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authorAdrian Thurston <thurston@colm.net>2019-09-08 21:11:17 -0600
committerAdrian Thurston <thurston@colm.net>2019-09-08 21:11:17 -0600
commitc860c61607117582abd8f23881eed87957197484 (patch)
tree4d4e65dddc710e15f008189a9308d95924350c3f /src/fsmmin.cc
parentf37c916aed2600951b8966a86020406b0b0542cf (diff)
downloadcolm-c860c61607117582abd8f23881eed87957197484.tar.gz
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-/*
- * Copyright 2006-2018 Adrian Thurston <thurston@colm.net>
- *
- * Permission is hereby granted, free of charge, to any person obtaining a copy
- * of this software and associated documentation files (the "Software"), to
- * deal in the Software without restriction, including without limitation the
- * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
- * sell copies of the Software, and to permit persons to whom the Software is
- * furnished to do so, subject to the following conditions:
- *
- * The above copyright notice and this permission notice shall be included in all
- * copies or substantial portions of the Software.
- *
- * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
- * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
- * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
- * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
- * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
- * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
- * SOFTWARE.
- */
-
-#include <stdbool.h>
-#include <assert.h>
-
-#include <mergesort.h>
-
-#include "fsmgraph.h"
-
-int FsmGraph::partitionRound( FsmState **statePtrs, MinPartition *parts, int numParts )
-{
- /* Need a mergesort object and a single partition compare. */
- MergeSort<FsmState*, PartitionCompare> mergeSort;
- PartitionCompare partCompare;
-
- /* For each partition. */
- for ( int p = 0; p < numParts; p++ ) {
- /* Fill the pointer array with the states in the partition. */
- StateList::Iter state = parts[p].list;
- for ( int s = 0; state.lte(); state++, s++ )
- statePtrs[s] = state;
-
- /* Sort the states using the partitioning compare. */
- int numStates = parts[p].list.length();
- mergeSort.sort( statePtrs, numStates );
-
- /* Assign the states into partitions based on the results of the sort. */
- int destPart = p, firstNewPart = numParts;
- for ( int s = 1; s < numStates; s++ ) {
- /* If this state differs from the last then move to the next partition. */
- if ( partCompare.compare( statePtrs[s-1], statePtrs[s] ) < 0 ) {
- /* The new partition is the next avail spot. */
- destPart = numParts;
- numParts += 1;
- }
-
- /* If the state is not staying in the first partition, then
- * transfer it to its destination partition. */
- if ( destPart != p ) {
- FsmState *state = parts[p].list.detach( statePtrs[s] );
- parts[destPart].list.append( state );
- }
- }
-
- /* Fix the partition pointer for all the states that got moved to a new
- * partition. This must be done after the states are transfered so the
- * result of the sort is not altered. */
- for ( int newPart = firstNewPart; newPart < numParts; newPart++ ) {
- StateList::Iter state = parts[newPart].list;
- for ( ; state.lte(); state++ )
- state->alg.partition = &parts[newPart];
- }
- }
-
- return numParts;
-}
-
-/**
- * \brief Minimize by partitioning version 1.
- *
- * Repeatedly tries to split partitions until all partitions are unsplittable.
- * Produces the most minimal FSM possible.
- */
-void FsmGraph::minimizePartition1()
-{
- /* Need one mergesort object and partition compares. */
- MergeSort<FsmState*, InitPartitionCompare> mergeSort;
- InitPartitionCompare initPartCompare;
-
- /* Nothing to do if there are no states. */
- if ( stateList.length() == 0 )
- return;
-
- /*
- * First thing is to partition the states by final state status and
- * transition functions. This gives us an initial partitioning to work
- * with.
