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## org.apache.fop.layoutmgr
Class BreakingAlgorithm

    java.lang.Object
      org.apache.fop.layoutmgr.BreakingAlgorithm

Direct Known Subclasses:
  BalancingColumnBreakingAlgorithm

    public abstract class BreakingAlgorithm

extends java.lang.Object

The set of nodes is sorted into lines indexed into activeLines. The nodes in each line are linked together in a single linked list by the `BreakingAlgorithm.KnuthNode.next` field. The activeLines array contains a link to the head of the linked list in index 'line*2' and a link to the tail at index 'line*2+1'.

The set of active nodes can be traversed by

     for (int line = startLine; line < endLine; line++) {
         for (KnuthNode node = getNode(line); node != null; node = node.next) {
             // Do something with 'node'
         }
     }

Nested Class Summary
`protected class` | `BreakingAlgorithm.BestRecords` Class that stores, for each fitness class, the best active node that could start a line of the corresponding fitness ending at the current element.
`class` | `BreakingAlgorithm.KnuthNode` Class recording all the informations of a feasible breaking point.

Field Summary
`protected BreakingAlgorithm.KnuthNode[]` | `activeLines` The set of active nodes in ascending line order.
`protected int` | `activeNodeCount` The number of active nodes.
`protected int` | `alignment` Alignment of the paragraph/page.
`protected int` | `alignmentLast` Alignment of the paragraph's last line.
`static int` | `ALL_BREAKS` All feasible breaks are ok.
`protected BreakingAlgorithm.BestRecords` | `best` Best records.
`protected boolean` | `considerTooShort` If set to true, doesn't ignore break possibilities which are definitely too short.
`protected int` | `endLine` The highest + 1 available line in the set of active nodes.
`protected int` | `incompatibleFitnessDemerit` Demerit for consecutive lines belonging to incompatible fitness classes .
`protected boolean` | `indentFirstPart` Used to handle the text-indent property (indent the first line of a paragraph).
`protected static int` | `INFINITE_RATIO` Maximum adjustment ration
`protected int` | `lineWidth` The width of a line (or height of a column in page-breaking mode).
`protected static org.apache.commons.logging.Log` | `log` the logger for the class
`protected int` | `maxFlaggedPenaltiesCount` Maximum number of consecutive lines ending with a flagged penalty.
`static int` | `NO_FLAGGED_PENALTIES` This forbids hyphenation.
`static int` | `ONLY_FORCED_BREAKS` wrap-option = "no-wrap".
`protected KnuthSequence` | `par` The paragraph of KnuthElements.
`protected int` | `repeatedFlaggedDemerit` Demerit for consecutive lines ending at flagged penalties.
`protected int` | `startLine` The lowest available line in the set of active nodes.
`protected int` | `totalShrink` The total shrink of all elements handled so far.
`protected int` | `totalStretch` The total stretch of all elements handled so far.
`protected int` | `totalWidth` The total width of all elements handled so far.

Constructor Summary
`BreakingAlgorithm(int align, int alignLast, boolean first, boolean partOverflowRecovery, int maxFlagCount)` Create a new instance.

