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package com.crasmaru.sat;

import java.math.BigInteger;
import java.util.Random;
import java.util.Vector;

/**
 * Utility to generate SAT instances equivalent to Integer Factorization. Prints
 * a SAT instance in DIMACS format to the standard output.
 * 
 * Usage: java com.crasmaru.sat.IntFact2Sat factors_length_in_bits
 */
public class IntFact2Sat {
	int current_var_;
	int no_clauses_;
	int dim_;
	StringBuffer sb_;

	private int nextVar() {
		return ++current_var_;
	}

	private Vector nextVector() {
		Vector ret = new Vector();
		for (int i = 0; i < dim_; i++) {
			ret.add(nextVar());
		}
		return ret;
	}

	// Returns the complement of var.
	private int not(int var) {
		return -var;
	}

	// Returns a new var x so that x = a and b.
	private int and(int a, int b) {
		int x = nextVar();

		out(x + " " + not(a) + " " + not(b) + " 0");
		out(not(x) + " " + a + " 0");
		out(not(x) + " " + b + " 0");

		no_clauses_ += 3;
		return x;
	}

	// Returns a new var x so that x = a xor b xor c.
	private int xor(int a, int b, int c) {
		int x = nextVar();

		out(x + " " + not(a) + " " + b + " " + c + " 0");
		out(x + " " + a + " " + not(b) + " " + c + " 0");
		out(x + " " + a + " " + b + " " + not(c) + " 0");
		out(x + " " + not(a) + " " + not(b) + " " + not(c) + " 0");
		out(not(x) + " " + not(a) + " " + not(b) + " " + c + " 0");
		out(not(x) + " " + not(a) + " " + b + " " + not(c) + " 0");
		out(not(x) + " " + a + " " + not(b) + " " + not(c) + " 0");
		out(not(x) + " " + a + " " + b + " " + c + " 0");

		no_clauses_ += 8;
		return x;
	}

	// Returns a new var x so that x = a xor b.
	private int xor(int a, int b) {
		int x = nextVar();

		out(x + " " + not(a) + " " + b + " 0");
		out(x + " " + a + " " + not(b) + " 0");
		out(not(x) + " " + a + " " + b + " 0");
		out(not(x) + " " + not(a) + " " + not(b) + " 0");

		no_clauses_ += 4;
		return x;
	}

	// Returns a new var x so that x = carry(a + b + c).
	private int carry(int a, int b, int c) {
		int x = nextVar();

		out(x + " " + not(a) + " " + not(b) + " 0");
		out(x + " " + not(a) + " " + not(c) + " 0");
		out(x + " " + not(b) + " " + not(c) + " 0");
		out(not(x) + " " + a + " " + b + " 0");
		out(not(x) + " " + a + " " + c + " 0");
		out(not(x) + " " + b + " " + c + " 0");

		no_clauses_ += 6;
		return x;
	}

	// Returns a new var x so that x = carry(a + b).
	private int carry(int a, int b) {
		int x = nextVar();

		out(x + " " + not(a) + " " + not(b) + " 0");
		out(not(x) + " " + a + " 0");
		out(not(x) + " " + b + " 0");

		no_clauses_ += 3;
		return x;
	}

	// Returns an unary class that sets the var to value.
	private void set(int var, boolean value) {
		out((value ? var : not(var)) + " 0");
		no_clauses_++;
	}

	private void out(Object o) {
		sb_.append(o).append('\n');
	}

	private void generate() {
		Vector in_x = nextVector();
		Vector in_y = nextVector();
		Vector output = generateFactCircuit(in_x, in_y);

		Random rand = new Random();
		BigInteger big1 = dim_ > 2 ? BigInteger.probablePrime(dim_, rand) : BigInteger.valueOf(3);
		BigInteger big2 = dim_ > 2 ? BigInteger.probablePrime(dim_, rand) : BigInteger.valueOf(3);
		assert (big1.bitLength() == dim_);
		assert (big2.bitLength() == dim_);

		setOutputBits(in_x, output, big1, big2);
	}

	private void setOutputBits(Vector in_x, Vector output, BigInteger big1, BigInteger big2) {
		BigInteger ret = big1.multiply(big2);
		for (int i = 0; i < ret.bitLength(); i++) {
			set(output.get(i), ret.testBit(i));
		}
		for (int i = ret.bitLength(); i < output.size(); i++) {
			set(output.get(i), false);
		}

		StringBuffer sb1 = new StringBuffer();
		for (int i = 0; i < dim_; i++) {
			sb1.append((big2.testBit(i) ? in_x.get(i) : not(in_x.get(i))) + " ");
		}
		sb_.insert(0, "c " + big2 + ": " + sb1 + "\n");

		sb1 = new StringBuffer();
		for (int i = 0; i < dim_; i++) {
			sb1.append((big1.testBit(i) ? in_x.get(i) : not(in_x.get(i))) + " ");
		}
		sb_.insert(0, "c " + big1 + ": " + sb1 + "\n");

		sb_.insert(0, "p cnf " + current_var_ + " " + no_clauses_ + "\n");
	}

	@SuppressWarnings("unchecked")
	private Vector generateFactCircuit(Vector in_x, Vector in_y) {
		in_x.add(nextVar()); // pad in_x with a 0
		Vector last = (Vector) in_x.clone();

		Vector output = new Vector();
		Vector carry = new Vector();
		Vector result = new Vector();

		// Start from 1 because in_x[0] == 1.
		for (int in_y_indx = 1; in_y_indx < dim_; in_y_indx++) {
			carry.clear();
			result.clear();

			// gather output bits
			output.add(last.get(0));

			int a_0 = and(in_x.get(0), in_y.get(in_y_indx));
			result.add(xor(last.get(1), a_0));
			carry.add(carry(last.get(1), a_0));

			for (int j = 1; j < dim_; j++) {
				int a_j = and(in_x.get(j), in_y.get(in_y_indx));
				result.add(xor(last.get(j + 1), a_j, carry.get(j - 1)));
				carry.add(carry(last.get(j + 1), a_j, carry.get(j - 1)));
			}

			last = (Vector) result.clone();
			last.add(carry.lastElement());
		}
		for (int i = 0; i < last.size(); i++) {
			output.add(last.elementAt(i));
		}

		set(in_y.firstElement(), true);
		set(in_x.lastElement(), false);
		return output;
	}

	IntFact2Sat(int dim) {
		this.dim_ = dim;
		sb_ = new StringBuffer();
	}

	public static void main(String[] args) {
		IntFact2Sat minFact = new IntFact2Sat(args.length > 0 ? Integer.parseInt(args[0]) : 2);
		minFact.generate();
		System.out.println(minFact.sb_);
	}
}