- */
-
- /* Make a array of pointers to states. */
- int numStates = stateList.length();
- FsmState** statePtrs = new FsmState*[numStates];
-
- /* Fill up an array of pointers to the states for easy sorting. */
- StateList::Iter state = stateList;
- for ( int s = 0; state.lte(); state++, s++ )
- statePtrs[s] = state;
-
- /* Sort the states using the array of states. */
- mergeSort.sort( statePtrs, numStates );
-
- /* An array of lists of states is used to partition the states. */
- MinPartition *parts = new MinPartition[numStates];
-
- /* Assign the states into partitions. */
- int destPart = 0;
- for ( int s = 0; s < numStates; s++ ) {
- /* If this state differs from the last then move to the next partition. */
- if ( s > 0 && initPartCompare.compare( statePtrs[s-1], statePtrs[s] ) < 0 ) {
- /* Move to the next partition. */
- destPart += 1;
- }
-
- /* Put the state into its partition. */
- statePtrs[s]->alg.partition = &parts[destPart];
- parts[destPart].list.append( statePtrs[s] );
- }
-
- /* We just moved all the states from the main list into partitions without
- * taking them off the main list. So clean up the main list now. */
- stateList.abandon();
-
- /* Split partitions. */
- int numParts = destPart + 1;
- while ( true ) {
- /* Test all partitions for splitting. */
- int newNum = partitionRound( statePtrs, parts, numParts );
-
- /* When no partitions can be split, stop. */
- if ( newNum == numParts )
- break;
-
- numParts = newNum;
- }
-
- /* Fuse states in the same partition. The states will end up back on the
- * main list. */
- fusePartitions( parts, numParts );
-
- /* Cleanup. */
- delete[] statePtrs;
- delete[] parts;
-}
-
-/* Split partitions that need splittting, decide which partitions might need
- * to be split as a result, continue until there are no more that might need
- * to be split. */
-int FsmGraph::splitCandidates( FsmState **statePtrs, MinPartition *parts, int numParts )
-{
- /* Need a mergesort and a partition compare. */
- MergeSort<FsmState*, PartitionCompare> mergeSort;
- PartitionCompare partCompare;
-
- /* The lists of unsplitable (partList) and splitable partitions.
- * Only partitions in the splitable list are check for needing splitting. */
- PartitionList partList, splittable;
-
- /* Initially, all partitions are born from a split (the initial
- * partitioning) and can cause other partitions to be split. So any
- * partition with a state with a transition out to another partition is a
- * candidate for splitting. This will make every partition except possibly
- * partitions of final states split candidates. */
- for ( int p = 0; p < numParts; p++ ) {
- /* Assume not active. */
- parts[p].active = false;
-
- /* Look for a trans out of any state in the partition. */
- for ( StateList::Iter state = parts[p].list; state.lte(); state++ ) {
- /* If there is at least one transition out to another state then
- * the partition becomes splittable. */
- if ( state->outList.length() > 0 ) {
- parts[p].active = true;
- break;
- }
- }
-
- /* If it was found active then it goes on the splittable list. */
- if ( parts[p].active )
- splittable.append( &parts[p] );
- else
- partList.append( &parts[p] );
- }
-
- /* While there are partitions that are splittable, pull one off and try
- * to split it. If it splits, determine which partitions may now be split
- * as a result of the newly split partition. */
- while ( splittable.length() > 0 ) {
- MinPartition *partition = splittable.detachFirst();
-
- /* Fill the pointer array with the states in the partition. */
- StateList::Iter state = partition->list;
- for ( int s = 0; state.lte(); state++, s++ )
- statePtrs[s] = state;
-
- /* Sort the states using the partitioning compare. */
- int numStates = partition->list.length();
- mergeSort.sort( statePtrs, numStates );
-
- /* Assign the states into partitions based on the results of the sort. */
- MinPartition *destPart = partition;
- int firstNewPart = numParts;
- for ( int s = 1; s < numStates; s++ ) {
- /* If this state differs from the last then move to the next partition. */
- if ( partCompare.compare( statePtrs[s-1], statePtrs[s] ) < 0 ) {
- /* The new partition is the next avail spot. */
- destPart = &parts[numParts];
- numParts += 1;
- }
-
- /* If the state is not staying in the first partition, then