Method Summary
`protected void` | `activateNode(BreakingAlgorithm.KnuthNode node, int difference, double r, double demerits, int fitnessClass, int availableShrink, int availableStretch)` Activate the given node.
`protected void` | `addNode(int line, BreakingAlgorithm.KnuthNode node)` Add a node at the end of the given line's existing active nodes.
`protected void` | `calculateBreakPoints(BreakingAlgorithm.KnuthNode node, KnuthSequence par, int total)` Determines the set of optimal breakpoints corresponding to the given active node.
`protected BreakingAlgorithm.KnuthNode` | `compareNodes(BreakingAlgorithm.KnuthNode node1, BreakingAlgorithm.KnuthNode node2)` Compare two KnuthNodes and return the node with the least demerit.
`protected double` | `computeAdjustmentRatio(BreakingAlgorithm.KnuthNode activeNode, int difference)` Return the adjustment ratio needed to make up for the difference.
`protected double` | `computeDemerits(BreakingAlgorithm.KnuthNode activeNode, KnuthElement element, int fitnessClass, double r)` Computes the demerits of the current breaking (that is, up to the given element), if the next-to-last chosen breakpoint is the given active node.
`protected int` | `computeDifference(BreakingAlgorithm.KnuthNode activeNode, KnuthElement element, int elementIndex)` Return the difference between the natural width of a line that would be made between the given active node and the given element, and the available width of the real line.
`protected void` | `considerLegalBreak(KnuthElement element, int elementIdx)` Determines if the given breakpoint is a feasible breakpoint.
`protected BreakingAlgorithm.KnuthNode` | `createNode(int position, int line, int fitness, int totalWidth, int totalStretch, int totalShrink)` Creates a new active node for a break from the best active node of the given fitness class to the element at the given position.
`protected BreakingAlgorithm.KnuthNode` | `createNode(int position, int line, int fitness, int totalWidth, int totalStretch, int totalShrink, double adjustRatio, int availableShrink, int availableStretch, int difference, double totalDemerits, BreakingAlgorithm.KnuthNode previous)` Creates a new active node for a feasible breakpoint at the given position.
`protected void` | `deactivateNode(BreakingAlgorithm.KnuthNode node, int line)` Deactivate the given node
`protected boolean` | `elementCanEndLine(KnuthElement element, int line, int difference)` Check if the given `KnuthElement` can end the line with the given number.
`protected abstract int` | `filterActiveNodes()` Filter active nodes.
`int` | `findBreakingPoints(KnuthSequence par, double threshold, boolean force, int allowedBreaks)`
`int` | `findBreakingPoints(KnuthSequence par, int startIndex, double threshold, boolean force, int allowedBreaks)` Finds an optimal set of breakpoints for the given paragraph.
`protected void` | `finish()` Hook for subclasses to trigger special behavior after ending the main loop in `findBreakingPoints(KnuthSequence,int,double,boolean,int)`
`protected void` | `forceNode(BreakingAlgorithm.KnuthNode node, int line, int elementIdx, int difference, double r, double demerits, int fitnessClass, int availableShrink, int availableStretch)` Force the given `BreakingAlgorithm.KnuthNode`, and register it.
`int` | `getAlignment()`
`int` | `getAlignmentLast()`
`protected KnuthElement` | `getElement(int idx)` Return the element at index idx in the paragraph.
`protected int` | `getIPDdifference()` obtain ipd difference
`protected BreakingAlgorithm.KnuthNode` | `getLastTooShort()` Return the last node that yielded a too short line.
`protected int` | `getLineWidth()`
`protected int` | `getLineWidth(int line)` Returns the line/part width of a given line/part.
`protected int` | `getMaxRecoveryAttempts()`
`protected BreakingAlgorithm.KnuthNode` | `getNode(int line)` Returns the first active node for the given line.
`protected void` | `handleBox(KnuthBox box)` Handle a `KnuthBox`.
`protected KnuthElement` | `handleElementAt(int position, boolean previousIsBox, int allowedBreaks)` Generic handler for a `KnuthElement` at the given `position`, taking into account whether the preceding element was a box, and which type(s) of breaks are allowed.
`protected void` | `handleGlueAt(KnuthGlue glue, int position, boolean previousIsBox, int allowedBreaks)` Handle a `KnuthGlue` at the given position, taking into account the additional parameters.
`protected int` | `handleIpdChange()` handle ipd change
`protected void` | `handlePenaltyAt(KnuthPenalty penalty, int position, int allowedBreaks)` Handle a `KnuthPenalty` at the given position, taking into account the type of breaks allowed.
`protected void` | `initialize()` Initializes the algorithm's variables.
`protected boolean` | `isPartOverflowRecoveryActivated()` Controls the behaviour of the algorithm in cases where the first element of a part overflows a line/page.
`protected BreakingAlgorithm.KnuthNode` | `recoverFromOverflow()` Recover from an overflow condition.
`protected BreakingAlgorithm.KnuthNode` | `recoverFromTooLong(BreakingAlgorithm.KnuthNode lastTooLong)` Recover from a `BreakingAlgorithm.KnuthNode` leading to a line that is too long.
`protected void` | `removeNode(int line, BreakingAlgorithm.KnuthNode node)` Remove the given active node registered for the given line.
`protected void` | `replaceLastDeactivated()` Replace the last too-long or too-short node by the last deactivated node, if applicable.
`protected int` | `restartFrom(BreakingAlgorithm.KnuthNode restartingNode, int currentIndex)` Restart from the given node at the given index.
`void` | `setConstantLineWidth(int lineWidth)`
`java.lang.String` | `toString(java.lang.String prepend)` Creates a string representation of the active nodes.
`abstract void` | `updateData1(int total, double demerits)` Empty method, hook for subclasses.
`abstract void` | `updateData2(BreakingAlgorithm.KnuthNode bestActiveNode, KnuthSequence sequence, int total)` Empty method, hook for subclasses.

