RussellAndrewEdson

/* Here we create the constraints for the "backward diagonals" where
 * we move along the first row.
 *   ie. x_1,j + the sum of x_1+m,j-m <= 1 for all j=1,...,n.
 */
double[][] rowBackwardConstraintsMatrix = new double[n][n*n];
for (int row = 0; row < n; row++) {
    for (int column = row; column < n*row + 1; column += (n-1)) {
        rowBackwardConstraintsMatrix[row][column] = 1;
    }
}

RussellAndrewEdson

/* Here we create the constraints for the "forward diagonals" where
 * we move along the first column.
 *   ie. x_i,1 + the sum of x_i+m,1+m <= 1 for all i=1,...,n.
 */
double[][] columnForwardConstraintsMatrix = new double[n][n*n];
for (int row = 0; row < n; row++) {
    for (int column = n*row; column < n*n; column += (n+1)) {
        columnForwardConstraintsMatrix[row][column] = 1;
    }
}

RussellAndrewEdson

/* Here we create the constraints for the "forward diagonals" where
 * we move along the first row.
 *   ie. x_1,j + the sum of x_1+m,j+m is <= 1 for all j=1,...,n.
 */
double[][] rowForwardConstraintsMatrix = new double[n][n*n];
for (int row = 0; row < n; row++) {
    for (int column = row; column < n*n - row*n; column += (n+1)) {
        rowForwardConstraintsMatrix[row][column] = 1;
    }
}

RussellAndrewEdson

/**
 * Adds the "one queen per column" constraints to the linear program,
 *   ie. the sum from i=1 to n of x_i,j = 1 for all j=1,...,n.
 */
public static void makeQueenColumnConstraints(int n, LinearProgram lp) {
    double[][] columnConstraintsMatrix = new double[n][n*n];
    for (int row = 0; row < n; row++) {
        for (int column = row; column < n*n; column += n) {
            columnConstraintsMatrix[row][column] = 1;
        }

RussellAndrewEdson

/**
 * Adds the "one queen per row" constraints to the linear program,
 *   ie. the sum from j=1 to n of x_i,j = 1 for all i=1,...,n.
 */
public static void makeQueenRowConstraints(int n, LinearProgram lp) {
    double[][] rowConstraintsMatrix = new double[n][n*n];
    for (int row = 0; row < n; row++) {
        for (int column = n*row; column < n*row + n; column++) {
            rowConstraintsMatrix[row][column] = 1;
        }

RussellAndrewEdson

; Clojure functions for solving the N-Queens Puzzle.

(defn adjoin-position
  "Adds the new (row, column) position to the given positions list."
  [row column positions]
  (cons (list row column) positions))

(defn same-row?
  "Returns true if the given queens q1 and q2 are on the same row."
  [q1 q2]

RussellAndrewEdson

import java.util.function.BinaryOperator;
import java.util.function.Function;

public class FilteredAccumulate {

    /**
     * Returns the total obtained by applying the given operation across
     * the values of f(i), for i = a to b in which i satisfies the given
     * predicate (using the nullValue to get us started.)
     */

RussellAndrewEdson

import java.util.function.BinaryOperator;
import java.util.function.Function;

public class Accumulate {

    /**
     * Returns the total obtained by applying the given operation across
     * the values of f(i), for i = a to b, using the given null value.
     */
    public static double accumulate(

RussellAndrewEdson

import java.util.function.Function;

public class Product {

    /** Returns the accumulated product from i = a to b of f(i). */
    public static double product(Function<Integer, Double> f, int a, int b) {
        double result = 1.0;

        for (int i = a; i <= b; i++) {
            result *= f.apply(i);

RussellAndrewEdson

import java.util.function.Function;

public class Sum {

    /** Returns the accumulated sum from i = a to b of f(i). */
    public static double sum(Function<Integer, Double> f, int a, int b) {
        double result = 0.0;

        for (int i = a; i <= b; i++) {
            result += f.apply(i);