Create a new version of paste:

<?php
class Namespace_Modulename_Block_Catalog_Product_List extends Mage_Catalog_Block_Product_List
{
    /**
     * return the search results with the category filters added
     * 
     * @return Mage_Catalog_Model_Resource_Product_Collection|false
     */
    public function getCategoryProductSearchResults()
    {
        $productCollection = $this->getData('product_collection');
        return $productCollection;
    }
}
	
<?php
/**
 * reuse existing magento default category filters
 * in order to display the categories and the corresponding products
 */
class Namespace_Modulename_Block_CatalogSearch_Layer_Filter_Category extends Mage_Catalog_Block_Layer_Filter_Category
{
    public $_filter;

    /**
     * Initialize filter template
     *
     */
    public function __construct()
    {
        parent::__construct();
        $this->setTemplate('catalogsearch/layer/filter.phtml');
    }

    /**
     * set product collection based on the search term
     * add to the block and render the block HTML
     * 
     * @param Mage_Catalog_Model_Category $_item
     * @param string $count
     * 
     * @return HTML
     */
    public function getCategoryProductSearchResultHtml($_item, $count)
    {
        $block = '';

        //form the search query once again based on the keyword to get the complete product collection
        $term = Mage::helper('catalogsearch')->getQueryText();
        $query = Mage::getModel('catalogsearch/query')->setQueryText($term)->prepare();

        Mage::getResourceModel('catalogsearch/fulltext')->prepareResult(
            Mage::getModel('catalogsearch/fulltext'),
            $term,
            $query
        );

        //get complete product collection based on the search term
        $collection = Mage::getResourceModel('catalog/product_collection');
        $collection->getSelect()->joinInner(
            array('search_result' => $collection->getTable('catalogsearch/result')),
            $collection->getConnection()->quoteInto(
                'search_result.product_id=e.entity_id AND search_result.query_id=?',
                $query->getId()
            ),
            array('relevance' => 'relevance')
        );

        //add category filter for each category
        $categoryId = $this->getCategoryId($_item);        
        $collection->joinField('category_id','catalog/category_product','category_id','product_id=entity_id',null,'left')
                    ->addAttributeToFilter('category_id', array('in' => $categoryId));


        Mage::getSingleton('catalog/product_status')->addVisibleFilterToCollection($collection);
        Mage::getSingleton('catalog/product_visibility')->addVisibleInSearchFilterToCollection($collection);       

        //$productIds = array();
        //$productIds = $collection->getAllIds();
        //Zend_Debug::dump($productIds);
        //$this->_productCollection = $collection;
        //$collection->printLogQuery(true);

        if(count($collection))
        {
            $block = $this->getLayout()->createBlock('namespace_modulename/catalog_product_list')  
                ->setProductCollection($collection)
                ->setTemplate('catalogsearch/product/list.phtml');

            return $block->toHtml(); 
        }
    }

    /**
     * get the category id based on the name/label of the category filter
     * 
     * @param Mage_Catalog_Model_Category $_item
     * @return string
     */
    public function getCategoryId($_item)
    {
        $categoryCollection = Mage::getModel('catalog/category')->getCollection()
                ->addAttributeToSelect('*')
                ->addAttributeToFilter('name', trim($_item->getLabel()))
                ;

        foreach ($categoryCollection as $data)
        {
            return $data->getId();
        }
    }
}
	
<?php
/**
 * reuse the concept of state_renderers from default magento
 * change the template for search results page only
 */
class Namespace_Modulename_Block_CatalogSearch_Layer_State extends Mage_Catalog_Block_Layer_State
{
    /**
     * Initialize Layer State template
     *
     */
    public function __construct()
    {
        parent::__construct();
        $this->setTemplate('catalogsearch/layer/state.phtml');
    }
}
	
<?php
/**
 * reuse the default magento layer concept
 * add a new block if its a search page with new template
 * load the existing block to display the HTML
 */
class Namespace_Modulename_Block_CatalogSearch_Layer extends Mage_CatalogSearch_Block_Layer
{
    protected $_searchStateBlockName;

    protected $_searchFilterHtmlBlockName;

