implement validations of pagination URLs

java/org/chromium/distiller/PageParameterDetector.java

-// Copyright 2016 The Chromium Authors. All rights reserved.
+// Copyright 2015 The Chromium Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 package org.chromium.distiller;
 
 import com.google.gwt.regexp.shared.MatchResult;
 import com.google.gwt.regexp.shared.RegExp;
 
 import java.util.ArrayList;
 import java.util.Arrays;
@@ skipping 10 matching lines @@
  *   by webmaster.  Each partial page has outlinks pointing to the adjacent partial pages.  The
  *   anchor text of those outlinks is numeric.  Meanwhile, there may be a page which contains the
  *   whole content, called "single page".
  *
  * Definitions:
  * A single page document is a document that contains the whole content.
  * A paging document is one of the partial pages.
  * "digital" means the text contains only digits.
  * A page pattern is a paging URL whose page parameter value is replaced with a place holder
  * (PAGE_PARAM_PLACEHOLDER).
- * Example: if the original url is "http: *www.foo.com/a/b-3.html", the page pattern is
- * "http: *www.foo.com/a/b-[*!].html".
+ * Example: if the original url is "http://www.foo.com/a/b-3.html", the page pattern is
+ * "http://www.foo.com/a/b-[*!].html".
  *
  * This class extracts the page parameter from a document's outlinks.
  * The basic idea:
  *   #1. Collect groups of adjacent plain text numbers and outlinks with digital anchor text.
  *   #2. For each group, determine the relationship between digital anchor texts and digital parts
  *       (either a query value or a path component) in URL.  If one part of a URL is always a linear
  *        map from its digital anchor text, we guess the part is the page parameter of the URL.
  *
- * As an example, consider a document http: *a/b?c=1&p=10, which contains the following digital
+ * As an example, consider a document http://a/b?c=1&p=10, which contains the following digital
  * outlinks:
- *   <a href=http: *a/b?c=1&p=20>3</a>
- *   <a href=http: *a/b?c=1&p=30>4</a>
- *   <a href=http: *a/b?c=1&p=40>5</a>
- *   <a href=http: *a/b?c=1&p=all>single page</a>
+ *   <a href=http://a/b?c=1&p=20>3</a>
+ *   <a href=http://a/b?c=1&p=30>4</a>
+ *   <a href=http://a/b?c=1&p=40>5</a>
+ *   <a href=http://a/b?c=1&p=all>single page</a>
  * This class finds that the "p" parameter is always equal to "anchor text" * 10 - 10, and so
- * guesses it is the page parameter.  The associated page pattern is http: *a/b?c=1&p=[*!].
+ * guesses it is the page parameter.  The associated page pattern is http://a/b?c=1&p=[*!].
  * Then, this class extracts the single page based on page parameter info.  The single page url is
- * http: *a/b?c=1&p=all.
+ * http://a/b?c=1&p=all.
  */
 public class PageParameterDetector {
-    private static final String PAGE_PARAM_PLACEHOLDER = "[*!]";
+    private static final int MIN_LINKS_TO_JUSTIFY_LINEAR_MAP = 2;
+
+    static final String PAGE_PARAM_PLACEHOLDER = "[*!]";
+    static final int PAGE_PARAM_PLACEHOLDER_LEN = PAGE_PARAM_PLACEHOLDER.length();
+    static final int PAGE_NUM_ADJACENT_MASK = 1 << 0;
+    static final int PAGE_NUM_CONSECUTIVE_MASK = 1 << 1;
+
+    /**
+     * The interface that page pattern handlers must implement to detect page parameter from
+     * potential pagination URLs.
+     */
+    interface PagePattern {
+       /**
+        * Returns the string of the URL page pattern.
+        */
+        String toString();
+
+       /**
+        * Returns the page number extracted from the URL during creation of object that implements
+        * this interface.
+        */
+        int getPageNumber();
+        
+        /**
+         * Validates this page pattern according to the current document URL through a pipeline of
+         * rules.
+         *
+         * Returns true if page pattern is valid.
+         *
+         * @param docUrl the current document URL
+         */
+        boolean isValidFor(ParsedUrl docUrl);
+
+        /**
+         * Returns true if a URL matches this page pattern based on a pipeline of rules.
+         *
+         * @param url the URL to evalutate
+         */
+        boolean isPagingUrl(String url);
+    }
 