- * transfer it to its destination partition. */
- if ( destPart != partition ) {
- FsmState *state = partition->list.detach( statePtrs[s] );
- destPart->list.append( state );
- }
- }
-
- /* Fix the partition pointer for all the states that got moved to a new
- * partition. This must be done after the states are transfered so the
- * result of the sort is not altered. */
- int newPart;
- for ( newPart = firstNewPart; newPart < numParts; newPart++ ) {
- StateList::Iter state = parts[newPart].list;
- for ( ; state.lte(); state++ )
- state->alg.partition = &parts[newPart];
- }
-
- /* Put the partition we just split and any new partitions that came out
- * of the split onto the inactive list. */
- partition->active = false;
- partList.append( partition );
- for ( newPart = firstNewPart; newPart < numParts; newPart++ ) {
- parts[newPart].active = false;
- partList.append( &parts[newPart] );
- }
-
- if ( destPart == partition )
- continue;
-
- /* Now determine which partitions are splittable as a result of
- * splitting partition by walking the in lists of the states in
- * partitions that got split. Partition is the faked first item in the
- * loop. */
- MinPartition *causalPart = partition;
- newPart = firstNewPart - 1;
- while ( newPart < numParts ) {
- /* Loop all states in the causal partition. */
- StateList::Iter state = causalPart->list;
- for ( ; state.lte(); state++ ) {
- /* Walk all transition into the state and put the partition
- * that the from state is in onto the splittable list. */
- for ( TransInList::Iter trans = state->inList; trans.lte(); trans++ ) {
- MinPartition *fromPart = trans->fromState->alg.partition;
- if ( ! fromPart->active ) {
- fromPart->active = true;
- partList.detach( fromPart );
- splittable.append( fromPart );
- }
- }
- }
-
- newPart += 1;
- causalPart = &parts[newPart];
- }
- }
- return numParts;
-}
-
-
-/**
- * \brief Minimize by partitioning version 2 (best alg).
- *
- * Repeatedly tries to split partitions that may splittable until there are no
- * more partitions that might possibly need splitting. Runs faster than
- * version 1. Produces the most minimal fsm possible.
- */
-void FsmGraph::minimizePartition2()
-{
- /* Need a mergesort and an initial partition compare. */
- MergeSort<FsmState*, InitPartitionCompare> mergeSort;
- InitPartitionCompare initPartCompare;
-
- /* Nothing to do if there are no states. */
- if ( stateList.length() == 0 )
- return;
-
- /*
- * First thing is to partition the states by final state status and
- * transition functions. This gives us an initial partitioning to work
- * with.
- */
-
- /* Make a array of pointers to states. */
- int numStates = stateList.length();
- FsmState** statePtrs = new FsmState*[numStates];
-
- /* Fill up an array of pointers to the states for easy sorting. */
- StateList::Iter state = stateList;
- for ( int s = 0; state.lte(); state++, s++ )
- statePtrs[s] = state;
-
- /* Sort the states using the array of states. */
- mergeSort.sort( statePtrs, numStates );
-
- /* An array of lists of states is used to partition the states. */
- MinPartition *parts = new MinPartition[numStates];
-
- /* Assign the states into partitions. */
- int destPart = 0;
- for ( int s = 0; s < numStates; s++ ) {
- /* If this state differs from the last then move to the next partition. */
- if ( s > 0 && initPartCompare.compare( statePtrs[s-1], statePtrs[s] ) < 0 ) {
- /* Move to the next partition. */
- destPart += 1;
- }
-
- /* Put the state into its partition. */
- statePtrs[s]->alg.partition = &parts[destPart];
- parts[destPart].list.append( statePtrs[s] );
- }
-
- /* We just moved all the states from the main list into partitions without
- * taking them off the main list. So clean up the main list now. */
- stateList.abandon();
-
- /* Split partitions. */
- int numParts = splitCandidates( statePtrs, parts, destPart+1 );
-
- /* Fuse states in the same partition. The states will end up back on the
- * main list. */
- fusePartitions( parts, numParts );
-
- /* Cleanup. */
- delete[] statePtrs;
- delete[] parts;
-}
-
-void FsmGraph::initialMarkRound( MarkIndex &markIndex )
-{
- /* P and q for walking pairs. */
- FsmState *p = stateList.head, *q;
-
- /* Need an initial partition compare. */
- InitPartitionCompare initPartCompare;
-
- /* Walk all unordered pairs of (p, q) where p != q.
