BigR1Array.java

package org.drip.spaces.big;

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

/*!
 * Copyright (C) 2020 Lakshmi Krishnamurthy
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * Copyright (C) 2018 Lakshmi Krishnamurthy
 * Copyright (C) 2017 Lakshmi Krishnamurthy
 * Copyright (C) 2016 Lakshmi Krishnamurthy
 * Copyright (C) 2015 Lakshmi Krishnamurthy
 * 
 *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
 *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
 *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
 *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
 *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
 *      and computational support.
 *  
 *      https://lakshmidrip.github.io/DROP/
 *  
 *  DROP is composed of three modules:
 *  
 *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
 *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
 *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
 * 
 *  DROP Product Core implements libraries for the following:
 *  - Fixed Income Analytics
 *  - Loan Analytics
 *  - Transaction Cost Analytics
 * 
 *  DROP Portfolio Core implements libraries for the following:
 *  - Asset Allocation Analytics
 *  - Asset Liability Management Analytics
 *  - Capital Estimation Analytics
 *  - Exposure Analytics
 *  - Margin Analytics
 *  - XVA Analytics
 * 
 *  DROP Computational Core implements libraries for the following:
 *  - Algorithm Support
 *  - Computation Support
 *  - Function Analysis
 *  - Model Validation
 *  - Numerical Analysis
 *  - Numerical Optimizer
 *  - Spline Builder
 *  - Statistical Learning
 * 
 *  Documentation for DROP is Spread Over:
 * 
 *  - Main                     => https://lakshmidrip.github.io/DROP/
 *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
 *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
 *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
 *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
 *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
 *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
 *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
 *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
 *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
 *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
 * 
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *      you may not use this file except in compliance with the License.
 *   
 *  You may obtain a copy of the License at
 *      http://www.apache.org/licenses/LICENSE-2.0
 *  
 *  Unless required by applicable law or agreed to in writing, software
 *      distributed under the License is distributed on an "AS IS" BASIS,
 *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  
 *  See the License for the specific language governing permissions and
 *      limitations under the License.
 */

/**
 * <i>BigR1Array</i> contains an Implementation of a variety of in-place Sorting Algorithms for Big Double
 * Arrays.
 * 
 * <br><br>
 *  <ul>
 *      <li>
 *          C A R Hoare's Quick Sort
 *      </li>
 *      <li>
 *          J von Neumann's Merge Sort
 *      </li>
 *      <li>
 *          R W Floyd's Heap Sort
 *      </li>
 *      <li>
 *          Insertion Sort
 *      </li>
 *  </ul>
 * 
 * <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/StatisticalLearningLibrary.md">Statistical Learning Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spaces/README.md">R<sup>1</sup> and R<sup>d</sup> Vector/Tensor Spaces (Validated and/or Normed), and Function Classes</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/spaces/big/README.md">Big-data In-place Manipulator</a></li>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class BigR1Array {
    private int _iLength = -1;
    private double[] _adblA = null;

    private void swapLocations (
        final int i1,
        final int i2)
    {
        double dblTemp = _adblA[i1];
        _adblA[i1] = _adblA[i2];
        _adblA[i2] = dblTemp;
    }

    private int dropOffIndex (
        final int iPickupIndex)
    {
        for (int i = 0; i < iPickupIndex; ++i) {
            if (_adblA[i] > _adblA[iPickupIndex]) return i;
        }

        return iPickupIndex;
    }

    /**
     * BigR1Array Constructor
     * 
     * @param adblA The Array to be Sorted
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public BigR1Array (
        final double[] adblA)
        throws java.lang.Exception
    {
        if (null == (_adblA = adblA) || 0 == (_iLength = _adblA.length))
            throw new java.lang.Exception ("BigR1Array Constructor => Invalid Inputs");
    }