     /**
      * Stores information about the link (anchor) after the page parameter is detected:
      * - the page number (as represented by the original plain text) for the link
      * - the original page parameter numeric component in the URL (this component would be replaced
      *   by PAGE_PARAM_PLACEHOLDER in the URL pattern)
      * - the position of this link in the list of ascending numbers.
      */
     static class LinkInfo {
         private int mPageNum;
         private int mPageParamValue;
         private int mPosInAscendingList;
 
         LinkInfo(int pageNum, int pageParamValue, int posInAscendingList) {
             mPageNum = pageNum;
             mPageParamValue = pageParamValue;
             mPosInAscendingList = posInAscendingList;
         }
-    }  // LinkInfo
+    }
 
     /**
      * Stores a map of URL pattern to its associated list of LinkInfo's.
      */
     private static class PageCandidatesMap {
-        private final Map<String, List<LinkInfo>> map = new HashMap<String, List<LinkInfo>>();
+        private static class Info {
+            private final PagePattern mPattern;
+            private final List<LinkInfo> mLinks;
+
+            Info(PagePattern pattern, LinkInfo link) {
+                mPattern = pattern;
+                mLinks = new ArrayList<LinkInfo>();
+                mLinks.add(link);
+            }
+        }
+
+        private final Map<String, Info> map = new HashMap<String, Info>();
 
         /**
          * Adds urlPattern with its LinkInfo into the map.  If the urlPattern already exists, adds
          * the link to the list of LinkInfo's.  Otherwise, creates a new map entry.
          */
-        private void add(String urlPattern, LinkInfo link) {
-            if (map.containsKey(urlPattern)) {
-                map.get(urlPattern).add(link);
+        private void add(PagePattern pattern, LinkInfo link) {
+            final String patternStr = pattern.toString();
+            if (map.containsKey(patternStr)) {
+                map.get(patternStr).mLinks.add(link);
             } else {
-                List<LinkInfo> links = new ArrayList<LinkInfo>();
-                links.add(link);
-                map.put(urlPattern, links);
+                map.put(patternStr, new Info(pattern, link));
             }
         }
-
-    }  // PageCandidatesMap
+    }
 
     // All the known bad page param names.
     private static Set<String> sBadPageParamNames = null;
 
     /**
      * Extracts page parameter candidates from the query part of given URL and adds the associated
      * links into pageCandidates which is keyed by page pattern.
      *
      * A page parameter candidate is one where:
      * - the name of a query name-value component is not one of sBadPageParamNames, and
      * - the value of the query component is a plain number (>= 0).
      * E.g. a URL query with 3 plain number query values will generate 3 URL page patterns with 3
      * LinkInfo's, and hence 3 page parameter candidates.
      *
      * @param url ParsedUrl of the URL to process
      * @param pageNum the page number as represented in original plain text
      * @param posInAscendingNumbers position of this page number in the list of ascending numbers
      * @param pageCandidates the map of URL pattern to its associated list of LinkInfo's
      */
     private static void extractPageParamCandidatesFromQuery(ParsedUrl url, int pageNum,
             int posInAscendingNumbers, PageCandidatesMap pageCandidates) {
         String[][] queryParams = url.getQueryParams();
         if (queryParams.length == 0) return;  // No query.
 
         for (String[] nameValue : queryParams) {
-            final String queryName = nameValue[0];
-            final String queryValue = nameValue[1];
-            if (!queryName.isEmpty() && !queryValue.isEmpty() &&
-                    StringUtil.isStringAllDigits(queryValue) && !isPageParamNameBad(queryName)) {
-                int value = StringUtil.toNumber(queryValue);
-                if (value >= 0) {
-                    pageCandidates.add(
-                            url.replaceQueryValue(queryName, queryValue, PAGE_PARAM_PLACEHOLDER),
-                            new LinkInfo(pageNum, value, posInAscendingNumbers));
-                }
+            PagePattern pattern = QueryParamPagePattern.create(url, nameValue[0], nameValue[1]);
+            if (pattern != null) {
+                pageCandidates.add(pattern,
+                        new LinkInfo(pageNum, pattern.getPageNumber(), posInAscendingNumbers));
             }
         }
-    }  // extractPageParamCandidatesFromQuery
+    }
 
     private static RegExp sDigitsRegExp = null;  // Match at least 1 digit.
 
