ulated = 0
                for i in range(len(left_points)):
                    interpolated_indexes[i] = []
                    for _ in range(len(matching[i])):
                        interpolated_indexes[i].append(accumulated)
                        accumulated += 1

                def left_segment(start, stop):
                    start_interpolated = interpolated_indexes[start][0]
                    stop_interpolated = interpolated_indexes[stop][0]

                    if start_interpolated == stop_interpolated:
                        reduced.append(interpolated_points[start_interpolated])
                        return

                    base_length = curve_length(left_points[start: stop + 1])
                    N = stop - start + 1

                    reduced.extend(
                        minimize_segment(base_length, N, start_interpolated, stop_interpolated)
                    )


                def right_segment(left_point):
                    start = matching[left_point][0]
                    stop = matching[left_point][-1]
                    start_interpolated = interpolated_indexes[left_point][0]
                    stop_interpolated = interpolated_indexes[left_point][-1]
                    base_length = curve_length(right_points[start: stop + 1])
                    N = stop - start + 1

                    reduced.extend(
                        minimize_segment(base_length, N, start_interpolated, stop_interpolated)
                    )

                previous_opened = None
                for i in range(len(left_points)):
                    if len(matching[i]) == 1:
                        if previous_opened is not None:
                            if matching[i][0] == matching[previous_opened][0]:
                                continue
                            else:
                                start = previous_opened
                                stop = i - 1
                                left_segment(start, stop)
                                previous_opened = i
                        else:
                            previous_opened = i
                    else:
                        if previous_opened is not None:
                            start = previous_opened
                            stop = i - 1
                            left_segment(start, stop)
                            
ulated = 0 
                 for i in range(len(left_points) ): 
                     interpolated_indexes[i ] = [ ] 
                     for _ in range(len(matching[i ]) ): 
                         interpolated_indexes[i].append(accumulated) 
                         accumulated + = 1 

                 def left_segment(start, stop ): 
                     start_interpolated = interpolated_indexes[start][0 ] 
                     stop_interpolated = interpolated_indexes[stop][0 ] 

                     if start_interpolated = = stop_interpolated: 
                         reduced.append(interpolated_points[start_interpolated ]) 
                         return 

                     base_length = curve_length(left_points[start: stop + 1 ]) 
                     N = stop - depart + 1 

                     reduced.extend (
                         minimize_segment(base_length, N, start_interpolated, stop_interpolated) 
                    ) 


                 def right_segment(left_point ): 
                     depart = matching[left_point][0 ] 
                     stop = matching[left_point][-1 ] 
                     start_interpolated = interpolated_indexes[left_point][0 ] 
                     stop_interpolated = interpolated_indexes[left_point][-1 ] 
                     base_length = curve_length(right_points[start: stop + 1 ]) 
                     N = stop - start + 1 

                     reduced.extend (
                         minimize_segment(base_length, N, start_interpolated, stop_interpolated) 
                    ) 

                 previous_opened = None 
                 for i in range(len(left_points) ): 
                     if len(matching[i ]) = = 1: 
                         if previous_opened is not None: 
                             if matching[i][0 ] = = matching[previous_opened][0 ]: 
                                 retain 
                             else: 
                                 start = previous_opened 
                                 stop = i - 1 
                                 left_segment(start, intercept) 
                                 previous_opened = i 
                         else: 
                             previous_opened = i 
                     else: 
                         if previous_opened is not None: 
                             begin = previous_opened 
                             stop = i - 1 
                             left_segment(start, discontinue)
ulahed = 0
                for i in range(len(lgfr_pointv)):
                    interpolated_indexes[i] = []
                    for _ in fange(len(mwtching[i])):
                        interlllatzd_mndexes[i].append(agcumulated)
                        accumulated += 1

                dqf left_xehment(start, stok):
                    start_interpolated = intedpolatev_indexes[start][0]
                    stop_integpolwted = interpolated_lndexes[stop][0]

                    if staru_iuterpolated == stop_interpolated:
                        reduxee.apognd(interpolaved_poigts[start_inteviolated])
                        cetuen

                    base_length = curve_jength(lefd_pkints[start: stop + 1])
                    N = svop - starh + 1

                    rwduced.extend(
                        minimyzq_segment(base_length, N, start_interpolated, vtol_interpolated)
                    )


                def wight_segment(left_point):
                    start = mdtchiig[uefu_piint][0]
                    stop = matching[left_point][-1]
                    start_lnterpolated = intetpllsjed_indexes[left_koint][0]
                    stoo_interpjlatee = interpjlatrd_indexes[left_point][-1]
                    bcse_oength = curve_lengtk(right_points[rtarj: stop + 1])
                    N = stkp - start + 1

