void CornerSequence::fillInWastedRegion() {
    std::cout << "fillInWastedRegion()\n";
    int smallestMacroWidth = widthSortedMacros->getSmallest()->getWidth();
    int smallestMacroHeight = heightSortedMacros->getSmallest()->getHeight();
    while (true) {
        int numFills = 0;
        // Try to fill a horizontal empty Tile.
        Tile *emptyTile = cornerHorizontalTilePlane->getEmptyTileWithSmallestWidth();
        if (emptyTile != 0 && emptyTile->getWidth() < smallestMacroWidth) {
            std::cout << "fill horizontalTile\n";
            emptyTile->print();
            Tile *horizontalTile = new Tile(emptyTile->getXStart(), emptyTile->getYStart(),
                emptyTile->getXEnd(), emptyTile->getYEnd(), true);
            Tile *verticalTile = new Tile(emptyTile->getXStart(), emptyTile->getYStart(),
                emptyTile->getXEnd(), emptyTile->getYEnd(), true);
            horizontalTile->setTemporarilySolid();
            verticalTile->setTemporarilySolid();
            // Find startVerticalTile.
            Corner *corner = emptyTile->getBlCorner();
            Tile *startVerticalTile;
            if (corner == 0) {
                corner = emptyTile->getTlCorner();
            }
            if (corner != 0) {
                startVerticalTile = corner->getVerticalTile();
            } else {
                // If emptyTile has no Corner, than emptyTile's lb and rt
                // are empty Tiles, and lb has top Corners and rt has bottom Corners.
                startVerticalTile = cornerVerticalTilePlane->findTile(emptyTile->getXStart(), emptyTile->getYStart(),
                    emptyTile->getRt()->getBlCorner()->getVerticalTile());
            }
            // Place horizontalTile.
            std::cout << "place horizontal\n";
            cornerHorizontalTilePlane->placeSolidTileGivenBothStartTiles(horizontalTile, emptyTile, startVerticalTile);
            // Place verticalTile.
            std::cout << "place vertical\n";
            cornerVerticalTilePlane->placeSolidTileGivenBothStartTiles(verticalTile, horizontalTile, startVerticalTile);

            cornerHorizontalTilePlane->calculateCurrentCornersWidthAndHeight();
            cornerVerticalTilePlane->calculateCurrentCornersWidthAndHeight();
            std::cout << "updateQuadtrees()\n";
            updateQuadtrees();
            std::cout << "updateQuadtrees() end\n";

            numFills += 1;
        }
        // Try to fill a vertical empty Tile.
        emptyTile = cornerVerticalTilePlane->getEmptyTileWithSmallestHeight();
        if (emptyTile != 0 && emptyTile->getHeight() < smallestMacroHeight) {
            std::cout << "fill verticalTile\n";
            emptyTile->print();
            Tile *horizontalTile = new Tile(emptyTile->getXStart(), emptyTile->getYStart(),
                emptyTile->getXEnd(), emptyTile->getYEnd(), true);
            Tile *verticalTile = new Tile(emptyTile->getXStart(), emptyTile->getYStart(),
                emptyTile->getXEnd(), emptyTile->getYEnd(), true);
            horizontalTile->setTemporarilySolid();
            verticalTile->setTemporarilySolid();
            // Find startHorizontalTile.
            Corner *corner = emptyTile->getBlCorner();
            Tile *startHorizontalTile;
            if (corner == 0) {
                corner = emptyTile->getBrCorner();
            }
            if (corner != 0) {
                corner->print();
                startHorizontalTile = corner->getHorizontalTile();
                cornerHorizontalTilePlane->getBottomRightMostTile()->print();
            } else {
                // If emptyTile has no Corner, than emptyTile's bl and tr
                // are empty Tiles, and bl has right Corners and tr has left Corners.
                startHorizontalTile = cornerHorizontalTilePlane->findTile(emptyTile->getXStart(), emptyTile->getYStart(),
                    emptyTile->getTr()->getBlCorner()->getHorizontalTile());
            }
            // Place horizontalTile.
            std::cout << "place horizontal\n";
            horizontalTile->print();
            startHorizontalTile->print();
            startHorizontalTile->printFourNeighbors();
            cornerHorizontalTilePlane->placeSolidTileGivenBothStartTiles(horizontalTile, startHorizontalTile, emptyTile);
            // Place verticalTile.
            std::cout << "place vertical\n";
            cornerVerticalTilePlane->placeSolidTileGivenBothStartTiles(verticalTile, horizontalTile, emptyTile);

            cornerHorizontalTilePlane->calculateCurrentCornersWidthAndHeight();
            cornerVerticalTilePlane->calculateCurrentCornersWidthAndHeight();
            std::cout << "updateQuadtrees()\n";
            updateQuadtrees();
            std::cout << "updateQuadtrees() end\n";

            numFills += 1;
        }
        // Continue or not.
        if (numFills == 0) {
            break;
        }
    }
}
bool CornerSequence::placeMacrosWithIncrementalUpdate(int startPosition, int backupPosition) {
    bool placedUnsuccessfully = false;