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Field Detail

### log

    protected static final org.apache.commons.logging.Log log

  the logger for the class

### INFINITE_RATIO

    protected static final int INFINITE_RATIO

  Maximum adjustment ration

  See Also:
    Constant Field Values

### ALL_BREAKS

    public static final int ALL_BREAKS

  All feasible breaks are ok.

  See Also:
    Constant Field Values

### NO_FLAGGED_PENALTIES

    public static final int NO_FLAGGED_PENALTIES

  This forbids hyphenation.

  See Also:
    Constant Field Values

### ONLY_FORCED_BREAKS

    public static final int ONLY_FORCED_BREAKS

  wrap-option = "no-wrap".

  See Also:
    Constant Field Values

### repeatedFlaggedDemerit

    protected int repeatedFlaggedDemerit

  Demerit for consecutive lines ending at flagged penalties.

### incompatibleFitnessDemerit

    protected int incompatibleFitnessDemerit

  Demerit for consecutive lines belonging to incompatible fitness classes .

### maxFlaggedPenaltiesCount

    protected int maxFlaggedPenaltiesCount

  Maximum number of consecutive lines ending with a flagged penalty. Only a value >= 1 is a significant limit.

### par

    protected KnuthSequence par

  The paragraph of KnuthElements.

### lineWidth

    protected int lineWidth

  The width of a line (or height of a column in page-breaking mode). -1 indicates that the line widths are different for each line.

### considerTooShort

    protected boolean considerTooShort

  If set to true, doesn't ignore break possibilities which are definitely too short.

### alignment

    protected int alignment

  Alignment of the paragraph/page. One of EN_START, EN_JUSTIFY, etc.

### alignmentLast

    protected int alignmentLast

  Alignment of the paragraph's last line.

### indentFirstPart

    protected boolean indentFirstPart

  Used to handle the text-indent property (indent the first line of a paragraph).

### activeLines

    protected BreakingAlgorithm.KnuthNode[] activeLines

  The set of active nodes in ascending line order. For each line l, activeLines[2l] contains a link to l's first active node, and activeLines[2l+1] a link to l's last active node. The line number l corresponds to the number of the line ending at the node's breakpoint.

### activeNodeCount

    protected int activeNodeCount

  The number of active nodes.

### startLine

    protected int startLine

  The lowest available line in the set of active nodes.

### endLine

    protected int endLine

  The highest + 1 available line in the set of active nodes.

### totalWidth

    protected int totalWidth

  The total width of all elements handled so far.

### totalStretch

    protected int totalStretch

  The total stretch of all elements handled so far.

### totalShrink

    protected int totalShrink

  The total shrink of all elements handled so far.

### best

    protected BreakingAlgorithm.BestRecords best

  Best records.

Constructor Detail

### BreakingAlgorithm

    public BreakingAlgorithm(int align,
                             int alignLast,
                             boolean first,
                             boolean partOverflowRecovery,
                             int maxFlagCount)

  Create a new instance.