     /**
      * Extracts page parameter candidates from the path part of given URL (without query components)
      * and adds the associated links into pageCandidates which is keyed by page pattern.
      *
      * A page parameter candidate is one where a path component contains consecutive digits which
      * can be converted to a plain number (>= 0).
      * E.g. a URL path with 3 path components that contain plain numbers will generate 3 URL page
@@ skipping 15 matching lines @@
         final String urlStr = url.toString();
         final int pathStart = url.getOrigin().length();
         if (sDigitsRegExp == null) sDigitsRegExp = RegExp.compile("(\\d+)", "gi");
         sDigitsRegExp.setLastIndex(pathStart);
         while (true) {
             MatchResult match = sDigitsRegExp.exec(urlStr);
             if (match == null) break;
 
             final int matchEnd = sDigitsRegExp.getLastIndex();
             final int matchStart = matchEnd - match.getGroup(1).length();
-
-            if (isLastNumericPathComponentBad(urlStr, pathStart, matchStart, matchEnd)) continue;
-
-            int value = StringUtil.toNumber(urlStr.substring(matchStart, matchEnd));
-            if (value >= 0) {
-                pageCandidates.add(urlStr.substring(0, matchStart) + PAGE_PARAM_PLACEHOLDER +
-                        urlStr.substring(matchEnd),
-                        new LinkInfo(pageNum, value, posInAscendingNumbers));
+            PagePattern pattern = PathComponentPagePattern.create(url, pathStart, matchStart,
+                    matchEnd);
+            if (pattern != null) {
+                pageCandidates.add(pattern,
+                        new LinkInfo(pageNum, pattern.getPageNumber(), posInAscendingNumbers));
             }
         }  // while there're matches
-    }  // extractPageParamCandidatesFromPath
+    }
+
+    /**
+     * Evaluates if the given list of LinkInfo's is a list of paging URLs:
+     * - page numbers in list of LinkInfo's must be adjacent
+     * - page numbers in list of ascending numbers must either
+     *   - be consecutive and form a page number sequence, or
+     *   - must construct a linear map with a linear formula: page_parameter = a * page_number + b
+     * - if there's only 1 LinkInfo, the first ascending number must be page 1, first page URL must
+     *   match page pattern, and the only outlink must be 2nd or 3rd page.
+     *
+     * Returns a populated PageParamInfo if evaluated true.  Otherwise, returns null.
+     *
+     * @param allLinkInfo the list of LinkInfo's to evaluate
+     * @param pagePattern the URL pattern to use
+     * @param ascendingNumbers list of PageInfo's with ascending mPageNum's
+     * @param firstPageUrl the URL of the PageInfo with mPageNum=1
+     */
+    private static PageParamInfo getPageParamInfo(PagePattern pagePattern,

[cjhopman, 2015/04/16 21:58:32]

I feel like we have to many SomethingInfo types here and it's really unclear to
me what they actually are from the type names and I find myself having to go
look at the comments on those classes. It would be nice if I didn't have to do
that, but it's not something that needs to be fixed/changed right now.

[cjhopman, 2015/04/16 21:58:32]

Would it make sense for this function to be in the PageParamInfo class? I'm not
really sure.

[kuan, 2015/04/20 23:11:13]

i'm bad at names, and ran out of them :(

[kuan, 2015/04/20 23:11:13]

Done.  to avoid cross-access between PageParameterDetector.LinkInfo and
PageParamInfo, i extracted the former into its own class PageLinkInfo.