    /**
     * Initialize blocks names
     */
    protected function _initBlocks()
    {
        parent::_initBlocks();

        $route = Mage::app()->getRequest()->getRouteName();
        if ( $route == 'catalogsearch' )
        {
            $this->_searchStateBlockName = 'namespace_modulename/catalogsearch_layer_state';
            $this->_searchFilterHtmlBlockName = 'namespace_modulename/catalogsearch_layer_filter_category';
        }
    }

    /**
     * Get search categories layered navigation state html
     *
     * @return string
     */
    public function getSearchStateHtml()
    {                
        if ( $this->_searchStateBlockName != NULL )
        {
            $searchStateBlock = $this->getLayout()->createBlock($this->_searchStateBlockName)->setLayer($this->getLayer());
            $this->setChild('search_layer_state', $searchStateBlock);
        }

        return $this->getChildHtml('search_layer_state');
    }

    /**
     * return the manipulated filter html from the PHTML for search
     * 
     * @param Mage_Catalog_Model_Layer_Filter_Abstract|false $_filter
     * @return HTML
     */
    public function getSearchFilterHtml($_filter)
    {
        if ( $this->_searchStateBlockName != NULL )
        {
            $block = $this->getLayout()->createBlock($this->_searchFilterHtmlBlockName)
                    ->setLayer($this->getLayer())
                    ;
            $block->_filter = $_filter;

            return $block->toHtml();
        }
    }
}
	
<?xml version="1.0" encoding="UTF-8"?>
<config>
    <modules>
        <Namespace_Modulename>
            <version>1.0.0</version>
        </Namespace_Modulename>
    </modules>
    <global>
        <blocks>
            <namespace_modulename>
                <class>Namespace_Modulename_Block</class>
            </namespace_modulename>
            <catalog>
                <rewrite>
                    <product_list>Namespace_Modulename_Block_Catalog_Product_List</product_list>
                </rewrite>
            </catalog>
            <catalogsearch>
                <rewrite>
                    <layer>Namespace_Modulename_Block_CatalogSearch_Layer</layer>
                </rewrite>
            </catalogsearch>
        </blocks>
        <helpers>
            <namespace_modulename>
                <class>Namespace_Modulename_Helper</class>
            </namespace_modulename>
        </helpers>
    </global>
</config>
	
...
    <catalogsearch_result_index translate="label">
        <label>Quick Search Form</label>
        <reference name="root">
            <action method="setTemplate"><template>page/3columns.phtml</template></action>
        </reference>
        <!--reference name="left_first">
            <block type="catalogsearch/layer" name="catalogsearch.leftnav" after="currency" template="catalog/layer/view.phtml">
                <block type="core/text_list" name="catalog.leftnav.state.renderers" as="state_renderers" />
            </block>
        </reference-->
        <reference name="content">
            <block type="catalogsearch/result" name="search.result" template="catalogsearch/result.phtml">
                <!--block type="catalog/product_list" name="search_result_list" template="catalog/product/list.phtml"-->
                <block type="namespace_modulename/catalog_product_list" name="search_result_list" template="catalogsearch/product/list.phtml">
                    <block type="namespace_modulename/catalogsearch_layer" name="catalogsearch.leftnav" after="currency" template="catalogsearch/layer/view.phtml">
                        <block type="core/text_list" name="catalog.leftnav.state.renderers" as="state_renderers" />
                    </block>
                </block>
            </block>
        </reference>
    </catalogsearch_result_index>
...
	
<?php echo $this->getChildHtml('catalogsearch.leftnav'); ?>
<?php
    $_productCollection=$this->getCategoryProductSearchResults();

    if (count($_productCollection))
    {
        $_helper = $this->helper('catalog/output');
?>
    <div class="category-products">

