Problem:


Score : 500 points

Problem Statement

You are given a sequence with N integers: A = \{ A_1, A_2, \cdots, A_N \}.
For each of these N integers, we will choose a color and paint the integer with that color. Here the following condition must be satisfied:

If A_i and A_j (i < j) are painted with the same color, A_i < A_j.

Find the minimum number of colors required to satisfy the condition.

Constraints

1 \leq N \leq 10^5

0 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the minimum number of colors required to satisfy the condition.

Sample Input 1

5
2
1
4
5
3

Sample Output 1

2

We can satisfy the condition with two colors by, for example, painting 2 and 3 red and painting 1, 4, and 5 blue.

Sample Input 2

4
0
0
0
0

Sample Output 2

4

We have to paint all the integers with distinct colors.



Sample input:
5
2
1
4
5
3


Sample output:
2

Submission status: Time Limit Exceeded

Solution code:
N=int(input())
A=[int(input()) for _ in range(N)]

dp=[1]*N
for i in range(N):
    for j in range(i):
        if A[j]<A[i]:
            dp[i]=max(dp[i],dp[j]+1)

print(sum([1 for v in dp if v==1]))

Submission status: Time Limit Exceeded

Solution code:
from bisect import bisect_left

N = int(input())
A = [int(input()) for _ in range(N)]
INF = float('inf')

cnt = 0
X = A
while len(X) > 0:
    cnt += 1
    Y = []
    dp = [INF] * (len(X) + 1)
    for a in X:
        idx = bisect_left(dp, a)
        if dp[idx] == INF:
            dp[idx] = a
        else:
            Y.append(a)
    X = Y


print(cnt)

Submission status: Time Limit Exceeded

Solution code:
n=int(input())
a=[int(input()) for i in range(n)]
ans=0
INF=-10**9
k=0
while max(a)>=0:
  de=[]
  f=a[k]
  de.append(k)
  if f<0:
    k+=1
    continue
  for i in range(k+1,n):
    if f<a[i]:
      de.append(i)
      f=a[i]
  for i in de:
    a[i]=INF
  ans+=1
  k+=1
print(ans)

Submission status: Time Limit Exceeded

Solution code:
import bisect

N = int(input())
A = [int(input()) for _ in range(N)]

x = []

for i, a in enumerate(A):
    if i == 0:
        x.append(a)
    else:
        r = bisect.bisect_left(x, a)
        if r == 0:
            x.insert(0, a)
        else:
            x[r - 1] = a

print(len(x))

Submission status: Time Limit Exceeded

Solution code:
N = int(input())
A = [int(input()) for _ in range(N)]

x = []

for i, a in enumerate(A):
    if i == 0:
        x.append(a)
    else:
        r = len(x) - 1
        l = 0
        while r - l != 1 and r - l != 0:
            m = (r + l) // 2
            if a > x[m]:
                l = m
            else:
                r = m

        if a > x[r]:
            x[r] = a
        elif a > x[l]:
            x[l] = a
        else:
            x.append(a)
        x.sort()

print(len(x))

Submission status: Time Limit Exceeded

Solution code:
N = int(input())
A = [int(input()) for _ in range(N)]

color = []
for i in range(N):
    if i == 0:
        color.append(A[i])
    else:
        for j in range(len(color)):
            if A[i] > color[j]:
                color[j] = A[i]
                break
        else:
            color.append(A[i])

print(len(color))

Submission status: Time Limit Exceeded

Solution code:
def main():
    N = int(input())
    A = [int(input()) for _ in range(N)]

    check = [False] * N
    index = 0
    ans = 0
    cnt = 0
    while True:
        pre = -1
        for i in range(index,N,1):
            if check[i]:
                continue
            if A[i] > pre:
                pre = A[i]
                check[i] = True
                cnt += 1
            else:
                cnt = min(cnt,i)

        ans += 1
        if cnt == N:
            break
    
    print(ans)

if __name__ == "__main__":
    main()

Submission status: Time Limit Exceeded

Solution code:
import bisect
def main():
  N=int(input())
  a=[int(input())]
  for _ in range(N-1):
    num=int(input())
    if num<=a[0]:
      a=[num]+a
    else:
      a[bisect.bisect_left(a, num)-1]=num
  print(len(a))
if __name__=='__main__':
  main()

Submission status: Time Limit Exceeded

Solution code:
import bisect
N=int(input())
a=[int(input())]
for _ in range(N-1):
  num=int(input())
  if num<=a[0]:
    a=[num]+a
  else:
    a[bisect.bisect_left(a, num)-1]=num
print(len(a))