+            List<LinkInfo> allLinkInfo, List<PageParamInfo.PageInfo> ascendingNumbers,
+            String firstPageUrl) {
+        if (allLinkInfo.size() >= MIN_LINKS_TO_JUSTIFY_LINEAR_MAP) {
+            int result = arePageNumsAdjacentAndConsecutive(allLinkInfo, ascendingNumbers);
+            if ((result & PAGE_NUM_ADJACENT_MASK) == 0) return null;
+
+            PageParamInfo.LinearFormula linearFormula = getPageParamLinearFormula(allLinkInfo);
+
+            // PageParamInfo.Type.PAGE_NUMBER: ascending numbers must be consecutive and of a page
+            // number sequence.
+            if ((result & PAGE_NUM_CONSECUTIVE_MASK) != PAGE_NUM_CONSECUTIVE_MASK) return null;
+            if (!isPageNumberSequence(ascendingNumbers)) return null;
+            PageParamInfo pageParamInfo = new PageParamInfo();

[cjhopman, 2015/04/16 21:58:32]

Could we move some of the logic of creating the pageParamInfo here into a
PageParamInfo constructor? Same for the construction of one in the next block.

[kuan, 2015/04/20 23:11:13]

Done.

+            pageParamInfo.mType = PageParamInfo.Type.PAGE_NUMBER;
+            pageParamInfo.mFormula = linearFormula;
+            for (LinkInfo link : allLinkInfo) {
+                pageParamInfo.mAllPageInfo.add(new PageParamInfo.PageInfo(link.mPageNum,
+                        ascendingNumbers.get(link.mPosInAscendingList).mUrl));
+            }
+            return pageParamInfo;
+        }
+
+        // Most of news article have no more than 3 pages and the first page probably doesn't have
+        // any page parameter.  If the first page url matches the the page pattern, we treat it as
+        // the first page of this pattern.
+        if (allLinkInfo.size() == 1 && !firstPageUrl.isEmpty()) {
+            final LinkInfo onlyLink = allLinkInfo.get(0);
+            boolean secondPageIsOutlink = onlyLink.mPageNum == 2 &&
+                    onlyLink.mPosInAscendingList == 1;
+            boolean thirdPageIsOutlink = onlyLink.mPageNum == 3 &&
+                    onlyLink.mPosInAscendingList == 2 &&
+                    // onlyLink's pos is 2 (evaluated right before), so ascendingNumbers has >= 3
+                    // elements; check if previous element is previous page.
+                    ascendingNumbers.get(1).mPageNum == 2;
+            // 1 LinkInfo means ascendingNumbers has >= 1 element.
+            if (ascendingNumbers.get(0).mPageNum == 1 &&
+                    (secondPageIsOutlink || thirdPageIsOutlink) &&
+                    pagePattern.isPagingUrl(firstPageUrl)) {
+                // Has valid PageParamInfo, create and populate it.
+                PageParamInfo pageParamInfo = new PageParamInfo();
+                pageParamInfo.mType = PageParamInfo.Type.PAGE_NUMBER;
+                int coefficient;
+                int delta = onlyLink.mPageParamValue - onlyLink.mPageNum;
+                if (delta == 0 || delta == 1) {
+                    coefficient = 1;
+                } else {
+                    coefficient = onlyLink.mPageParamValue;
+                    delta = 0;
+                }
+                pageParamInfo.mFormula = new PageParamInfo.LinearFormula(coefficient, delta);
+                pageParamInfo.mAllPageInfo.add(new PageParamInfo.PageInfo(1, firstPageUrl));
+                pageParamInfo.mAllPageInfo.add(new PageParamInfo.PageInfo(onlyLink.mPageNum,
+                        ascendingNumbers.get(onlyLink.mPosInAscendingList).mUrl));
+                return pageParamInfo;
+            }
+        }
+
+        return null;
+    }
 