        <?php // Grid Mode ?>
        <?php $_collectionSize = $_productCollection->count() ?>
        <?php $_columnCount = $this->getColumnCount(); ?>
        <ul class="products-grid products-grid--max-<?php echo $_columnCount; ?>-col">
            <?php $i=0; foreach ($_productCollection as $_product): ?>
                <?php /*if ($i++%$_columnCount==0): ?>
                <?php endif*/ ?>
                <li class="item<?php if(($i-1)%$_columnCount==0): ?> first<?php elseif($i%$_columnCount==0): ?> last<?php endif; ?>">
                    <a href="<?php echo $_product->getProductUrl() ?>" title="<?php echo $this->stripTags($this->getImageLabel($_product, 'small_image'), null, true) ?>" class="product-image">
                        <?php $_imgSize = 210; ?>
                        <img id="product-collection-image-<?php echo $_product->getId(); ?>"
                             src="<?php echo $this->helper('catalog/image')->init($_product, 'small_image')->resize($_imgSize); ?>"
                             alt="<?php echo $this->stripTags($this->getImageLabel($_product, 'small_image'), null, true) ?>" />
                    </a>
                    <div class="product-info">
                        <h2 class="product-name"><a href="<?php echo $_product->getProductUrl() ?>" title="<?php echo $this->stripTags($_product->getName(), null, true) ?>"><?php echo $_helper->productAttribute($_product, $_product->getName(), 'name') ?></a></h2>
                        <?php
                        // Provides extra blocks on which to hang some features for products in the list
                        // Features providing UI elements targeting this block will display directly below the product name
                        if ($this->getChild('name.after')) {
                            $_nameAfterChildren = $this->getChild('name.after')->getSortedChildren();
                            foreach ($_nameAfterChildren as $_nameAfterChildName) {
                                $_nameAfterChild = $this->getChild('name.after')->getChild($_nameAfterChildName);
                                $_nameAfterChild->setProduct($_product);
                                echo $_nameAfterChild->toHtml();
                            }
                        }
                        ?>
                        <?php echo $this->getPriceHtml($_product, true) ?>
                        <?php if($_product->getRatingSummary()): ?>
                        <?php echo $this->getReviewsSummaryHtml($_product, 'short') ?>
                        <?php endif; ?>
                        <div class="actions">
                            <?php if(!$_product->canConfigure() && $_product->isSaleable()): ?>
                                <button type="button" title="<?php echo $this->quoteEscape($this->__('Add to Cart')) ?>" class="button btn-cart" onclick="setLocation('<?php echo $this->getAddToCartUrl($_product) ?>')"><span><span><?php echo $this->__('Add to Cart') ?></span></span></button>
                            <?php elseif($_product->getStockItem() && $_product->getStockItem()->getIsInStock()): ?>
                                <a title="<?php echo $this->quoteEscape($this->__('View Details')) ?>" class="button" href="<?php echo $_product->getProductUrl() ?>"><?php echo $this->__('View Details') ?></a>
                            <?php else: ?>
                                <p class="availability out-of-stock"><span><?php echo $this->__('Out of stock') ?></span></p>
                            <?php endif; ?>
                            <ul class="add-to-links">
                                <?php if ($this->helper('wishlist')->isAllow()) : ?>
                                    <li><a href="<?php echo $this->helper('wishlist')->getAddUrl($_product) ?>" class="link-wishlist"><?php echo $this->__('Add to Wishlist') ?></a></li>
                                <?php endif; ?>
                                <?php if($_compareUrl=$this->getAddToCompareUrl($_product)): ?>
                                    <li><span class="separator">|</span> <a href="<?php echo $_compareUrl ?>" class="link-compare"><?php echo $this->__('Add to Compare') ?></a></li>
                                <?php endif; ?>
                            </ul>
                        </div>

                        <?php
                        // Provides extra blocks on which to hang some features for products in the list
                        // Features providing UI elements targeting this block will display directly below the product name
                        if ($this->getChild('price.cart.after')) {
                            $_priceCartAfterChildren = $this->getChild('price.cart.after')->getSortedChildren();
                            foreach ($_priceCartAfterChildren as $_priceCartAfterChildName) {
                                $_priceCartAfterChild = $this->getChild('price.cart.after')->getChild($_priceCartAfterChildName);
                                $_priceCartAfterChild->setProduct($_product);
                                echo $_priceCartAfterChild->toHtml();
                            }
                        }
                        ?>
                    </div>
                </li>
                <?php /*if ($i%$_columnCount==0 || $i==$_collectionSize): ?>
                <?php endif*/ ?>
            <?php endforeach ?>
        </ul>
        <script type="text/javascript">decorateGeneric($$('ul.products-grid'), ['odd','even','first','last'])</script>
    </div>
    <?php
    // Provides a block where additional page components may be attached, primarily good for in-page JavaScript
    if ($this->getChild('after')) {
        $_afterChildren = $this->getChild('after')->getSortedChildren();
        foreach ($_afterChildren as $_afterChildName) {
            $_afterChild = $this->getChild('after')->getChild($_afterChildName);
            //set product collection on after blocks
            $_afterChild->setProductCollection($_productCollection);
            echo $_afterChild->toHtml();
        }
    }
}
?>
	
