args) {
Matrix mat = new Matrix(Arrays.asList(1d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, -1d, 0d, 0d),
Arrays.asList(0d, 1d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, -1d, 0d),
Arrays.asList(0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, -1d, 1d, -1d),
Arrays.asList(0d, 0d, 1d, 0d, 0d, 0d, 0d, 0d, 0d, -1d, 0d),
Arrays.asList(0d, 0d, 0d, 1d, 0d, 0d, 0d, 0d, 0d, 0d, -1d),
Arrays.asList(1d, 1d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d),
Arrays.asList(0d, 1d, 1d, 0d, -1d, 0d, 0d, 0d, 0d, 0d, 0d),
Arrays.asList(0d, 0d, 1d, 1d, 0d, -1d, 0d, 0d, 0d, 0d, 0d),
Arrays.asList(0d, 0d, 0d, 0d, -1d, 0d, 1d, 0d, 0d, 0d, 0d),
Arrays.asList(0d, 0d, 0d, 0d, 1d, 1d, 0d, -1d, 0d, 0d, 0d),
Arrays.asList(0d, 0d, 0d, 0d, 0d, 0d, 1d, 1d, 0d, 0d, 0d));
List<Double> b = Arrays.asList(11d, 11d, 0d, 4d, 4d, 40d, 0d, 0d, 40d, 0d, 151d);
List<Double> solution = cramersRule(mat, b);
System.out.println("Solution = " + cramersRule(mat, b));
System.out.printf("X = %.2f%n", solution.get(8));
System.out.printf("Y = %.2f%n", solution.get(9));
System.out.printf("Z = %.2f%n", solution.get(10));
}
private static List<Double> cramersRule(Matrix matrix, List<Double> b) {
double denominator = matrix.determinant();
List<Double> result = new ArrayList<>();
for ( int i = 0 ; i < b.size() ; i++ ) {
result.add(matrix.replaceColumn(b, i).determinant() / denominator);
}
return result;
}
private static class Matrix {
private List<List<Double>> matrix;
@Override
public String toString() {
return matrix.toString();
}
@SafeVarargs
public Matrix(List<Double> ... lists) {
matrix = new ArrayList<>();
for ( List<Double> list : lists) {
matrix.add(list);
}
}
public Matrix(List<List<Double>> mat) {
matrix = mat;
}
public double determinant() {
if ( matrix.size() == 1 ) {
return get(0, 0);
}
if ( matrix.size() == 2 ) {
return get(0, 0) * get(1, 1) - get(0, 1) * get(1, 0);
}
double sum = 0;
double sign = 1;
for ( int i = 0 ; i < matrix.size() ; i++ ) {
sum += sign * get(0, i) * coFactor(0, i).determinant();
sign *= -1;
}
return sum;
}
private Matrix coFactor(int row, int col) {
List<List<Double>> mat = new ArrayList<>();
for ( int i = 0 ; i < matrix.size() ; i++ ) {
if ( i == row ) {
continue;
}
List<Double> list = new ArrayList<>();
for ( int j = 0 ; j < matrix.size() ; j++ ) {
if ( j == col ) {
continue;
}
list.add(get(i, j));
}
mat.add(list);
}
return new Matrix(mat);
}
private Matrix replaceColumn(List<Double> b, int column) {
List<List<Double>> mat = new ArrayList<>();
for ( int row = 0 ; row < matrix.size() ; row++ ) {
List<Double> list = new ArrayList<>();
for ( int col = 0 ; col < matrix.size() ; col++ ) {
double value = get(row, col);
if ( col == column ) {
value = b.get(row);
}
list.add(value);
}
mat.add(list);
}
return new Matrix(mat);
}
private double get(int row, int col) {
return matrix.get(row).get(col);
}
}
}
</lang>
{{out}}
<pre>
Solution = [16.0, 24.0, 17.0, 12.0, 41.0, 29.0, 81.0, 70.0, 5.0, 13.0, 8.0]
X = 5.00
Y = 13.00
Z = 8.00
pre>
=={{header|Julia}}==
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