Problem: Takahashi has an ability to generate a tree using a permutation (p_1,p_2,...,p_n) of (1,2,...,n), in the following process:  First, prepare Vertex 1, Vertex 2, ..., Vertex N. For each i=1,2,...,n, perform the following operation:    * If p_i = 1, do nothing.   * If p_i \neq 1, let j' be the largest j such that p_j < p_i. Span an edge between Vertex i and Vertex j'.  Takahashi is trying to make his favorite tree with this ability. His favorite tree has n vertices from Vertex 1 through Vertex n, and its i-th edge connects Vertex v_i and w_i. Determine if he can make a tree isomorphic to his favorite tree by using a proper permutation. If he can do so, find the lexicographically smallest such permutation.

Submission attempts (in order):
import sys
input = sys.stdin.readline

N = int(input())
VW = [[int(x)-1 for x in input().split()] for _ in range(N-1)]



graph = [[] for _ in range(N)]
deg = [0] * (N)
for v,w in VW:
    graph[v].append(w)
    graph[w].append(v)
    deg[v] += 1
    deg[w] += 1

def dijkstra(start):
    INF = 10**10
    dist = [INF] * N
    q = [(start,0)]
    while q:
        qq = []
        for v,d in q:
            dist[v] = d
            for w in graph[v]:
                if dist[w] == INF:
                    qq.append((w,d+1))
        q = qq
    return dist

dist = dijkstra(0)
v = dist.index(max(dist))
dist = dijkstra(v)
w = dist.index(max(dist))
diag = v,w


import sys
input = sys.stdin.readline

N = int(input())
VW = [[int(x)-1 for x in input().split()] for _ in range(N-1)]



graph = [[] for _ in range(N)]
deg = [0] * N
for v,w in VW:
    graph[v].append(w)
    graph[w].append(v)
    deg[v] += 1
    deg[w] += 1

def dijkstra(start):
    INF = 10**10
    dist = [INF] * N
    q = [(start,0)]
    while q:
        qq = []
        for v,d in q:
            dist[v] = d
            for w in graph[v]:
                if dist[w] == INF:
                    qq.append((w,d+1))
        q = qq
    return dist

dist = dijkstra(0)
v = dist.index(max(dist))
dist = dijkstra(v)
w = dist.index(max(dist))
diag = v,w

def create_perm(v,parent,next_p,arr):
    next_v = None
    V1 = []
    V2 = []
    for w in graph[v]:
        if w == parent:
            continue
        if deg[w] == 1:
            V1.append(w)
        else:
            V2.append(w)
    if len(V1) == 0 and len(V2) == 0:
        arr.append(next_p)
        return
    if len(V2) > 0:
        next_v = V2[0]
    else:
        next_v = V1[-1]
        V1 = V1[:-1]
    arr += list(range(next_p+1,next_p+len(V1)+1))
    arr.append(next_p)
    next_p += len(V1)+1
    #create_perm(next_v,v,next_p,arr)

P = []
create_perm(diag[1],None,1,P)

Q = []
create_perm(diag[0],None,1,Q)

if len(P) != N:
    answer = -1
else:
    if P > Q:
        P = Q
    answer = ' '.join(map(str,P))
print(answer)



import sys
input = sys.stdin.readline

N = int(input())
VW = [[int(x)-1 for x in input().split()] for _ in range(N-1)]



graph = [[] for _ in range(N)]
deg = [0] * (N)
for v,w in VW:
    graph[v].append(w)
    graph[w].append(v)
    deg[v] += 1
    deg[w] += 1

def dijkstra(start):
    INF = 10**10
    dist = [INF] * N
    q = [(start,0)]
    while q:
        qq = []
        for v,d in q:
            dist[v] = d
            for w in graph[v]:
                if dist[w] == INF:
                    qq.append((w,d+1))
        q = qq
    return dist

dist = dijkstra(0)
v = dist.index(max(dist))
dist = dijkstra(v)
w = dist.index(max(dist))
diag = v,w

def create_perm(v,parent,next_p,arr):
    next_v = None
    V1 = []
    V2 = []
    for w in graph[v]:
        if w == parent:
            continue
        if deg[w] == 1:
            V1.append(w)
        else:
            V2.append(w)
    if len(V1) == len(V2) == 0:
        arr.append(next_p)
        return
#    next_v = V2[0] if V2 else V1.pop()
#    arr += list(range(next_p+1,next_p+len(V1)+1))
#    arr.append(next_p)
#    next_p += len(V1)+1
    create_perm(next_v,v,next_p,arr)