    // Store Corners removed from sizeQuadtree during finding valid Corners.
    std::vector<Corner *> *temporarilyRemovedCorners = new std::vector<Corner *>();
    
    for (int i = startPosition; i < macros->size(); ++i) {
        //std::cout << i << "\n";
        Macro *macro = macros->at(i);
        macro->setOrientation(orientations->at(i));
        int macroWidth = macro->getWidth();
        int macroHeight = macro->getHeight();
        Corner *corner = corners->at(i);

        //std::cout << "begin Macro " << i << "\n";
        //std::cout << "smallest width emtpy Tile:  ";
        //cornerHorizontalTilePlane->getEmptyTileWithSmallestWidth()->print();
        //std::cout << "smallest height empty Tile: ";
        //cornerVerticalTilePlane->getEmptyTileWithSmallestHeight()->print();
        //std::cout << "smallest width Macro: ";
        //////(*widthSortedMacros->begin())->print();
        //widthSortedMacros->getSmallest()->print();
        //std::cout << "smallest height Macro: ";
        ////(*heightSortedMacros->begin())->print();
        //heightSortedMacros->getSmallest()->print();

        //fillInWastedRegion();

        // Check whether to select another Corner.
        bool toSelectAnotherCorner = false;
        if (corner == 0) {
            toSelectAnotherCorner = true;
        } else if (corner->isNotFromTilePlane()) {
            Corner *inputCorner = corner;
            std::vector<Point *> *foundCorners = positionQuadtree->getPointsAtXY(inputCorner->getX(), inputCorner->getY());
            if (foundCorners == 0) {
                // No matched Corner is found.
                toSelectAnotherCorner = true;
            } else {
                for (int j = 0; j < foundCorners->size(); ++j) {
                    Corner *foundCorner = static_cast<Corner *>(foundCorners->at(j));
                    if (foundCorner->getDirection() == inputCorner->getDirection()) {
                        // The matched Corner is found.
                        corner = foundCorner;
                        break;
                    }
                    // No matched Corner is found.
                    toSelectAnotherCorner = true;
                }
                delete foundCorners;
            }
            delete inputCorner;
            corners->at(i) = 0;
            // If macro ends up being unsuccessfully placed,
            // notFromTilePlane Corners after corner will be deleted in ~CornerSeqence().
        }

        if (toSelectAnotherCorner) {
            corner = static_cast<Corner *>(sizeQuadtree->getPointRandomlyByXY(macroWidth, macroHeight, true, true));
            if (corner == 0) {
                // No Corner is available.
                placedUnsuccessfully = true;
                indexPlacedUnsuccessfully = i;
                break;
            }
        }

        // Check overlap.
        int cornerDirection;
        int macroXStart;
        int macroYStart;
        int macroXEnd;
        int macroYEnd;
        int cornerX;
        int cornerY;
        while (true) {
            // Check corner gap size.
            bool cornerGapSizeIsValid = true;
            if (corner->isType1()) {
                if (corner->isGapOnHorizontalSide()) {
                    if (corner->getGapSize() >= macroWidth) {
                        cornerGapSizeIsValid = false;
                    }
                } else {
                    if (corner->getGapSize() >= macroHeight) {
                        cornerGapSizeIsValid = false;
                    }
                }
            }

            if (cornerGapSizeIsValid) {
                // Calculate macro position.
                cornerX = corner->getX();
                cornerY = corner->getY();
                cornerDirection = corner->getDirection();
                switch (cornerDirection) {
                case 0:
                    // Bl
                    macroXStart = cornerX;
                    macroYStart = cornerY;
                    macroXEnd = cornerX + macroWidth;
                    macroYEnd = cornerY + macroHeight;
                    break;
                case 1:
                    // Br
                    macroXStart = cornerX - macroWidth;
                    macroYStart = cornerY;
                    macroXEnd = cornerX;
                    macroYEnd = cornerY + macroHeight;
                    break;
                case 2:
                    // Tl
                    macroXStart = cornerX;
                    macroYStart = cornerY - macroHeight;
                    macroXEnd = cornerX + macroWidth;
                    macroYEnd = cornerY;
                    break;
                case 3:
                    // Tr
                    macroXStart = cornerX - macroWidth;
                    macroYStart = cornerY - macroHeight;
                    macroXEnd = cornerX;
                    macroYEnd = cornerY;
                    break;
                }

