programming-examples/java/Data_Structures/Simplex.java

import java.util.*;

public class Simplex {

	// returns max c*x such that A*x <= b, x >= 0
	public static Rational simplex(Rational[][] A, Rational[] b, Rational[] c, Rational[] x) {
		int m = A.length;
		int n = A[0].length + 1;
		int[] index = new int[n + m];
		for (int i = 0; i < n + m; i++) {
			index[i] = i;
		}
		Rational[][] a = new Rational[m + 2][n + 1];
		for (Rational[] a1 : a) {
			Arrays.fill(a1, Rational.ZERO);
		}
		int L = m;
		for (int i = 0; i < m; i++) {
			for (int j = 0; j < n - 1; j++) {
				a[i][j] = A[i][j].negate();
			}
			a[i][n - 1] = Rational.ONE;
			a[i][n] = b[i];
			if (a[L][n].compareTo(a[i][n]) > 0) {
				L = i;
			}
		}
		for (int j = 0; j < n - 1; j++) {
			a[m][j] = c[j];
		}
		a[m + 1][n - 1] = Rational.ONE.negate();
		for (int E = n - 1;;) {
			if (L < m) {
				int t = index[E];
				index[E] = index[L + n];
				index[L + n] = t;
				a[L][E] = a[L][E].inverse();
				for (int j = 0; j <= n; j++) {
					if (j != E) {
						a[L][j] = a[L][j].mul(a[L][E].negate());
					}
				}
				for (int i = 0; i <= m + 1; i++) {
					if (i != L) {
						for (int j = 0; j <= n; j++) {
							if (j != E) {
								a[i][j] = a[i][j].add(a[L][j].mul(a[i][E]));
							}
						}
						a[i][E] = a[i][E].mul(a[L][E]);
					}
				}
			}
			E = -1;
			for (int j = 0; j < n; j++) {
				if (E < 0 || index[E] > index[j]) {
					if (a[m + 1][j].signum() > 0 || a[m + 1][j].signum() == 0 && a[m][j].signum() > 0) {
						E = j;
					}
				}
			}
			if (E < 0) {
				break;
			}
			L = -1;
			for (int i = 0; i < m; i++) {
				if (a[i][E].signum() < 0) {
					Rational d;
					if (L < 0 || (d = a[L][n].div(a[L][E]).sub(a[i][n].div(a[i][E]))).signum() < 0 || d.signum() == 0
							&& index[L + n] > index[i + n]) {
						L = i;
					}
				}
			}
			if (L < 0) {
				return Rational.POSITIVE_INFINITY;
			}
		}
		if (a[m + 1][n].signum() < 0) {
			return null;
		}
		if (x != null) {
			Arrays.fill(x, Rational.ZERO);
			for (int i = 0; i < m; i++)
				if (index[n + i] < n - 1)
					x[index[n + i]] = a[i][n];
		}
		return a[m][n];
	}

	// Usage example
	public static void main(String[] args) {
		long[][] a = { { 4, -1 }, { 2, 1 }, { -5, 2 } };
		long[] b = { 8, 10, 2 };
		long[] c = { 1, 1 };
		Rational[] x = new Rational[c.length];
		Rational res = simplex(cnv(a), cnv(b), cnv(c), x);
		System.out.println(new Rational(8).equals(res));
		System.out.println(Arrays.toString(x));

		a = new long[][] { { 3, 4, -3 }, { 5, -4, -3 }, { 7, 4, 11 } };
		b = new long[] { 23, 10, 30 };
		c = new long[] { -1, 1, 2 };
		x = new Rational[c.length];
		res = simplex(cnv(a), cnv(b), cnv(c), x);
		System.out.println(new Rational(57, 8).equals(res));
		System.out.println(Arrays.toString(x));

		// no feasible non-negative solutions
		a = new long[][] { { 4, -1 }, { 2, 1 }, { -5, 2 } };
		b = new long[] { 8, -10, 2 };
		c = new long[] { 1, 1 };
		res = simplex(cnv(a), cnv(b), cnv(c), null);
		System.out.println(null == res);

		// unbounded problem
		a = new long[][] { { -4, 1 }, { -2, -1 }, { -5, 2 } };
		b = new long[] { -8, -10, 2 };
		c = new long[] { 1, 1 };
		res = simplex(cnv(a), cnv(b), cnv(c), null);
		System.out.println(Rational.POSITIVE_INFINITY == res);

		// no feasible solutions
		a = new long[][] { { 1 }, { -1 } };
		b = new long[] { 1, -2 };
		c = new long[] { 0 };
		res = simplex(cnv(a), cnv(b), cnv(c), null);
		System.out.println(null == res);

		// infinite number of solutions, but only one is returned
		a = new long[][] { { 1, 1 } };
		b = new long[] { 0 };
		c = new long[] { 1, 1 };
		x = new Rational[c.length];
		res = simplex(cnv(a), cnv(b), cnv(c), x);
		System.out.println(Arrays.toString(x));
	}

	static Rational[] cnv(long[] a) {
		Rational[] res = new Rational[a.length];
		for (int i = 0; i < a.length; i++) {
			res[i] = new Rational(a[i]);
		}
		return res;
	}

	static Rational[][] cnv(long[][] a) {
		Rational[][] res = new Rational[a.length][];
		for (int i = 0; i < a.length; i++) {
			res[i] = cnv(a[i]);
		}
		return res;
	}
}