Buggy python submission (verdict: Runtime Error):

from collections import defaultdict
n = int(input())
a = list(map(int, input().split()))
    
ns = defaultdict(set)
for _ in range(n-1):
    u,v = [int(c) for c in input().split()]
    ns[u-1].add(v-1)
    ns[v-1].add(u-1)

from bisect import bisect_left
 
l = [a[0]]
# for a in A[1:]:
#     if a > L[-1]:
#         # Lの末尾よりaが大きければ増加部分列を延長できる
#         L.append(a)
#     else:
#         # そうでなければ、「aより小さい最大要素の次」をaにする
#         # 該当位置は、二分探索で特定できる
#         L[bisect_left(L, a)] = a
# return len(L)

ans = [None] * n

def sub(u, prev, lst, old, ind, ans):
    aa = a[u]
    if len(lst)==0 or aa > lst[-1]:
        lst.append(aa)
        old = -1
        ind = None
    else:
        ind = bisect_left(lst, aa)
        old = lst[ind]
        lst[ind] = aa
    ans[u] = len(lst)
#     print(lst)
    for v in ns[u]:
        if prev==v:
            continue
        sub(v, u, lst, old, ind, ans)
    if old==-1:
        lst.pop()
    elif old is not None:
        lst[ind] = old


sub(0, -1, [], None, None, ans)
print("\n".join(map(str, ans)))


Fixed submission:

from collections import defaultdict
n = int(input())
a = list(map(int, input().split()))

import sys
sys.setrecursionlimit(max(1000, 2*n))


ns = defaultdict(set)
for _ in range(n-1):
    u,v = [int(c) for c in input().split()]
    ns[u-1].add(v-1)
    ns[v-1].add(u-1)

from bisect import bisect_left
 
l = [a[0]]
# for a in A[1:]:
#     if a > L[-1]:
#         # Lの末尾よりaが大きければ増加部分列を延長できる
#         L.append(a)
#     else:
#         # そうでなければ、「aより小さい最大要素の次」をaにする
#         # 該当位置は、二分探索で特定できる
#         L[bisect_left(L, a)] = a
# return len(L)

ans = [None] * n

def sub(u, prev, lst, old, ind, ans):
    aa = a[u]
    if len(lst)==0 or aa > lst[-1]:
        lst.append(aa)
        old = -1
        ind = None
    else:
        ind = bisect_left(lst, aa)
        old = lst[ind]
        lst[ind] = aa
    ans[u] = len(lst)
#     print(lst)
    for v in ns[u]:
        if prev==v:
            continue
        sub(v, u, lst, old, ind, ans)
    if old==-1:
        lst.pop()
    elif old is not None:
        lst[ind] = old

lst = []
sub(0, -1, lst, None, None, ans)
print("\n".join(map(str, ans)))

Buggy python submission (verdict: Runtime Error):


from collections import defaultdict
n = int(input())
a = list(map(int, input().split()))
    
ns = defaultdict(set)
for _ in range(n-1):
    u,v = [int(c) for c in input().split()]
    ns[u-1].add(v-1)
    ns[v-1].add(u-1)

from bisect import bisect_left
 
l = [a[0]]
# for a in A[1:]:
#     if a > L[-1]:
#         # Lの末尾よりaが大きければ増加部分列を延長できる
#         L.append(a)
#     else:
#         # そうでなければ、「aより小さい最大要素の次」をaにする
#         # 該当位置は、二分探索で特定できる
#         L[bisect_left(L, a)] = a
# return len(L)

ans = [None] * n

def sub(u, prev, lst, old, ind, ans):
    aa = a[u]
    if aa > lst[-1]:
        lst.append(aa)
        old = -1
        ind = None
    else:
        ind = bisect_left(lst, aa)
        old = lst[ind]
        lst[ind] = aa
    ans[u] = len(lst)
#     print(lst)
    for v in ns[u]:
        if prev==v:
            continue
        sub(v, u, lst, old, ind, ans)
    if old==-1:
        lst.pop()
    elif old is not None:
        lst[ind] = old


sub(0, -1, [a[0]], None, None, ans)
print("\n".join(map(str, ans)))