     /**
      * Returns true if given name is backlisted as a known bad page param name.
      */
-    private static boolean isPageParamNameBad(String name) {
+    static boolean isPageParamNameBad(String name) {
         initBadPageParamNames();
         return sBadPageParamNames.contains(name.toLowerCase());
-    }  // isPageParamNameBad
-
-    private static RegExp sExtRegExp = null;  // Match trailing .(s)htm(l).
-    private static RegExp sLastPathComponentRegExp = null;  // Match last path component.
-
-    /**
-     * Returns true if:
-     * - the digitStart to digitEnd of urlStr is the last path component, and
-     * - the entire path component is numeric, and
-     * - the previous path component is a bad page param name.
-     * E.g. "www.foo.com/tag/2" will return true because of the above reasons and "tag" is a bad
-     * page param.
-     */
-    static boolean isLastNumericPathComponentBad(String urlStr, int pathStart,
-            int digitStart, int digitEnd) {
-        if (urlStr.charAt(digitStart - 1) == '/' && // Digit is at start of path component.
-                pathStart < digitStart - 1) { // Not the first path component.
-            String postMatch = urlStr.substring(digitEnd).toLowerCase();
-            // Checks that this is the last path component, and trailing characters, if available,
-            // are (s)htm(l) extensions.
-            if (sExtRegExp == null) sExtRegExp = RegExp.compile("(.s?html?)?$", "i");
-            if (sExtRegExp.test(postMatch)) {
-                // Entire component is numeric, get previous path component.
-               if (sLastPathComponentRegExp == null) {
-                   sLastPathComponentRegExp = RegExp.compile("([^/]*)\\/$", "i");
-                }
-                MatchResult prevPathComponent = sLastPathComponentRegExp.exec(
-                        urlStr.substring(pathStart + 1, digitStart));
-                if (prevPathComponent != null && prevPathComponent.getGroupCount() > 1 &&
-                        isPageParamNameBad(prevPathComponent.getGroup(1))) {
-                    return true;
-                }
-            }  // last numeric path component
-        }
-
-        return false;
-    }  // isLastNumericPathComponentBad
+    }
+
+    /**
+     * Detects if page numbers in list of LinkInfo's are adjacent, and if page numbers in list of
+     * PageParamInfo.PageInfo's are consecutive.
+     *
+     * For adjacency, the page numbers in list of LinkInfo's must either be adjacent, or separated
+     * by at most 1 plain text number which must represent the current page number in one of the
+     * PageParamInfo.PageInfo's.
+     * For consecutiveness, there must be at least one pair of consecutive number values in the list
+     * of LinkInfo's, or between a LinkInfo and a plain text number.  Otherwise, these outlinks are
+     * likely to be page size selection links (e.g. in the document "See 1-10, 11-20...").
+     *
+     * Returns a int value that is a combination of bits:
+     * - bit for PAGE_PARAM_ADJACENT_MASK is set if allLinkInfo are adjacent
+     * - bit for PAGE_PARAM_CONSECUTIVE_MASK is set if ascendingNumbers are consecutive.
+     *
+     * @param allLinkInfo the list of LinkInfo's to evaluate
+     * @param ascendingNumbers list of PageInfo's with ascending mPageNum's
+     */
+    static int arePageNumsAdjacentAndConsecutive(List<LinkInfo> allLinkInfo,
+            List<PageParamInfo.PageInfo> ascendingNumbers) {
+        int result = 0;
+
+        // Check if elements in allLinkInfo are adjacent or there's only 1 gap i.e. the gap is
+        // current page number respresented in plain text.
+        int firstPos = -1;
+        int lastPos = -1;
+        int gapPos = -1;
+        Set<Integer> pageParamSet = new HashSet<Integer>();  // To check that page number is unique.
+        for (LinkInfo linkInfo : allLinkInfo) {
+            final int currPos = linkInfo.mPosInAscendingList;
+            if (lastPos == -1) {
+                firstPos = currPos;
+            } else if (currPos != lastPos + 1) {
+                // If position is not strictly ascending, or the gap size is > 1 (e.g. "[3] [4] 5 6