  Parameters:
    `align` - alignment of the paragraph/page. One of `Constants.EN_START`, `Constants.EN_JUSTIFY`, `Constants.EN_CENTER`, `Constants.EN_END`. For pages, `Constants.EN_BEFORE` and `Constants.EN_AFTER` are mapped to the corresponding inline properties, `Constants.EN_START` and `Constants.EN_END`.
    `alignLast` - alignment of the paragraph's last line
    `first` - for the text-indent property (`true` if the first line of a paragraph should be indented)
    `partOverflowRecovery` - `true` if too long elements should be moved to the next line/part
    `maxFlagCount` - maximum allowed number of consecutive lines ending at a flagged penalty item

Method Detail

### getMaxRecoveryAttempts

    protected int getMaxRecoveryAttempts()

  Returns:
    the number of times the algorithm should try to move overflowing content to the next line/page.

### isPartOverflowRecoveryActivated

    protected boolean isPartOverflowRecoveryActivated()

  Controls the behaviour of the algorithm in cases where the first element of a part overflows a line/page.

  Returns:
    true if the algorithm should try to send the element to the next line/page.

### updateData1

    public abstract void updateData1(int total,
                                     double demerits)

  Empty method, hook for subclasses. Called before determining the optimal breakpoints corresponding to a given active node.

  Parameters:
    `total` - number of lines for the active node
    `demerits` - total demerits of the paragraph for the active node

### updateData2

    public abstract void updateData2(BreakingAlgorithm.KnuthNode bestActiveNode,
                                     KnuthSequence sequence,
                                     int total)

  Empty method, hook for subclasses. Called when determining the optimal breakpoints for a given active node.

  Parameters:
    `bestActiveNode` - a node in the chain of best active nodes, corresponding to one of the optimal breakpoints
    `sequence` - the corresponding paragraph
    `total` - the number of lines into which the paragraph will be broken

### setConstantLineWidth

    public void setConstantLineWidth(int lineWidth)

  Parameters:
    `lineWidth` - the line width

### findBreakingPoints

    public int findBreakingPoints(KnuthSequence par,
                                  double threshold,
                                  boolean force,
                                  int allowedBreaks)

  Parameters:
    `par` - the paragraph to break
    `threshold` - upper bound of the adjustment ratio
    `force` - `true` if a set of breakpoints must be found, even if there are no feasible ones
    `allowedBreaks` - the type(s) of breaks allowed. One of `ONLY_FORCED_BREAKS`, `NO_FLAGGED_PENALTIES` or `ALL_BREAKS`.
  Returns:
    the number of effective breaks
  See Also:
    `findBreakingPoints(KnuthSequence, int, double, boolean, int)`

### findBreakingPoints

    public int findBreakingPoints(KnuthSequence par,
                                  int startIndex,
                                  double threshold,
                                  boolean force,
                                  int allowedBreaks)

  Finds an optimal set of breakpoints for the given paragraph.

  Parameters:
    `par` - the paragraph to break
    `startIndex` - index of the Knuth element at which the breaking must start
    `threshold` - upper bound of the adjustment ratio
    `force` - `true` if a set of breakpoints must be found, even if there are no feasible ones
    `allowedBreaks` - the type(s) of breaks allowed. One of `ONLY_FORCED_BREAKS`, `NO_FLAGGED_PENALTIES` or `ALL_BREAKS`.
  Returns:
    the number of effective breaks

### getIPDdifference

    protected int getIPDdifference()

  obtain ipd difference

  Returns:
    an integer

### handleIpdChange

    protected int handleIpdChange()

  handle ipd change

  Returns:
    an integer

### recoverFromTooLong

    protected BreakingAlgorithm.KnuthNode recoverFromTooLong(BreakingAlgorithm.KnuthNode lastTooLong)

  Recover from a `BreakingAlgorithm.KnuthNode` leading to a line that is too long. The default implementation creates a new node corresponding to a break point after the previous node that led to a line that was too short.

  Parameters:
    `lastTooLong` - the node that leads to a "too long" line
  Returns:
    node corresponding to a breakpoint after the previous "too short" line

### initialize

    protected void initialize()

  Initializes the algorithm's variables.