<?php
/**
 * Magento
 *
 * NOTICE OF LICENSE
 *
 * This source file is subject to the Academic Free License (AFL 3.0)
 * that is bundled with this package in the file LICENSE_AFL.txt.
 * It is also available through the world-wide-web at this URL:
 * http://opensource.org/licenses/afl-3.0.php
 * If you did not receive a copy of the license and are unable to
 * obtain it through the world-wide-web, please send an email
 * to license@magento.com so we can send you a copy immediately.
 *
 * DISCLAIMER
 *
 * Do not edit or add to this file if you wish to upgrade Magento to newer
 * versions in the future. If you wish to customize Magento for your
 * needs please refer to http://www.magento.com for more information.
 *
 * @category    design
 * @package     rwd_default
 * @copyright   Copyright (c) 2006-2015 X.commerce, Inc. (http://www.magento.com)
 * @license     http://opensource.org/licenses/afl-3.0.php  Academic Free License (AFL 3.0)
 */
?>
<?php
/**
 * Template for filter items block
 *
 * @see Mage_Catalog_Block_Layer_Filter
 */
?>

<ol>
     <?php $count = 1; ?>
<?php foreach ($this->getItems() as $_item): ?>
    <li>
        <?php if ($_item->getCount() > 0): ?>
            <?php /*<a href="<?php echo $this->urlEscape($_item->getUrl()) ?>">*/ ?>
                <?php echo $_item->getLabel() ?>
                <?php if ($this->shouldDisplayProductCount()): ?>
                <span class="count">(<?php echo $_item->getCount() ?>)</span>
                <?php endif; ?>
                <?php echo $this->getCategoryProductSearchResultHtml($_item, $count); ?>
            <?php /*</a>*/ ?>
        <?php else: ?>
            <span>
                <?php echo $_item->getLabel(); ?>
                <?php if ($this->shouldDisplayProductCount()): ?>
                    <span class="count">(<?php echo $_item->getCount() ?>)</span>
                <?php endif; ?>
            </span>
        <?php endif; ?>
    </li>
<?php endforeach ?>
</ol>
	
<?php
/**
 * Magento
 *
 * NOTICE OF LICENSE
 *
 * This source file is subject to the Academic Free License (AFL 3.0)
 * that is bundled with this package in the file LICENSE_AFL.txt.
 * It is also available through the world-wide-web at this URL:
 * http://opensource.org/licenses/afl-3.0.php
 * If you did not receive a copy of the license and are unable to
 * obtain it through the world-wide-web, please send an email
 * to license@magento.com so we can send you a copy immediately.
 *
 * DISCLAIMER
 *
 * Do not edit or add to this file if you wish to upgrade Magento to newer
 * versions in the future. If you wish to customize Magento for your
 * needs please refer to http://www.magento.com for more information.
 *
 * @category    design
 * @package     rwd_default
 * @copyright   Copyright (c) 2006-2015 X.commerce, Inc. (http://www.magento.com)
 * @license     http://opensource.org/licenses/afl-3.0.php  Academic Free License (AFL 3.0)
 */
?>
<?php
/**
 * Category layered navigation state
 *
 * @see Mage_Catalog_Block_Layer_State
 */
?>
<?php
$_filters = $this->getActiveFilters();
$_renderers = $this->getParentBlock()->getChild('state_renderers')->getSortedChildren();
?>
<?php if(!empty($_filters)): ?>
<div class="currently">
    <ol>
    <?php foreach ($_filters as $_filter): ?>
        <?php
        $_rendered = false;
        foreach ($_renderers as $_rendererName):
            $_renderer = $this->getParentBlock()->getChild('state_renderers')->getChild($_rendererName);
            if (method_exists($_renderer, 'shouldRender') && $_renderer->shouldRender($_filter)):
                $_renderer->setFilter($_filter);
                echo $_renderer->toHtml();
                $_rendered = true;
                break;
            endif;
        endforeach;