    /**
     * Retrieve the Array Contents
     * 
     * @return The Array Contents
     */

    public double[] array()
    {
        return _adblA;
    }

    /**
     * Transfer all Elements from the Pickup Index to the Drop Off Index, and contiguously Shift the
     *  Intermediate Array
     *
     * @param iPickupIndex The Pickup Index
     * @param iDropOffIndex The Drop off Index
     * 
     * @return TRUE - Successfully transferred the Pickup to the Drop off Locations and the related
     *  Translations
     */

    public boolean transfer (
        final int iPickupIndex,
        final int iDropOffIndex)
    {
        if (iPickupIndex < 0 || iPickupIndex >= _iLength || iDropOffIndex < 0 || iDropOffIndex >= _iLength)
            return false;

        if (iPickupIndex == iDropOffIndex) return true;

        double dblTemp = _adblA[iPickupIndex];

        if (iPickupIndex > iDropOffIndex) {
            for (int i = iPickupIndex; i > iDropOffIndex; --i)
                _adblA[i] = _adblA[i - 1];
        } else {
            for (int i = iPickupIndex; i > iDropOffIndex; ++i)
                _adblA[i] = _adblA[i + 1];
        }

        _adblA[iDropOffIndex] = dblTemp;
        return true;
    }

    /**
     * Sort the Specified Range in the Array using Quick Sort
     * 
     * @param iLow Lower Index of the Range (Inclusive)
     * @param iHigh Upper Index of the Range (Inclusive)
     * 
     * @return TRUE - The Range has been successfully sorted
     */

    public boolean quickSort (
        final int iLow,
        final int iHigh)
    {
        if (iLow < 0 || iLow >= iHigh || iLow >= _iLength)
        {
            return false;
        }

        int iLeft = iLow;
        int iRight = iHigh;
        double dblPivot = _adblA[(iLow + iHigh) / 2];

        while (iLeft <= iRight)
        {
            while (_adblA[iLeft] < dblPivot)
            {
                ++iLeft;
            }

            while (_adblA[iRight] > dblPivot)
            {
                --iRight;
            }

            if (iLeft <= iRight)
            {
                swapLocations (iLeft, iRight);

                ++iLeft;
                --iRight;
            }
        }

        if (iLow < iRight && !quickSort (iLow, iRight)) return false;

        if (iLeft < iHigh && !quickSort (iLeft, iHigh)) return false;

        return true;
    }

    /**
     * Sort the Full Array using Quick Sort
     * 
     * @return TRUE - The Full Array has been successfully sorted
     */

    public boolean quickSort()
    {
        return quickSort (0, _iLength - 1);
    }

    /**
     * Merge the Sorted Sub Array Pair
     * 
     * @param i1Start The Left Starting Index (Inclusive)
     * @param i1End The Left Ending Index (Inclusive)
     * @param i2Start The Right Starting Index (Inclusive)
     * @param i2End The Right End Index (Inclusive)
     * 
     * @return TRUE - Successfully Merged the Sorted Array Pair and Re-assigned Back to the Master
     */

    public boolean mergeSort (
        final int i1Start,
        final int i1End,
        final int i2Start,
        final int i2End)
    {
        if (i1Start >= _iLength || i1Start > i1End || i2Start > i2End || i1End >= i2Start) return false;

        if (i1Start == i1End && i2Start == i2End) {
            if (_adblA[i1Start] > _adblA[i2Start]) swapLocations (i1Start, i2Start);
        } else {
            if (i1Start == i1End) {
                int i2Mid = (i2Start + i2End) / 2;

                if (!mergeSort (i2Start, i2Mid, i2Mid + 1, i2End)) return false;
            }
        }

        int i = 0;
        int i1 = i1Start;
        int i2 = i2Start;
        double[] adblMerged = new double[i1End - i1Start + i2End - i2Start + 2];

        while (i1 <= i1End && i2 <= i2End) {
            if (_adblA[i1] < _adblA[i2])
                adblMerged[i++] = _adblA[i1++];
            else if (_adblA[i1] > _adblA[i2])
                adblMerged[i++] = _adblA[i2++];
            else {
                adblMerged[i++] = _adblA[i1++];
                adblMerged[i++] = _adblA[i2++];
            }
        }