Submission status: Time Limit Exceeded

Solution code:
def f(a, num):
  if a[0]>=num:
    a=[num]+a
    return a
  if a[-1]<num:
    a[-1]=num
    return a
  x=0
  y=len(a)
  while y-x>1:
    z=(x+y)//2
    if a[z]>=num:
      y=z
    else:
      x=z
  a=a[:x]+[num]+a[y:]
  return a
      
  
N=int(input())
a=[int(input())]
for _ in range(N-1):
  a=f(a, int(input()))
print(len(a))

Submission status: Time Limit Exceeded

Solution code:
N = int(input())
A = [int(input()) for i in range(N)]
cnt = 0
while A != []:
  B = []
  for i in range(1, len(A)):
    if A[0] >= A[i]:
      B = B[:] + [A[i]]
    if A[i] == max(A):
      B = B[:] + A[i+1:]
      break
  A = B[:]
  cnt += 1
print(cnt)

Submission status: Time Limit Exceeded

Solution code:
n = int(input())
A = [int(input()) for _ in range(n)]
L = []
for i in A:
  for j in range(len(L)):
    if L[j] < i:
      L[j] = i
      break
  else:
    L.append(i)
print(len(L))

Submission status: Time Limit Exceeded

Solution code:
import bisect
n=int(input())
A=[int(input())]

for i in range(n-1):
  a=int(input())
  b=bisect.bisect_left(A,a,lo=0,hi=len(A))
  if b==0:
    A.insert(0,a)
  else:
    A[b-1]=a
print(len(A))

Submission status: Time Limit Exceeded

Solution code:
import bisect
n=int(input())
A=[int(input())]
for i in range(n-1):
  a=int(input())
  b=bisect.bisect_right(A,a,lo=0,hi=len(A))
  if b!=0 and A[b-1]<a:
    A[b-1]=a
  elif A[b-1]==a:
    b=bisect.bisect_right(A,a-1,lo=0,hi=len(A))
    if b!=0:
      A[b-1]=a
    else:
      A.insert(0,a)
  else:
    A.insert(0,a)
print(len(A))

Submission status: Time Limit Exceeded

Solution code:
import bisect

n=int(input())
a=list(int(input()) for i in range(n))
b=[]
b.append(-1)


for i in range(n):
    if a[i]>b[0]:
        x=bisect.bisect_right(b,a[i]-1)
        b[x-1]=a[i]
    else:
        b.insert(0,a[i])
print(len(b))

Submission status: Time Limit Exceeded

Solution code:
import sys
import bisect
N =int(input())
A = [int(i) for i in sys.stdin.readlines()]
lis = [A.pop(0)]
for i in A:
    if lis[0] >= i:
        lis.insert(0,i)
    else:
        ind = bisect.bisect_left(lis,i) -1
        lis[ind] = i
print(len(lis))

Submission status: Time Limit Exceeded

Solution code:
import bisect
from collections import deque
n=int(input())
a=[int(input()) for _ in range(n)]

q=deque()

for sa in a:
    lq = list(q)
    t = bisect.bisect_left(lq,sa)
    if t ==0:
        q.appendleft(sa)
    else:
        q[t-1] = sa

print(len(q))

Submission status: Time Limit Exceeded

Solution code:
def solve():
	N, *A = map(int, open(0).read().split())

	top = [A[0]]
	for i in range(1, N):
		da_min = 10**9
		color = -1
		for j in range(len(top)):
			da = A[i] - top[j]
			if da > 0:
				if da_min > da:
					da_min = da
					color = j
		if color != -1:
			top[color] = A[i]
		else:
			top.append(A[i])

	print(len(top))


if __name__ == '__main__':
	solve()

Submission status: Time Limit Exceeded

Solution code:
def solve():
	N, *A = map(int, open(0).read().split())
	
	top = [A[0]]
	for i in range(1, N):
		da_min = 10**9
		color = -1
		for j in range(len(top)):
			da = A[i] - top[j]
			if da > 0:
				if da_min > da:
					da_min = da
					color = j
		if color != -1:
			top[color] = A[i]
		else:
			top.append(A[i])
	
	print(len(top))


if __name__ == '__main__':
	solve()

Submission status: Time Limit Exceeded

Solution code:
import bisect
n = int(input())
color = [int(input())]
for i in range(1,n):
    num = int(input())
    if min(color) >= num:
        color.append(num)
    else:
        color = sorted(color)
        bis = bisect.bisect_left(color, num)
        color[bis-1] = num
print(len(color))

Submission status: Time Limit Exceeded

Solution code:
def main(sample_file = ''):

    """ convenient functions
    # for i, a in enumerate(iterable)
    # q, mod = divmod(a, b)
    # divmod(x, y) returns the tuple (x//y, x%y)
    # Higher-order function: reduce(operator.mul, xyz_count, 1)
    # manage median(s) using two heapq https://atcoder.jp/contests/abc127/tasks/abc127_f
    """