+                // [7]"), or there's more than 1 gap (e.g. "[3] 4 [5] 6 [7]"), allLinkInfo is not
+                // adjacent.
+                if (currPos <= lastPos || currPos != lastPos + 2 || gapPos != -1) return result;
+                gapPos = currPos - 1;
+            }
+            // Make sure page param value, i.e. page number represented in plain text, is unique.
+            if (!pageParamSet.add(linkInfo.mPageParamValue)) return result;
+            lastPos = currPos;
+        }  // for all LinkInfo's
+
+        result |= PAGE_NUM_ADJACENT_MASK;
+
+        // Now, determine if page numbers in ascendingNumbers are consecutive.
+
+        // First, handle the gap.
+        if (gapPos != -1) {
+           if (gapPos <= 0 || gapPos >= ascendingNumbers.size() - 1) return result;
+           // The "gap" should represent current page number in plain text.
+           // Check if its adjacent page numbers are consecutive.
+           // e.g. "[1] [5] 6 [7] [12]" is accepted; "[4] 8 [16]" is rejected.
+           // This can eliminate links affecting the number of items on a page.
+           final int currPageNum = ascendingNumbers.get(gapPos).mPageNum;
+           if (ascendingNumbers.get(gapPos - 1).mPageNum == currPageNum - 1 &&
+                   ascendingNumbers.get(gapPos + 1).mPageNum == currPageNum + 1) {
+               return result | PAGE_NUM_CONSECUTIVE_MASK;
+           }
+           return result;
+        }
+
+        // There is no gap.  Check if at least one of the following cases is satisfied:
+        // Case #1: "[1] [2] ..." or "1 [2] ... ".
+        if ((firstPos == 0 || firstPos == 1) && ascendingNumbers.get(0).mPageNum == 1 &&
+                ascendingNumbers.get(1).mPageNum == 2) {
+            return result | PAGE_NUM_CONSECUTIVE_MASK;
+        }
+        // Case #2: "[1] 2 [3] ..." where [1] doesn't belong to current pattern.
+        if (firstPos == 2 && ascendingNumbers.get(2).mPageNum == 3 &&
+                ascendingNumbers.get(1).mUrl.isEmpty() && !ascendingNumbers.get(0).mUrl.isEmpty()) {
+            return result | PAGE_NUM_CONSECUTIVE_MASK;
+        }
+        // Case #3: "... [n-1] [n]" or "... [n - 1] n".
+        final int numbersSize = ascendingNumbers.size();
+        if ((lastPos == numbersSize - 1 || lastPos == numbersSize - 2) &&
+                ascendingNumbers.get(numbersSize - 2).mPageNum + 1 ==
+                        ascendingNumbers.get(numbersSize - 1).mPageNum) {
+            return result | PAGE_NUM_CONSECUTIVE_MASK;
+        }
+        // Case #4: "... [i-1] [i] [i+1] ...".
+        for (int i = firstPos + 1; i < lastPos; i++) {
+            if (ascendingNumbers.get(i - 1).mPageNum + 2 == ascendingNumbers.get(i + 1).mPageNum) {
+                return result | PAGE_NUM_CONSECUTIVE_MASK;
+            }
+        }
+
+        // Otherwise, there's no pair of consecutive values.
+        return result;
+    }
+
+    /**
+     *
+     * Determines if the list of LinkInfo's form a linear formula:
+     *   pageParamValue = coefficient * pageNum + delta (delta == -coefficient or delta == 0).
+     *
+     * The coefficient and delta are calculated from the page parameter values and page numbers of 2
+     * LinkInfo's, and then validated against the remaining LinkInfo's.
+     * The order of page numbers doesn't matter.
+     *
+     * Returns PageParamInfo.LinearFormula, containing the coefficient and delta, if the page
+     * parameter forumla could be determined.  Otherwise, returns null.
+     *
+     * @param allLinkInfo the list of LinkInfo's to evaluate
+     */
+    // TODO(kuan): As this gets rolled out, reassesss the necessity of non-1 coefficient support.
+    private static PageParamInfo.LinearFormula getPageParamLinearFormula(
+            List<LinkInfo> allLinkInfo) {
+        if (allLinkInfo.size() < MIN_LINKS_TO_JUSTIFY_LINEAR_MAP) return null;
+
+        final LinkInfo firstLink = allLinkInfo.get(0);
+        final LinkInfo secondLink = allLinkInfo.get(1);
+
+        if (allLinkInfo.size() == 2 && Math.max(firstLink.mPageNum, secondLink.mPageNum) > 4) {
+            return null;
+        }
+