### createNode

    protected BreakingAlgorithm.KnuthNode createNode(int position,
                                                     int line,
                                                     int fitness,
                                                     int totalWidth,
                                                     int totalStretch,
                                                     int totalShrink,
                                                     double adjustRatio,
                                                     int availableShrink,
                                                     int availableStretch,
                                                     int difference,
                                                     double totalDemerits,
                                                     BreakingAlgorithm.KnuthNode previous)

  Creates a new active node for a feasible breakpoint at the given position. Only called in forced mode.

  Parameters:
    `position` - index of the element in the Knuth sequence
    `line` - number of the line ending at the breakpoint
    `fitness` - fitness class of the line ending at the breakpoint. One of 0, 1, 2, 3.
    `totalWidth` - accumulated width of the KnuthElements up to after the breakpoint
    `totalStretch` - accumulated stretchability of the KnuthElements up to after the breakpoint
    `totalShrink` - accumulated shrinkability of the KnuthElements up to after the breakpoint
    `adjustRatio` - adjustment ratio if the line ends at this breakpoint
    `availableShrink` - available stretch of the line ending at this breakpoint
    `availableStretch` - available shrink of the line ending at this breakpoint
    `difference` - difference between target and actual line width
    `totalDemerits` - minimum total demerits up to the breakpoint
    `previous` - active node for the preceding breakpoint
  Returns:
    a new node

### createNode

    protected BreakingAlgorithm.KnuthNode createNode(int position,
                                                     int line,
                                                     int fitness,
                                                     int totalWidth,
                                                     int totalStretch,
                                                     int totalShrink)

  Creates a new active node for a break from the best active node of the given fitness class to the element at the given position.

  Parameters:
    `position` - index of the element in the Knuth sequence
    `line` - number of the line ending at the breakpoint
    `fitness` - fitness class of the line ending at the breakpoint. One of 0, 1, 2, 3.
    `totalWidth` - accumulated width of the KnuthElements up to after the breakpoint
    `totalStretch` - accumulated stretchability of the KnuthElements up to after the breakpoint
    `totalShrink` - accumulated shrinkability of the KnuthElements up to after the breakpoint
  Returns:
    a new node
  See Also:
    `createNode(int, int, int, int, int, int, double, int, int, int, double, org.apache.fop.layoutmgr.BreakingAlgorithm.KnuthNode)`, `BreakingAlgorithm.BestRecords`

### getLastTooShort

    protected final BreakingAlgorithm.KnuthNode getLastTooShort()

  Return the last node that yielded a too short line.

  Returns:
    the node corresponding to the last too short line

### handleElementAt

    protected final KnuthElement handleElementAt(int position,
                                                 boolean previousIsBox,
                                                 int allowedBreaks)

  Generic handler for a `KnuthElement` at the given `position`, taking into account whether the preceding element was a box, and which type(s) of breaks are allowed. Non-overridable. This method simply serves to route the call to one of the more specific handlers (`handleBox(KnuthBox)`, `handleGlueAt(KnuthGlue,int,boolean,int)` or `handlePenaltyAt(KnuthPenalty,int,int)`. The specialized handlers can be overridden by subclasses to add to or modify the default behavior for the different types of elements.

  Parameters:
    `position` - the position index of the element in the paragraph
    `previousIsBox` - `true` if the previous element is a box
    `allowedBreaks` - the type(s) of breaks allowed; should be one of `ALL_BREAKS`, `NO_FLAGGED_PENALTIES` or `ONLY_FORCED_BREAKS`
  Returns:
    the handled element

### handleBox

    protected void handleBox(KnuthBox box)

  Handle a `KnuthBox`.
  Note: default implementation just adds the box's width to the total content width. Subclasses that do not keep track of this themselves, but override this method, should remember to call `super.handleBox(box)` to avoid unwanted side-effects.

  Parameters:
    `box` - the `KnuthBox` to handle

### handleGlueAt

    protected void handleGlueAt(KnuthGlue glue,
                                int position,
                                boolean previousIsBox,
                                int allowedBreaks)

  Handle a `KnuthGlue` at the given position, taking into account the additional parameters.