    """convenient decorator
    # @functools.lru_cache():
    # to facilitate use of recursive function
        # ex:
        # from functools import lru_cache
        # import sys
        # sys.setrecursionlimit(10**9)
        # @lru_cache(maxsize=None)
        # def fib(n):
        #     if n < 2:
        #         return n
        #     return fib(n-1) + fib(n-2)
        # print(fib(1000))
    """
    
    # import numpy as np
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product # https://docs.python.org/ja/3/library/itertools.html
    # accumulate() returns iterator! to get list: list(accumulate())
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  # prime factor
        b, e = 2, 0  # base, exponent
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        # TODO: How should I do when n - r is negative?
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict # https://docs.python.org/ja/3/library/collections.html#collections.deque
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest # https://docs.python.org/ja/3/library/heapq.html
    from copy import deepcopy, copy # https://docs.python.org/ja/3/library/copy.html
    import operator
    from operator import itemgetter #sort 
    # ex1: List.sort(key=itemgetter(1))
    # ex2: sorted(tuples, key=itemgetter(1,2))
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd # Deprecated since version 3.5: Use math.gcd() instead.
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    # first create factorial_list
    # fac_list = mod_factorial_list(n)
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    modpow = lambda a, n, p = MOD: pow(a, n, p) # Recursive function in python is slow!
    def modinv(a, p = MOD):
        # evaluate reciprocal using Fermat's little theorem:
        # a**(p-1) is identical to 1 (mod p) when a and p is coprime
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        # fac_list = modfactorial_list(100)
        # print(modcomb(100, 5, modfactorial_list(100)))
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    # Graph: https://en.wikipedia.org/wiki/Directed_graph
    # Bellman-Ford: O(|V||E|). Use this if there exists an edge with negative length in the graph
    # After N steps, the shortest path has converded if there doesn't exist an cycle of edges with negative
    # Watch out: d[N] == d[2*N] doesn't necessarily mean the graph doesn't have negative cycle
    # ref: https://www.youtube.com/watch?v=1Z6ofKN03_Y

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    """ initialize variables and set inputs
    # initialize variables
        # to initialize list, use [0] * n
        # to initialize two dimentional array:
            # ex) [[0] * N for _ in range(N)]
            # ex2) dp = [[0] * (N+1) for _ in range(W*2)]
    # set inputs
        # put inputs between specific values (almost as quickly)
        # ex) S = [-INF] + [int(r()) for _ in range(A)] + [INF]
        # open(0).read() is sometimes useful:
        # ex) n, m, *x = map(int, open(0).read().split())
        #     min(x[::2]) - max(x[1::2])
        # ex2) *x, = map(int, open(0).read().split())
        #     don't forget to add comma after *x if only one variable is used
    # preprocessing
        # transpose = [x for x in zip(*data)]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [(1, 4, 7), (2, 5, 8), (3, 6, 9)]
        # flat = [flatten for inner in data for flatten in inner]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [1, 2, 3, 4, 5, 6, 7, 8, 9]
    # calculate and output
        # output pattern
        # ex1) print(*l) => when l = [2, 5, 6], printed 2 5 6
    """

    # functions to read input
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    r_float = lambda: float(r())
    R = lambda: list(map(int, r().split()))
    R_map = lambda: map(int, r().split())
    R_float = lambda: list(map(float, r().split()))
    R_tuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    # single int: int(r())
    # single string: r()
    # single float: float(r())
    # line int: R()
    # line string: r().split()
    # line (str, int, int): [j if i == 0 else int(j) for i, j in enumerate(r().split())]
    # lines int: [R() for _ in range(n)]
    """

    # for test
    if sample_file:
        sys.stdin = open(sample_file)
        
    # ----------------------------------
    # main

    N = r_int()
    A = [r_int() for _ in range(N)]
    dp = [[-1]*(N+1) for _ in range(N+1)]
    # search maximum length
    for i in range(N+1):
        dp[0][i] = INF
    for j in range(N):
        for i in range(N):
            if dp[i][j] == -1:
                break
            dp[i][j+1] = max(dp[i][j], dp[i][j+1])
            if dp[i][j] >= A[j]:
                dp[i+1][j+1] = A[j]
    for i in range(N, -1, -1):
        if dp[i][N] != -1:
            print(i)
            return
    print(-1)
    # to finish code, use return instead of exit()
    # end of main
    # ----------------------------------

    """memo: how to use defaultdict of list
    # initialize
    Dic = defaultdict(list)
    # append / extend
    Dic[x].append(y)
    # three methods for loop: keys(), values(), items()
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    # to make binary digits text
    >>> a = 5
    >>> bin_str_a = format(a, '#06b')
    >>> print(bin_str_a)
    0b0101 # first 2 strings (='0b') indicates it is binary
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()