        while (i1 <= i1End)
            adblMerged[i++] = _adblA[i1++];

        while (i2 <= i2End)
            adblMerged[i++] = _adblA[i2++];

        i = 0;

        for (int j = i1Start; j <= i1End; ++j)
            _adblA[j] = adblMerged[i++];

        for (int j = i2Start; j <= i2End; ++j)
            _adblA[j] = adblMerged[i++];

        return true;
    }

    /**
     * Contiguous Stretch Merge Sort
     * 
     * @param iStart The Master Starting Index (Inclusive)
     * @param iEnd The Master Ending Index (Inclusive)
     * 
     * @return TRUE - Successfully Merged the Sorted Array Stretch and Re-assigned Back to the Master
     */

    public boolean mergeSort (
        final int iStart,
        final int iEnd)
    {
        if (iStart < 0 || iStart > iEnd || iStart >= _iLength) return false;

        if (iStart == iEnd) return true;

        if (iStart == iEnd - 1) {
            if (_adblA[iStart] > _adblA[iEnd]) swapLocations (iStart, iEnd);

            return true;
        }

        double[] adblMerged = new double[iEnd - iStart + 1];
        int iMid = (iStart + iEnd) / 2;
        int iRightStart = iMid + 1;
        int iRight = iRightStart;
        int iLeftStart = iStart;
        int iLeft = iLeftStart;
        int iRightEnd = iEnd;
        int iLeftEnd = iMid;
        int i = 0;

        if (!mergeSort (iLeftStart, iLeftEnd) || !mergeSort (iRightStart, iRightEnd)) return false;

        while (iLeft <= iLeftEnd && iRight <= iRightEnd) {
            if (_adblA[iLeft] < _adblA[iRight])
                adblMerged[i++] = _adblA[iLeft++];
            else if (_adblA[iLeft] > _adblA[iRight])
                adblMerged[i++] = _adblA[iRight++];
            else {
                adblMerged[i++] = _adblA[iLeft++];
                adblMerged[i++] = _adblA[iRight++];
            }
        }

        while (iLeft <= iLeftEnd)
            adblMerged[i++] = _adblA[iLeft++];

        while (iRight <= iRightEnd)
            adblMerged[i++] = _adblA[iRight++];

        i = 0;

        for (int j = iLeftStart; j <= iLeftEnd; ++j)
            _adblA[j] = adblMerged[i++];

        for (int j = iRightStart; j <= iRightEnd; ++j)
            _adblA[j] = adblMerged[i++];

        return true;
    }

    /**
     * In-place Big Array Merge Sort
     * 
     * @return TRUE - Successfully Merged the Big Double Array and Re-assigned Back to the Master
     */

    public boolean mergeSort()
    {
        return mergeSort (0, _iLength - 1);
    }

    /**
     * Heap Sort the Big Array
     * 
     * @return TRUE - Successfully Merged the Big Double Array and Re-assigned Back to the Master
     */

    public boolean heapSort()
    {
        org.drip.spaces.big.BinaryTree bt = null;

        try {
            bt = new org.drip.spaces.big.BinaryTree (_adblA[0], null);
        } catch (java.lang.Exception e) {
            e.printStackTrace();

            return false;
        }

        for (int i = 1; i < _iLength; ++i) {
            if (null == bt.insert (_adblA[i])) return false;
        }

        try {
            return _iLength == bt.ascendingNodeArray (_adblA, 0);
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return false;
    }

    /**
     * Insertion Sort the Big Array
     * 
     * @return TRUE - Successfully Merged the Big Double Array and Re-assigned Back to the Master
     */

    public boolean insertionSort()
    {
        for (int iPickupIndex = 1; iPickupIndex < _iLength; ++iPickupIndex) {
            if (!transfer (iPickupIndex, dropOffIndex (iPickupIndex))) return false;
        }

        return true;
    }
}