neighbour finder finding the same closest candidate, which is already allotted

Have you looked at the following related questions?

https://community.safe.com/s/question/0D54Q00008DpOYsSAN/neighborfinder-each-candidate-available-just-once

https://community.safe.com/s/question/0D54Q000080hTpkSAE/neighborfinder-and-excluding-candidates-after-matched

I think you would have to use the NeighborFinder in a loop which is tricky but not impossible.

https://docs.safe.com/fme/html/FME_Desktop_Documentation/FME_Workbench/Workbench/looping_with_blocking_transformer.htm

As soon as "A" is matched with "1". then 1 should be excluded from the set. when b comes in, it should search only with 2 and 3, and now B will be matched to a closest candidate"2". and "2" excluded. and C will come and only one left, that is "3"

I used Python caller for this and achieved the target.

I used list exploder after neighbor finder, then stored the feature and its attributes to list @ pythoncaller's input method. 

And in the close() method, 

created one new list , and appended only valid feature and its attributes. No duplicate base or candidates.(ID not in List then only append)

I got the Result what I want.

Thanks For Everyone, who Answered my Q.

import fme
import fmeobjects
 
 
class FeatureProcessor(object):
    def __init__(self):
        self.featureList = []
        self.mylist = []
        self.mylist2 = []
 
    def input(self,feature):
        self.featureList.append(feature)
        self.mylist.append(str(feature.getAttribute('tid')))
        self.mylist2.append(str(feature.getAttribute('cid')))
        #self.mylist2.append(feature.getAttribute('_creation_instance'))
        
 
    def close(self):
        outlist1=[]
        outlist2=[]
        mylist1=self.mylist
        mylist2=self.mylist2
        i = 0
        while i < len(mylist1):
            tid=(mylist1[i])
            cid=(mylist2[i])
            if tid not in outlist1 and cid not in outlist2:
                outlist1.append(str(tid))
                outlist2.append(str(cid))
                print(tid)
                print(cid)
                self.featureList[i].setAttribute('tid',tid)
                self.featureList[i].setAttribute('cid',cid)
                self.pyoutput(self.featureList[i])
            i = i + 1
 

Thanks to All