  Parameters:
    `glue` - the `KnuthGlue` to handle
    `position` - the position of the glue in the list
    `previousIsBox` - `true` if the preceding element is a box
    `allowedBreaks` - the type of breaks that are allowed

### handlePenaltyAt

    protected void handlePenaltyAt(KnuthPenalty penalty,
                                   int position,
                                   int allowedBreaks)

  Handle a `KnuthPenalty` at the given position, taking into account the type of breaks allowed.

  Parameters:
    `penalty` - the `KnuthPenalty` to handle
    `position` - the position of the penalty in the list
    `allowedBreaks` - the type of breaks that are allowed

### replaceLastDeactivated

    protected final void replaceLastDeactivated()

  Replace the last too-long or too-short node by the last deactivated node, if applicable.

### recoverFromOverflow

    protected BreakingAlgorithm.KnuthNode recoverFromOverflow()

  Recover from an overflow condition.

  Returns:
    the new `lastForced` node

### restartFrom

    protected int restartFrom(BreakingAlgorithm.KnuthNode restartingNode,
                              int currentIndex)

  Restart from the given node at the given index.

  Parameters:
    `restartingNode` - the `BreakingAlgorithm.KnuthNode` to restart from
    `currentIndex` - the current position index
  Returns:
    the index of the restart point

### considerLegalBreak

    protected void considerLegalBreak(KnuthElement element,
                                      int elementIdx)

  Determines if the given breakpoint is a feasible breakpoint. That is, if a decent line may be built between one of the currently active nodes and this breakpoint.

  Parameters:
    `element` - the paragraph's element to consider
    `elementIdx` - the element's index inside the paragraph

### elementCanEndLine

    protected boolean elementCanEndLine(KnuthElement element,
                                        int line,
                                        int difference)

  Check if the given `KnuthElement` can end the line with the given number.

  Parameters:
    `element` - the element
    `line` - the line number
    `difference` - an integer
  Returns:
    `true` if the element can end the line

### forceNode

    protected void forceNode(BreakingAlgorithm.KnuthNode node,
                             int line,
                             int elementIdx,
                             int difference,
                             double r,
                             double demerits,
                             int fitnessClass,
                             int availableShrink,
                             int availableStretch)

  Force the given `BreakingAlgorithm.KnuthNode`, and register it.

  Parameters:
    `node` - the node
    `line` - the line number
    `elementIdx` - the position index of the element
    `difference` - the difference between content-length and avaialable width
    `r` - the adjustment ratio
    `demerits` - demerits produced by the node
    `fitnessClass` - the fitness class
    `availableShrink` - the available amount of shrink
    `availableStretch` - tha available amount of stretch

### activateNode

    protected void activateNode(BreakingAlgorithm.KnuthNode node,
                                int difference,
                                double r,
                                double demerits,
                                int fitnessClass,
                                int availableShrink,
                                int availableStretch)

  Activate the given node. Will result in the given `BreakingAlgorithm.KnuthNode` being registered as a feasible breakpoint, if the `demerits` are better than that of the best node registered for the given `fitnessClass`.

  Parameters:
    `node` - the node
    `difference` - the difference between content-length and available width
    `r` - the adjustment ratio
    `demerits` - demerits produced by the node
    `fitnessClass` - the fitness class
    `availableShrink` - the available amount of shrink
    `availableStretch` - the available amount of stretch

### deactivateNode

    protected void deactivateNode(BreakingAlgorithm.KnuthNode node,
                                  int line)

  Deactivate the given node

  Parameters:
    `node` - the node
    `line` - the line number

### computeDifference

    protected int computeDifference(BreakingAlgorithm.KnuthNode activeNode,
                                    KnuthElement element,
                                    int elementIndex)

  Return the difference between the natural width of a line that would be made between the given active node and the given element, and the available width of the real line.

  Parameters:
    `activeNode` - node for the previous breakpoint
    `element` - currently considered breakpoint
    `elementIndex` - index of the element that is considered as a breakpoint
  Returns:
    The difference in width. Positive numbers mean extra space in the line, negative number that the line overflows.