P = [] * N
create_perm(diag[1],None,1,P)

Q = [] * N
create_perm(diag[0],None,1,Q)

if len(P) != N:
    answer = -1
else:
    if P > Q:
        P = Q
    answer = ' '.join(map(str,P))
print(answer)


import sys
input = sys.stdin.readline

N = int(input())
VW = [[int(x)-1 for x in input().split()] for _ in range(N-1)]



graph = [[] for _ in range(N)]
deg = [0] * N
for v,w in VW:
    graph[v].append(w)
    graph[w].append(v)
    deg[v] += 1
    deg[w] += 1

def dijkstra(start):
    INF = 10**10
    dist = [INF] * N
    q = [(start,0)]
    while q:
        qq = []
        for v,d in q:
            dist[v] = d
            for w in graph[v]:
                if dist[w] == INF:
                    qq.append((w,d+1))
        q = qq
    return dist

dist = dijkstra(0)
v = dist.index(max(dist))
dist = dijkstra(v)
w = dist.index(max(dist))
diag = v,w

def create_perm(v,parent,next_p,arr):
    next_v = None
    V1 = []
    V2 = []
    for w in graph[v]:
        if w == parent:
            continue
        if deg[w] == 1:
            V1.append(w)
        else:
            V2.append(w)
    if len(V1) == len(V2) == 0:
        arr.append(next_p)
        return
    next_v = V2[0] if V2 else V1.pop()
#    arr += list(range(next_p+1,next_p+len(V1)+1))
#    arr.append(next_p)
#    next_p += len(V1)+1
    create_perm(next_v,v,next_p,arr)

P = []
create_perm(diag[1],None,1,P)

Q = []
create_perm(diag[0],None,1,Q)

if len(P) != N:
    answer = -1
else:
    if P > Q:
        P = Q
    answer = ' '.join(map(str,P))
print(answer)



import sys
sys.setrecursionlimit(10**7)
input = sys.stdin.readline

N = int(input())
VW = [[int(x)-1 for x in input().split()] for _ in range(N-1)]



graph = [[] for _ in range(N)]
deg = [0] * N
for v,w in VW:
    graph[v].append(w)
    graph[w].append(v)
    deg[v] += 1
    deg[w] += 1

def dijkstra(start):
    INF = 10**10
    dist = [INF] * N
    q = [(start,0)]
    while q:
        qq = []
        for v,d in q:
            dist[v] = d
            for w in graph[v]:
                if dist[w] == INF:
                    qq.append((w,d+1))
        q = qq
    return dist

dist = dijkstra(0)
v = dist.index(max(dist))
dist = dijkstra(v)
w = dist.index(max(dist))
diag = v,w

def create_perm(start):
    arr = []
    v = start
    parent = None
    next_p = 1
    while True:
        n = 0
        next_v = None
        for w in graph[v]:
            if w == parent:
                continue
            if next_v is None or deg[next_v] < deg[w]:
                next_v = w
            if deg[w] == 1:
                n += 1
        if next_v is None:
            return arr + [next_p]
        if deg[next_v] == 1:
            n -= 1
        arr += list(range(next_p+1,next_p+n+1))
        arr.append(next_p)
        next_p += n+1
        parent = v
        v = next_v

P = create_perm(diag[1])

Q = create_perm(diag[0])

if len(P) != N:
    answer = -1
else:
    if P > Q:
        P = Q
    answer = ' '.join(map(str,P))
print(answer)



Verdicts: Wrong Answer

Wrong Answer

Runtime Error

Runtime Error

Accepted