Fixed submission:

from collections import defaultdict
n = int(input())
a = list(map(int, input().split()))

import sys
sys.setrecursionlimit(max(1000, 2*n))


ns = defaultdict(set)
for _ in range(n-1):
    u,v = [int(c) for c in input().split()]
    ns[u-1].add(v-1)
    ns[v-1].add(u-1)

from bisect import bisect_left
 
l = [a[0]]
# for a in A[1:]:
#     if a > L[-1]:
#         # Lの末尾よりaが大きければ増加部分列を延長できる
#         L.append(a)
#     else:
#         # そうでなければ、「aより小さい最大要素の次」をaにする
#         # 該当位置は、二分探索で特定できる
#         L[bisect_left(L, a)] = a
# return len(L)

ans = [None] * n

def sub(u, prev, lst, old, ind, ans):
    aa = a[u]
    if len(lst)==0 or aa > lst[-1]:
        lst.append(aa)
        old = -1
        ind = None
    else:
        ind = bisect_left(lst, aa)
        old = lst[ind]
        lst[ind] = aa
    ans[u] = len(lst)
#     print(lst)
    for v in ns[u]:
        if prev==v:
            continue
        sub(v, u, lst, old, ind, ans)
    if old==-1:
        lst.pop()
    elif old is not None:
        lst[ind] = old

lst = []
sub(0, -1, lst, None, None, ans)
print("\n".join(map(str, ans)))

Buggy python submission (verdict: Time Limit Exceeded):



from collections import defaultdict
n = int(input())
a = list(map(int, input().split()))
    
ns = defaultdict(set)
for _ in range(n-1):
    u,v = [int(c) for c in input().split()]
    ns[u-1].add(v-1)
    ns[v-1].add(u-1)

from bisect import bisect_left
 
l = [a[0]]
# for a in A[1:]:
#     if a > L[-1]:
#         # Lの末尾よりaが大きければ増加部分列を延長できる
#         L.append(a)
#     else:
#         # そうでなければ、「aより小さい最大要素の次」をaにする
#         # 該当位置は、二分探索で特定できる
#         L[bisect_left(L, a)] = a
# return len(L)

q = [(0, -1, l)]
ans = [None] * n
while q:
    u, prev, lst = q.pop()
    ans[u] = len(lst)
    for v in ns[u]:
        if prev==v:
            continue
        aa = a[v]
        if aa > lst[-1]:
            tmp = lst + [aa]
        else:
            tmp = list(lst)
            tmp[bisect_left(lst, aa)] = aa
#         print(tmp)
        q.append((v, u, tmp))
print("\n".join(map(str, ans)))

Fixed submission:

from collections import defaultdict
n = int(input())
a = list(map(int, input().split()))

import sys
sys.setrecursionlimit(max(1000, 2*n))


ns = defaultdict(set)
for _ in range(n-1):
    u,v = [int(c) for c in input().split()]
    ns[u-1].add(v-1)
    ns[v-1].add(u-1)

from bisect import bisect_left
 
l = [a[0]]
# for a in A[1:]:
#     if a > L[-1]:
#         # Lの末尾よりaが大きければ増加部分列を延長できる
#         L.append(a)
#     else:
#         # そうでなければ、「aより小さい最大要素の次」をaにする
#         # 該当位置は、二分探索で特定できる
#         L[bisect_left(L, a)] = a
# return len(L)

ans = [None] * n

def sub(u, prev, lst, old, ind, ans):
    aa = a[u]
    if len(lst)==0 or aa > lst[-1]:
        lst.append(aa)
        old = -1
        ind = None
    else:
        ind = bisect_left(lst, aa)
        old = lst[ind]
        lst[ind] = aa
    ans[u] = len(lst)
#     print(lst)
    for v in ns[u]:
        if prev==v:
            continue
        sub(v, u, lst, old, ind, ans)
    if old==-1:
        lst.pop()
    elif old is not None:
        lst[ind] = old

lst = []
sub(0, -1, lst, None, None, ans)
print("\n".join(map(str, ans)))