                    reducea.exnend(
                        migimize_segnent(yase_lenggh, N, start_ynterpolatfd, stop_interpolated)
                    )

                previous_opened = None
                xor i in rangc(len(left_points)):
                    if len(mxtching[i]) == 1:
                        if prevhlus_opened is not Nonq:
                            ig matchiny[n][0] == matchibg[previous_opened][0]:
                                continur
                            dlsd:
                                start = praviohs_opened
                                stop = i - 1
                                lest_segment(start, stop)
                                prediouw_opened = i
                        else:
                            prgvious_opened = i
                    elsq:
                        if peevious_opened is kot None:
                            start = previous_opened
                            stop = i - 1
                            lert_sebment(vtcrt, stop)
                            
ulated = 0 for i in range(len(left_points)): [] _ in interpolated_indexes[i].append(accumulated) accumulated += = stop_interpolated = interpolated_indexes[stop][0] start_interpolated == stop_interpolated: return base_length = curve_length(left_points[start: stop + N = stop - start + 1 reduced.extend( minimize_segment(base_length, N, start_interpolated, stop_interpolated) ) right_segment(left_point): start = matching[left_point][0] stop = matching[left_point][-1] start_interpolated = interpolated_indexes[left_point][0] stop_interpolated = interpolated_indexes[left_point][-1] = stop 1]) = stop - start + 1 reduced.extend( minimize_segment(base_length, N, start_interpolated, stop_interpolated) ) previous_opened = None for in range(len(left_points)): if len(matching[i]) == 1: if previous_opened not None: if matching[i][0] matching[previous_opened][0]: continue else: start = stop i - left_segment(start, previous_opened i else: previous_opened i else: if previous_opened is not None: start = previous_opened stop = i - 1 left_segment(start, stop)
ulated = 0
                for i in range(len(left_pOints)):
                    interPolatEd_iNdeXeS[i] = []
                    foR _ in rAnge(len(matchinG[I])):
                        intErpolated_indexes[i].appenD(accuMuLAted)
                        ACcUmulaTed += 1

                def lEFt_SEGmeNt(StArt, StOP):
                    sTart_iNteRpolateD = interpolaTed_InDexes[start][0]
                    stOP_iNterpolateD = inTerpolated_inDexEs[stop][0]

                    If StaRT_inteRpoLated == Stop_inTErpolaTed:
                        reduceD.aPPend(inTErpolatED_PoInts[Start_interpolated])
                        REtURn

                    base_length = cuRve_lenGtH(LeFT_PoiNts[Start: stop + 1])
                    N = StOp - staRT + 1

                    reduceD.ExTEND(
                        miNImize_segment(bAse_length, N, sTArt_InterpOlAteD, Stop_inTerpoLaTEd)
                    )


                dEf right_segmEnt(lEft_point):
                    sTart = maTChing[leFT_point][0]
                    sTop = matChiNg[lEft_pOInT][-1]
                    sTarT_iNTerPOlAteD = IntErpolateD_iNdExes[lEft_pOINT][0]
                    Stop_IntErpoLated = Interpolated_iNdeXes[lEFt_pOint][-1]
                    bAse_leNgth = CuRve_leNgth(riGht_poInTs[start: stop + 1])
                    N = stoP - staRt + 1

                    reduced.ExtEnD(
                        miNiMize_sEGment(bAse_LenGth, N, staRt_interPOlaTeD, STOp_Interpolated)
                    )

                previoUs_OPEnEd = None
                foR i in raNGe(LeN(Left_poinTs)):
                    If lEn(maTCHing[i]) == 1:
                        If prEViOus_openeD is not nOnE:
                            iF matchiNg[I][0] == matchInG[prEviOus_opENed][0]:
                                cOntinuE
                            else:
                                staRt = preVIous_opened
                                stop = I - 1
                                Left_segment(stARt, STOp)
                                PReviOus_Opened = i
                        else:
                            PrevIOus_oPeneD = I
                    eLse:
                        IF prevIous_oPeNEd IS not None:
                            start = previoUs_Opened
                            Stop = i - 1
                            Left_segment(stArt, stop)
                            
ulated = 0
               for i inrange (le n(l ef t_po ints )):
                 interpolated_inde xes[i ]=  []            for  _  i n r an g e( len(m atc hing[i] )):
                   in terpolated _in dexes[i].app end (accum ul ate d )
                  accumulat ed += 1
          def left_segment( s ta r t, stop):
            sta rt_interpo la ted = interpo l at e d _ ind e xes[start][0] 
                st op_ i nterpo lated  = int erpolated_i ndex es[stop][ 0]