+        int deltaX = secondLink.mPageNum - firstLink.mPageNum;
+        if (deltaX == 0) return null;
+
+        int deltaY = secondLink.mPageParamValue - firstLink.mPageParamValue;
+        int coefficient = deltaY / deltaX;
+        if (coefficient == 0) return null;
+
+        int delta = firstLink.mPageParamValue - coefficient * firstLink.mPageNum;
+        if (delta != 0 && delta != -coefficient) return null;
+
+        // Check if the remaining elements are on the same linear map.
+        for (int i = 2; i < allLinkInfo.size(); i++) {
+            final LinkInfo link = allLinkInfo.get(i);
+            if (link.mPageParamValue != coefficient * link.mPageNum + delta) return null;
+        }
+
+        return new PageParamInfo.LinearFormula(coefficient, delta);
+    }
+
+    /**
+     * Returns true if page numbers in list of PageParamInfo.PageInfo's form a sequence, based on
+     * a pipeline of rules:
+     * - first PageInfo must have a URL unless it is the first page
+     * - there's only one plain number without URL in list
+     * - if only two pages, they must be siblings - 2nd page number must follow 1st
+     * - page numbers must be adjacent and consecutive; otherwise, 2 non-consecutive numbers must be
+     *   head/tail or have URLs.
+     *
+     * @param ascendingNumbers list of PageInfo's with ascending mPageNum's
+     */
+    private static boolean isPageNumberSequence(List<PageParamInfo.PageInfo> ascendingNumbers) {
+        if (ascendingNumbers.size() <= 1) return false;
+
+        // The first one must have a URL unless it is the first page.
+        final PageParamInfo.PageInfo firstPage = ascendingNumbers.get(0);
+        if (firstPage.mPageNum != 1 && firstPage.mUrl.isEmpty()) return false;
+
+        // There's only one plain number without URL in ascending numbers group.
+        boolean hasPlainNum = false;
+        for (PageParamInfo.PageInfo page : ascendingNumbers) {
+            if (page.mUrl.isEmpty()) {
+                if (hasPlainNum) return false;
+                hasPlainNum = true;
+            }
+        }
+
+        // If there are only two pages, they must be siblings.
+        if (ascendingNumbers.size() == 2) {
+            return firstPage.mPageNum + 1 == ascendingNumbers.get(1).mPageNum;
+        }
+
+        // Check if page numbers in ascendingNumbers are adjacent and consecutive.
+        for (int i = 1; i < ascendingNumbers.size(); i++) {
+            // If two adjacent numbers are not consecutive, we accept them only when:
+            // 1) one of them is head/tail, like [1],[n-i][n-i+1]..[n] or [1],[2], [3]...[i], [n].
+            // 2) both of them have URLs.
+            final PageParamInfo.PageInfo currPage = ascendingNumbers.get(i);
+            final PageParamInfo.PageInfo prevPage = ascendingNumbers.get(i - 1);
+            if (currPage.mPageNum - prevPage.mPageNum != 1) {
+                if (i != 1 && i != ascendingNumbers.size() - 1) return false;
+                if (currPage.mUrl.isEmpty() || prevPage.mUrl.isEmpty()) return false;
+            }
+        }
+
+        return true;
+    }
+
+    /**
+     * Returns true if given string can be converted to a number >= 0.
+     */
+    static boolean isPlainNumber(String str) {
+        return StringUtil.toNumber(str) >= 0;
+    }
 
     /**
      * If sBadPageParamNames is null, initialize it with all the known bad page param names, in
      * alphabetical order.
      */
     private static void initBadPageParamNames() {
         if (sBadPageParamNames != null) return;
 
         sBadPageParamNames = new HashSet<String>();
         sBadPageParamNames.add("baixar-gratis");
@@ skipping 18 matching lines @@
         sBadPageParamNames.add("search_keyword");
         sBadPageParamNames.add("search_query");
         sBadPageParamNames.add("sortby");
         sBadPageParamNames.add("subscriptions");
         sBadPageParamNames.add("tag");
         sBadPageParamNames.add("tags");
         sBadPageParamNames.add("video");
         sBadPageParamNames.add("videos");
         sBadPageParamNames.add("w");
         sBadPageParamNames.add("wiki");
-    }  // initBadPageParamNames
+    }
 
 }