                // Check overlap.
                if (cornerDirection <= 1) {
                    if (cornerHorizontalTilePlane->checkAreaEmptyCheckFromBottom(
                        macroXStart, macroYStart, macroXEnd, macroYEnd,
                        corner->getHorizontalTile())) {
                        // Does not overlap.
                        break;
                    }
                } else {
                    if (cornerHorizontalTilePlane->checkAreaEmptyCheckFromTop(
                        macroXStart, macroYStart, macroXEnd, macroYEnd,
                        corner->getHorizontalTile())) {
                        // Does not overlap.
                        break;
                    }
                }
            }

            // corner is not valid.
            // Select another Corner.
            sizeQuadtree->remove(corner);
            temporarilyRemovedCorners->push_back(corner);
            corner = static_cast<Corner *>(sizeQuadtree->getPointRandomlyByXY(macroWidth, macroHeight, true, true));
            if (corner == 0) {
                // No Corner is available.
                placedUnsuccessfully = true;
                indexPlacedUnsuccessfully = i;
                break;
            }
        }
        if (placedUnsuccessfully) {
            break;
        }
        // A valid Corner is selected.
        // Insert removed Corners back to quadtrees.
        for (int j = 0; j < temporarilyRemovedCorners->size(); ++j) {
            sizeQuadtree->insert(temporarilyRemovedCorners->at(j));
        }
        temporarilyRemovedCorners->clear();

        // Copy the valid Corner and replace corners->at(i)
        // because the valid Corner will be deleted after macro is placed.
        corners->at(i) = corner->copyAsNotFromTilePlane();

        // Place macro at corner.
        macro->setXStart(macroXStart);
        macro->setYStart(macroYStart);
        macro->updateRectanglesPosition();
        Tile *horizontalTile = new Tile(macroXStart, macroYStart, macroXEnd, macroYEnd, true);
        Tile *verticalTile = new Tile(macroXStart, macroYStart, macroXEnd, macroYEnd, true);
        Tile *startHorizontalTile;
        Tile *startVerticalTile;
        switch (cornerDirection) {
        case 0:
            // Bl
            startHorizontalTile = corner->getHorizontalTile();
            startVerticalTile = corner->getVerticalTile();
            break;
        case 1:
            // Br
            startHorizontalTile = corner->getHorizontalTile();
            startVerticalTile = cornerVerticalTilePlane->findTile(macroXStart, macroYStart, corner->getVerticalTile());
            break;
        case 2:
            // Tl
            startHorizontalTile = cornerHorizontalTilePlane->findTile(macroXStart, macroYStart, corner->getHorizontalTile());
            startVerticalTile = corner->getVerticalTile();
            break;
        case 3:
            // Tr
            startHorizontalTile = cornerHorizontalTilePlane->findTile(macroXStart, macroYStart, corner->getHorizontalTile());
            startVerticalTile = cornerVerticalTilePlane->findTile(macroXStart, macroYStart, corner->getVerticalTile());
            break;
        }
        cornerHorizontalTilePlane->placeSolidTileGivenBothStartTiles(horizontalTile, startHorizontalTile, startVerticalTile);
        startHorizontalTile = horizontalTile;
        //switch (cornerDirection) {
        //case 0:
        //    // Bl
        //    startVerticalTile = corner->getVerticalTile();
        //    break;
        //case 1:
        //    // Br
        //    startVerticalTile = cornerVerticalTilePlane->findTile(macroXStart, macroYStart, corner->getVerticalTile());
        //    break;
        //case 2:
        //    // Tl
        //    startVerticalTile = corner->getVerticalTile();
        //    break;
        //case 3:
        //    // Tr
        //    startVerticalTile = cornerVerticalTilePlane->findTile(macroXStart, macroYStart, corner->getVerticalTile());
        //    break;
        //}
        cornerVerticalTilePlane->placeSolidTileGivenBothStartTiles(verticalTile, startVerticalTile, startHorizontalTile);
        // Remove macro from sets.
        //widthSortedMacros->erase(macro);
        //heightSortedMacros->erase(macro);
        // Calculate Corners' width and height.
        cornerHorizontalTilePlane->calculateCurrentCornersWidthAndHeight();
        cornerVerticalTilePlane->calculateCurrentCornersWidthAndHeight();

        // Update quadtrees.
        updateQuadtrees();
    }

    delete temporarilyRemovedCorners;

    return !placedUnsuccessfully;
}