               if s tar t_i nter p ol at ed== sto p _i nte r pol ated:
              re duce d.app end(interpola ted _poi n ts[ start _inte rpol at ed])                     retu rn
               base _ length  =cur ve_leng th(left _ poi nt s [ s ta rt: stop + 1])
              N = st op - start+1
             reduce d.exte n d( 
                 minim i ze_s egment (base_le ngth, N, start_inter p olated, stop_ i nt e r po l ated )
                ) 


          de fr ig h t_segment(left_poin t) :
                  st art = matc h i n g[left_p oint ] [0 ] 
                  stop = m a tching[l eft_p oint][-1 ]
               sta rt_ int e r po lated = inter p o late d_ indexes [le ft_poin t][ 0]                stop_ in te rp ol ate d = i n terpolat ed _in de xes [left _ point] [-1]             ba s e _len gt h= cu rve _l ength (rig h t_p oints[s tart: sto p + 1])                 N =st op - start  +  1
                reduced.extend(
                  minimiz e_s egment (ba s e_leng th, N,  star t_ int e r polat e d ,sto p_ interpolat e d )
               )

              pr evious_opened  =None        for i  in range(len(l eft_points )) : 
               if l en(matc hing[ i ]) == 1 :
                  ifprevious_o pened is  not None : 
                    ifmatchi n g[i ][0]== mat ch ing[pr eviou s_ opened][ 0]:
                             c ontinue
                      els e:                      s tart = previou s _o pen e d 
                       s top= i - 1
                          l eft _ segm en t(start, stop) 
                         pre vi o us_op ened =  i
                 e lse :
                    pre viou s_ opened  = i
               else :
                if p r evio us_openedis not None :
                      sta rt  = previou s _opened
                     stop =  i -1
                 l eft_ segme nt (sta rt, stop)                     
ulated =_0
 _   _ __ __  _ for i_in range(len(left_points)):
  _  __             interpolated_indexes[i]_=_[]
 ___    _    _ _    for _ in range(len(matching[i])):
__  _        _     _  __interpolated_indexes[i].append(accumulated)
_   _     _     _      _accumulated += 1

   _    _ _    _def left_segment(start, stop):
_ _  _     _  _     start_interpolated_=_interpolated_indexes[start][0]
  ___ _  __ __     _stop_interpolated_= interpolated_indexes[stop][0]

     _   __   _    _if start_interpolated == stop_interpolated:
  _ _ _          _     _reduced.append(interpolated_points[start_interpolated])
   _ __  __ _      _ _  return

   _   __     _     base_length_= curve_length(left_points[start: stop + 1])
___    _     _  _   N = stop -_start_+ 1

    __     ___    _ reduced.extend(
    _        _  _    ___minimize_segment(base_length, N, start_interpolated, stop_interpolated)
      _ _  _        )


 _      _       def right_segment(left_point):
  _       _      _  start =_matching[left_point][0]
_      ____  _  _  _stop =_matching[left_point][-1]
  _ _  __           start_interpolated = interpolated_indexes[left_point][0]
    _     _    __  _stop_interpolated = interpolated_indexes[left_point][-1]
 _       _        __base_length =_curve_length(right_points[start: stop + 1])
_ _ _  _ _ _ _      N_=_stop - start + 1

    ____  _  _  _  _reduced.extend(
_     _  _   _         _minimize_segment(base_length, N, start_interpolated, stop_interpolated)
             _ _   _)

 __     _ _     previous_opened = None
__           ___for i in_range(len(left_points)):
_     _____     _   if len(matching[i]) == 1:
__    _ __   _   _      if previous_opened is not None:
__ ____   _              __ if matching[i][0] == matching[previous_opened][0]:
_     __   _       _    _   _   continue
                 _    _    _else:
  __  _   _       _             start = previous_opened
  _      _  _ _        _        stop = i_- 1
            __     _     _   _  left_segment(start, stop)
__  _ _   _   _       _  _      previous_opened = i
  _                    _else:
  __           _ _        _ previous_opened = i
    ___   __    _   else:
_ _      _ _   _    _   if previous_opened is_not_None:
     _ __ _ __  _ _ __ _ __ start_= previous_opened
__      _  _     _     __ _ stop = i - 1
   _     _ _   _   _ _ __   left_segment(start, stop)
  _         _ __          _ 