        if (!$_rendered):
        ?>
        <li>
            <?php
                $clearLinkUrl = $_filter->getClearLinkUrl();
                if ($clearLinkUrl):
            ?>
                <a  class="btn-previous" href="<?php echo $_filter->getRemoveUrl() ?>" title="<?php echo Mage::helper('core')->quoteEscape($this->__('Previous')) ?>"><?php echo $this->__('Previous') ?></a>
                <a  class="btn-remove" title="<?php echo $this->escapeHtml($_filter->getFilter()->getClearLinkText()) ?>" href="<?php echo $clearLinkUrl ?>"><?php echo $this->escapeHtml($_filter->getFilter()->getClearLinkText()) ?></a>
            <?php else: ?>
                <a  class="btn-remove" href="<?php echo $_filter->getRemoveUrl() ?>" title="<?php echo Mage::helper('core')->quoteEscape($this->__('Remove This Item')) ?>"><?php echo $this->__('Remove This Item') ?></a>
            <?php endif; ?>
            <span class="label"><?php echo $this->__($_filter->getName()) ?>:</span> <span class="value"><?php echo $this->stripTags($_filter->getLabel()) ?></span>
        </li>
        <?php endif; ?>
    <?php endforeach; ?>
    </ol>
</div>
<?php endif; ?>
	
<?php
/**
 * Magento
 *
 * NOTICE OF LICENSE
 *
 * This source file is subject to the Academic Free License (AFL 3.0)
 * that is bundled with this package in the file LICENSE_AFL.txt.
 * It is also available through the world-wide-web at this URL:
 * http://opensource.org/licenses/afl-3.0.php
 * If you did not receive a copy of the license and are unable to
 * obtain it through the world-wide-web, please send an email
 * to license@magento.com so we can send you a copy immediately.
 *
 * DISCLAIMER
 *
 * Do not edit or add to this file if you wish to upgrade Magento to newer
 * versions in the future. If you wish to customize Magento for your
 * needs please refer to http://www.magento.com for more information.
 *
 * @category    design
 * @package     rwd_default
 * @copyright   Copyright (c) 2006-2015 X.commerce, Inc. (http://www.magento.com)
 * @license     http://opensource.org/licenses/afl-3.0.php  Academic Free License (AFL 3.0)
 */
?>
<?php
/**
 * Category layered navigation
 *
 * @see Mage_Catalog_Block_Layer_View
 */
?>
<?php if($this->canShowBlock()): ?>
<div class="block block-layered-nav<?php if (!$this->getLayer()->getState()->getFilters()): ?> block-layered-nav--no-filters<?php endif; ?>">
    <?php /*<div class="block-title">
        <strong><span><?php echo $this->__('Shop By') ?></span></strong>
    </div>*/ ?>
    <!--div class="block-content toggle-content"-->
        <?php echo $this->getSearchStateHtml() ?>
        <?php /*if ($this->getLayer()->getState()->getFilters()): ?>
            <div class="actions"><a href="<?php echo $this->getClearUrl() ?>"><?php echo $this->__('Clear All') ?></a></div>
        <?php endif;*/ ?>
        <?php if($this->canShowOptions()): ?>
            <!--p class="block-subtitle block-subtitle--filter"><?php //echo $this->__('Filter') ?></p>
            <dl id="narrow-by-list"-->
                <?php $_filters = $this->getFilters() ?>
                <?php foreach ($_filters as $_filter): ?>
                <?php if($_filter->getItemsCount()): ?>
                    <dd><?php echo $this->getSearchFilterHtml($_filter); ?></dd>
                <?php endif; ?>
                <?php endforeach; ?>
            <!--/dl-->
            <script type="text/javascript">decorateDataList('narrow-by-list')</script>
        <?php endif; ?>
    <!--/div-->
</div>
<?php endif; ?>