- * The second depth of the walk stops before reaching p. This
- * gives us all unordered pairs of states (p, q) where p != q. */
- while ( p != 0 ) {
- q = stateList.head;
- while ( q != p ) {
- /* If the states differ on final state status, out transitions or
- * any transition data then they should be separated on the initial
- * round. */
- if ( initPartCompare.compare( p, q ) != 0 )
- markIndex.markPair( p->alg.stateNum, q->alg.stateNum );
-
- q = q->next;
- }
- p = p->next;
- }
-}
-
-bool FsmGraph::markRound( MarkIndex &markIndex )
-{
- /* P an q for walking pairs. Take note if any pair gets marked. */
- FsmState *p = stateList.head, *q;
- bool pairWasMarked = false;
-
- /* Need a mark comparison. */
- MarkCompare markCompare;
-
- /* Walk all unordered pairs of (p, q) where p != q.
- * The second depth of the walk stops before reaching p. This
- * gives us all unordered pairs of states (p, q) where p != q. */
- while ( p != 0 ) {
- q = stateList.head;
- while ( q != p ) {
- /* Should we mark the pair? */
- if ( !markIndex.isPairMarked( p->alg.stateNum, q->alg.stateNum ) ) {
- if ( markCompare.shouldMark( markIndex, p, q ) ) {
- markIndex.markPair( p->alg.stateNum, q->alg.stateNum );
- pairWasMarked = true;
- }
- }
- q = q->next;
- }
- p = p->next;
- }
-
- return pairWasMarked;
-}
-
-
-/**
- * \brief Minimize by pair marking.
- *
- * Decides if each pair of states is distinct or not. Uses O(n^2) memory and
- * should only be used on small graphs. Produces the most minmimal FSM
- * possible.
- */
-void FsmGraph::minimizeStable()
-{
- /* Set the state numbers. */
- setStateNumbers( 0 );
-
- /* This keeps track of which pairs have been marked. */
- MarkIndex markIndex( stateList.length() );
-
- /* Mark pairs where final stateness, out trans, or trans data differ. */
- initialMarkRound( markIndex );
-
- /* While the last round of marking succeeded in marking a state
- * continue to do another round. */
- int modified = markRound( markIndex );
- while (modified)
- modified = markRound( markIndex );
-
- /* Merge pairs that are unmarked. */
- fuseUnmarkedPairs( markIndex );
-}
-
-bool FsmGraph::minimizeRound()
-{
- /* Nothing to do if there are no states. */
- if ( stateList.length() == 0 )
- return false;
-
- /* Need a mergesort on approx compare and an approx compare. */
- MergeSort<FsmState*, ApproxCompare> mergeSort;
- ApproxCompare approxCompare;
-
- /* Fill up an array of pointers to the states. */
- FsmState **statePtrs = new FsmState*[stateList.length()];
- StateList::Iter state = stateList;
- for ( int s = 0; state.lte(); state++, s++ )
- statePtrs[s] = state;
-
- bool modified = false;
-
- /* Sort The list. */
- mergeSort.sort( statePtrs, stateList.length() );
-
- /* Walk the list looking for duplicates next to each other,
- * merge in any duplicates. */
- FsmState **pLast = statePtrs;
- FsmState **pState = statePtrs + 1;
- for ( int i = 1; i < stateList.length(); i++, pState++ ) {
- if ( approxCompare.compare( *pLast, *pState ) == 0 ) {
- /* Last and pState are the same, so fuse together. Move forward
- * with pState but not with pLast. If any more are identical, we
- * must */
- fuseEquivStates( *pLast, *pState );
- modified = true;
- }
- else {
- /* Last and this are different, do not set to merge them. Move
- * pLast to the current (it may be way behind from merging many
- * states) and pState forward one to consider the next pair. */
- pLast = pState;
- }
- }
- delete[] statePtrs;
- return modified;
-}
-
-/**
- * \brief Minmimize by an approximation.
