Problem: 2063C - Remove Exactly Two
Language: python

Solution 1 (runtime: 781 ms):
t = int(input())

for x in range(t):
    n = int(input())
    edges = []
    adj_list = []

    for y in range(n+1):
        adj_list.append([])

    for e in range(n-1):
        a,b = list(map(int, input().split(" ")))
        
        adj_list[a].append(b)
        adj_list[b].append(a)


    for i in range(2):
        cnt_max_edges = 0
        max_edges = []
        for node in range(1, n+1):
            if adj_list[node] != None:
                if len(adj_list[node]) > cnt_max_edges:
                    cnt_max_edges = len(adj_list[node])
                    max_edges = [node]
                elif len(adj_list[node]) == cnt_max_edges:
                    max_edges.append(node)


        if len(max_edges) <= 2 or i == 1:
            max_edges = [max_edges[0]]
        else:
            f = False
            for idx1 in range(0, len(max_edges)):
                if f: break
                for idx2 in range(idx1+1, len(max_edges)):
                    if not max_edges[idx2] in adj_list[max_edges[idx1]]:
                        max_edges = [max_edges[idx1], max_edges[idx2]]
                        f = True
                        break


        for most_edges_node in max_edges:
            for node in adj_list[most_edges_node]:
                adj_list[node].remove(most_edges_node)

            adj_list[most_edges_node] = None

        if len(max_edges) >= 2:
            break

    count_cc = 0
    connected = {}
    v = 1
    for node in range(1, n+1):
        if adj_list[node] != None and not node in connected:
            queue = [node]

            while len(queue) > 0:
                curr = queue.pop()
                connected[curr] = count_cc
                for adj_node in adj_list[curr]:
                    if not adj_node in connected:
                        queue.append(adj_node)
                        connected[adj_node] = count_cc

            count_cc += 1

    print(count_cc)

Solution 2 (runtime: 468 ms):
def max1(t) :
    indice=0
    nb=t[0]
    n=len(t)
    for i in range(1,n) :
        if t[i]>nb :
            indice=i
            nb=t[i]
    return nb,indice

def max2(t,j) :
    
    if j==0 :
        indice=1
        nb=t[1]
    
    else:
        nb=t[0]
        indice=0
    n=len(t)
    for i in range(1,n) :
        if i!=j :
            if t[i]>nb :
                indice=i
                nb=t[i]
    return nb,indice

for _ in range(int(input())):
    n=int(input())
    if n<=2 :
        for i in range(n-1):
            u,v=map(int,input().split())
        print(0)
    else:
        t=[0]*n
        t2=[0]*n
        l=[]
        for i in range(n-1):
            u,v=map(int,input().split())
            l.append((u,v))
            t[u-1]+=1
            t[v-1]+=1
            t2[u-1]+=1
            t2[v-1]+=1
        nb1,indice1=max1(t)
        nb3,indice3=max2(t2,indice1)
        t[indice1]=0
        t2[indice3]=0
        for i in l :
            if i[0]-1==indice1 :
                t[i[1]-1]-=1
            elif i[1]-1==indice1 :
                t[i[0]-1]-=1
        for i in l :
            if i[0]-1==indice3 :
                t2[i[1]-1]-=1
            elif i[1]-1==indice3 :
                t2[i[0]-1]-=1
        nb2,indice2=max1(t)
        nb4,indice4=max1(t2)
 
  
        print(max(nb1+nb2-1,nb3+nb4-1))