/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

/*

 Copyright (C) 2015 Ferdinando Ametrano

 Copyright (C) 2015 Paolo Mazzocchi

 This file is part of QuantLib, a free-software/open-source library

 for financial quantitative analysts and developers - http://quantlib.org/

 QuantLib is free software: you can redistribute it and/or modify it

 under the terms of the QuantLib license.  You should have received a

 copy of the license along with this program; if not, please email

 <quantlib-dev@lists.sf.net>. The license is also available online at

 <https://www.quantlib.org/license.shtml>.

 This program is distributed in the hope that it will be useful, but WITHOUT

 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS

 FOR A PARTICULAR PURPOSE.  See the license for more details.

*/

#include <ql/math/pascaltriangle.hpp>

#include <iterator>

namespace QuantLib {

    std::vector<std::vector<BigNatural> > PascalTriangle::coefficients_;

    const std::vector<BigNatural>& PascalTriangle::get(Size order) {

        if (coefficients_.empty()) {

            // order zero mandatory for bootstrap

            coefficients_.emplace_back(1, 1);

            coefficients_.emplace_back(2, 1);

            coefficients_.emplace_back(3, 1);

            coefficients_[2][1] = 2;

            coefficients_.emplace_back(4, 1);

            coefficients_[3][1] = coefficients_[3][2] = 3;

        }

        while (coefficients_.size()<=order)

            nextOrder();

        return coefficients_[order];

    }

    void PascalTriangle::nextOrder() {

        Size order = coefficients_.size();

        coefficients_.emplace_back(order + 1);

        coefficients_[order][0] = coefficients_[order][order] = 1;

        for (Size i=1; i<order/2+1; ++i) {

            coefficients_[order][i] = coefficients_[order][order-i] =

                coefficients_[order-1][i-1] + coefficients_[order-1][i];

        }

    }

}