- *
- * Repeatedly tries to find states with transitions out to the same set of
- * states on the same set of keys until no more identical states can be found.
- * Does not produce the most minimial FSM possible.
- */
-void FsmGraph::minimizeApproximate()
-{
- /* While the last minimization round succeeded in compacting states,
- * continue to try to compact states. */
- while ( true ) {
- bool modified = minimizeRound();
- if ( ! modified )
- break;
- }
-}
-
-
-/* Remove states that have no path to them from the start state. Recursively
- * traverses the graph marking states that have paths into them. Then removes
- * all states that did not get marked. */
-void FsmGraph::removeUnreachableStates()
-{
- /* Misfit accounting should be off and there should be no states on the
- * misfit list. */
- assert( !misfitAccounting && misfitList.length() == 0 );
-
- /* Mark all the states that can be reached
- * through the existing set of entry points. */
- markReachableFromHere( startState );
- for ( EntryMap::Iter en = entryPoints; en.lte(); en++ )
- markReachableFromHere( en->value );
-
- /* Delete all states that are not marked
- * and unmark the ones that are marked. */
- FsmState *state = stateList.head;
- while ( state ) {
- FsmState *next = state->next;
-
- if ( state->stateBits & SB_ISMARKED )
- state->stateBits &= ~ SB_ISMARKED;
- else {
- detachState( state );
- stateList.detach( state );
- delete state;
- }
-
- state = next;
- }
-}
-
-bool FsmGraph::outListCovers( FsmState *state )
-{
- /* Must be at least one range to cover. */
- if ( state->outList.length() == 0 )
- return false;
-
- /* The first must start at the lower bound. */
- TransList::Iter trans = state->outList.first();
- if ( keyOps->minKey < trans->lowKey )
- return false;
-
- /* Loop starts at second el. */
- trans.increment();
-
- /* Loop checks lower against prev upper. */
- for ( ; trans.lte(); trans++ ) {
- /* Lower end of the trans must be one greater than the
- * previous' high end. */
- Key lowKey = trans->lowKey;
- lowKey.decrement();
- if ( trans->prev->highKey < lowKey )
- return false;
- }
-
- /* Require that the last range extends to the upper bound. */
- trans = state->outList.last();
- if ( trans->highKey < keyOps->maxKey )
- return false;
-
- return true;
-}
-
-/* Remove states that that do not lead to a final states. Works recursivly traversing
- * the graph in reverse (starting from all final states) and marking seen states. Then
- * removes states that did not get marked. */
-void FsmGraph::removeDeadEndStates()
-{
- /* Misfit accounting should be off and there should be no states on the
- * misfit list. */
- assert( !misfitAccounting && misfitList.length() == 0 );
-
- /* Mark all states that have paths to the final states. */
- FsmState **st = finStateSet.data;
- int nst = finStateSet.length();
- for ( int i = 0; i < nst; i++, st++ )
- markReachableFromHereReverse( *st );
-
- /* Start state gets honorary marking. If the machine accepts nothing we
- * still want the start state to hang around. This must be done after the
- * recursive call on all the final states so that it does not cause the
- * start state in transitions to be skipped when the start state is
- * visited by the traversal. */
- startState->stateBits |= SB_ISMARKED;
-
- /* Delete all states that are not marked
- * and unmark the ones that are marked. */
- FsmState *state = stateList.head;
- while ( state != 0 ) {
- FsmState *next = state->next;
-
- if ( state->stateBits & SB_ISMARKED )
- state->stateBits &= ~ SB_ISMARKED;
- else {
- detachState( state );
- stateList.detach( state );
- delete state;
- }
-
- state = next;
- }
-}
-
-/* Remove states on the misfit list. To work properly misfit accounting should
- * be on when this is called. The detaching of a state will likely cause
- * another misfit to be collected and it can then be removed. */
-void FsmGraph::removeMisfits()
-{
- while ( misfitList.length() > 0 ) {
- /* Get the first state. */
- FsmState *state = misfitList.head;
-
- /* Detach and delete. */
- detachState( state );
-
- /* The state was previously on the misfit list and detaching can only
- * remove in transitions so the state must still be on the misfit
- * list. */
- misfitList.detach( state );
- delete state;
- }
-}
-
-/* Fuse src into dest because they have been deemed equivalent states.