### computeAdjustmentRatio

    protected double computeAdjustmentRatio(BreakingAlgorithm.KnuthNode activeNode,
                                            int difference)

  Return the adjustment ratio needed to make up for the difference. A ratio of
  - 0 means that the break has the exact right width
  - >= -1 && < 0 means that the break is wider than the line, but within the minimim values of the glues.
  - >0 && < 1 means that the break is smaller than the line width, but within the maximum values of the glues.
  - > 1 means that the break is too small to make up for the glues.

  Parameters:
    `activeNode` - the currently active node
    `difference` - the difference between content-length and available width
  Returns:
    The adjustment ratio.

### computeDemerits

    protected double computeDemerits(BreakingAlgorithm.KnuthNode activeNode,
                                     KnuthElement element,
                                     int fitnessClass,
                                     double r)

  Computes the demerits of the current breaking (that is, up to the given element), if the next-to-last chosen breakpoint is the given active node. This adds to the total demerits of the given active node, the demerits of a line starting at this node and ending at the given element.

  Parameters:
    `activeNode` - considered preceding line break
    `element` - considered current line break
    `fitnessClass` - fitness of the current line
    `r` - adjustment ratio for the current line
  Returns:
    the demerit of the current line

### finish

    protected void finish()

  Hook for subclasses to trigger special behavior after ending the main loop in `findBreakingPoints(KnuthSequence,int,double,boolean,int)`

### getElement

    protected KnuthElement getElement(int idx)

  Return the element at index idx in the paragraph.

  Parameters:
    `idx` - index of the element.
  Returns:
    the element at index idx in the paragraph.

### compareNodes

    protected BreakingAlgorithm.KnuthNode compareNodes(BreakingAlgorithm.KnuthNode node1,
                                                       BreakingAlgorithm.KnuthNode node2)

  Compare two KnuthNodes and return the node with the least demerit.

  Parameters:
    `node1` - The first knuth node.
    `node2` - The other knuth node.
  Returns:
    the node with the least demerit.

### addNode

    protected void addNode(int line,
                           BreakingAlgorithm.KnuthNode node)

  Add a node at the end of the given line's existing active nodes. If this is the first node in the line, adjust endLine accordingly.

  Parameters:
    `line` - number of the line ending at the node's corresponding breakpoint
    `node` - the active node to add

### removeNode

    protected void removeNode(int line,
                              BreakingAlgorithm.KnuthNode node)

  Remove the given active node registered for the given line. If there are no more active nodes for this line, adjust the startLine accordingly.

  Parameters:
    `line` - number of the line ending at the node's corresponding breakpoint
    `node` - the node to deactivate

### getNode

    protected BreakingAlgorithm.KnuthNode getNode(int line)

  Returns the first active node for the given line.

  Parameters:
    `line` - the line/part number
  Returns:
    the requested active node

### getLineWidth

    protected int getLineWidth(int line)

  Returns the line/part width of a given line/part.

  Parameters:
    `line` - the line/part number
  Returns:
    the width/length in millipoints

### getLineWidth

    protected int getLineWidth()

  Returns:
    the constant line/part width or -1 if there is no such value

### toString

    public java.lang.String toString(java.lang.String prepend)

  Creates a string representation of the active nodes. Used for debugging.

  Parameters:
    `prepend` - a string to prepend on each entry
  Returns:
    the requested string

### filterActiveNodes

    protected abstract int filterActiveNodes()

  Filter active nodes.

  Returns:
    an integer

### calculateBreakPoints

    protected void calculateBreakPoints(BreakingAlgorithm.KnuthNode node,
                                        KnuthSequence par,
                                        int total)

  Determines the set of optimal breakpoints corresponding to the given active node.

  Parameters:
    `node` - the active node
    `par` - the corresponding paragraph
    `total` - the number of lines into which the paragraph will be broken

### getAlignment

    public int getAlignment()

  Returns:
    the alignment for normal lines/parts

### getAlignmentLast

    public int getAlignmentLast()

  Returns:
    the alignment for the last line/part

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