- * Involves moving transitions into src to go into dest and invoking
- * callbacks. Src is deleted detached from the graph and deleted. */
-void FsmGraph::fuseEquivStates( FsmState *dest, FsmState *src )
-{
- /* This would get ugly. */
- assert( dest != src );
-
- /* Cur is a duplicate. We can merge it with trail. */
- inTransMove( dest, src );
-
- detachState( src );
- stateList.detach( src );
- delete src;
-}
-
-void FsmGraph::fuseUnmarkedPairs( MarkIndex &markIndex )
-{
- FsmState *p = stateList.head, *nextP, *q;
-
- /* Definition: The primary state of an equivalence class is the first state
- * encounterd that belongs to the equivalence class. All equivalence
- * classes have primary state including equivalence classes with one state
- * in it. */
-
- /* For each unmarked pair merge p into q and delete p. q is always the
- * primary state of it's equivalence class. We wouldn't have landed on it
- * here if it were not, because it would have been deleted.
- *
- * Proof that q is the primaray state of it's equivalence class: Assume q
- * is not the primary state of it's equivalence class, then it would be
- * merged into some state that came before it and thus p would be
- * equivalent to that state. But q is the first state that p is equivalent
- * to so we have a contradiction. */
-
- /* Walk all unordered pairs of (p, q) where p != q.
- * The second depth of the walk stops before reaching p. This
- * gives us all unordered pairs of states (p, q) where p != q. */
- while ( p != 0 ) {
- nextP = p->next;
-
- q = stateList.head;
- while ( q != p ) {
- /* If one of p or q is a final state then mark. */
- if ( ! markIndex.isPairMarked( p->alg.stateNum, q->alg.stateNum ) ) {
- fuseEquivStates( q, p );
- break;
- }
- q = q->next;
- }
- p = nextP;
- }
-}
-
-void FsmGraph::fusePartitions( MinPartition *parts, int numParts )
-{
- /* For each partition, fuse state 2, 3, ... into state 1. */
- for ( int p = 0; p < numParts; p++ ) {
- /* Assume that there will always be at least one state. */
- FsmState *first = parts[p].list.head, *toFuse = first->next;
-
- /* Put the first state back onto the main state list. Don't bother
- * removing it from the partition list first. */
- stateList.append( first );
-
- /* Fuse the rest of the state into the first. */
- while ( toFuse != 0 ) {
- /* Save the next. We will trash it before it is needed. */
- FsmState *next = toFuse->next;
-
- /* Put the state to be fused in to the first back onto the main
- * list before it is fuse. the graph. The state needs to be on
- * the main list for the detach from the graph to work. Don't
- * bother removing the state from the partition list first. We
- * need not maintain it. */
- stateList.append( toFuse );
-
- /* Now fuse to the first. */
- fuseEquivStates( first, toFuse );
-
- /* Go to the next that we saved before trashing the next pointer. */
- toFuse = next;
- }
-
- /* We transfered the states from the partition list into the main list without
- * removing the states from the partition list first. Clean it up. */
- parts[p].list.abandon();
- }
-}
-
-
-/* Merge neighboring transitions go to the same state and have the same
- * transitions data. */
-void FsmGraph::compressTransitions()
-{
- for ( StateList::Iter st = stateList; st.lte(); st++ ) {
- if ( st->outList.length() > 1 ) {
- for ( TransList::Iter trans = st->outList, next = trans.next(); next.lte(); ) {
- Key nextLow = next->lowKey;
- nextLow.decrement();
- if ( trans->highKey == nextLow && trans->toState == next->toState &&
- CmpActionTable::compare( trans->actionTable, next->actionTable ) == 0 )
- {
- trans->highKey = next->highKey;
- st->outList.detach( next );
- detachTrans( next->fromState, next->toState, next );
- delete next;
- next = trans.next();
- }
- else {
- trans.increment();
- next.increment();
- }
- }
- }
- }
-}