Problem:


Score: 400 points

Problem Statement

To become a millionaire, M-kun has decided to make money by trading in the next N days. Currently, he has 1000 yen and no stocks - only one kind of stock is issued in the country where he lives.

He is famous across the country for his ability to foresee the future. He already knows that the price of one stock in the next N days will be as follows:

A_1 yen on the 1-st day, A_2 yen on the 2-nd day, ..., A_N yen on the N-th day.

In the i-th day, M-kun can make the following trade any number of times (possibly zero), within the amount of money and stocks that he has at the time.

Buy stock: Pay A_i yen and receive one stock.

Sell stock: Sell one stock for A_i yen.

What is the maximum possible amount of money that M-kun can have in the end by trading optimally?

Constraints

2 \leq N \leq 80

100 \leq A_i \leq 200

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N

Output

Print the maximum possible amount of money that M-kun can have in the end, as an integer.

Sample Input 1

7
100 130 130 130 115 115 150

Sample Output 1

1685

In this sample input, M-kun has seven days of trading. One way to have 1685 yen in the end is as follows:

Initially, he has 1000 yen and no stocks.

Day 1: Buy 10 stocks for 1000 yen. Now he has 0 yen.

Day 2: Sell 7 stocks for 910 yen. Now he has 910 yen.

Day 3: Sell 3 stocks for 390 yen. Now he has 1300 yen.

Day 4: Do nothing.

Day 5: Buy 1 stock for 115 yen. Now he has 1185 yen.

Day 6: Buy 10 stocks for 1150 yen. Now he has 35 yen.

Day 7: Sell 11 stocks for 1650 yen. Now he has 1685 yen.

There is no way to have 1686 yen or more in the end, so the answer is 1685.

Sample Input 2

6
200 180 160 140 120 100

Sample Output 2

1000

In this sample input, it is optimal to do nothing throughout the six days, after which we will have 1000 yen.

Sample Input 3

2
157 193

Sample Output 3

1216

In this sample input, it is optimal to buy 6 stocks in Day 1 and sell them in Day 2, after which we will have 1216 yen.



Sample input:
7
100 130 130 130 115 115 150


Sample output:
1685

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python3
import sys
input = sys.stdin.readline


n = int(input())
a = [int(item) for item in input().split()]
prev = a[0]
a_uniq = [a[0]]
for item in a:
    if item == prev:
        continue
    a_uniq.append(item)
    prev = item

increasing = None
if a_uniq[0] < a_uniq[1]:
    increasing = True
else:
    increasing = False

money = 1000
kabu = 0
if increasing:
    p = money // a[0]
    money -= p * a[0]
    kabu = p

prev = a_uniq[0]
ans = 1000
for item in a_uniq[1:]:
    if item < prev and increasing:
        money += kabu * prev
        kabu = 0
        increasing = False
        ans = max(ans, money)
    if item > prev and not increasing:
        p = money // prev
        money -= p * prev
        kabu = p
        increasing = True
    prev = item
if kabu:
    money += a_uniq[-1] * kabu
    ans = max(ans, money)
print(ans)

Submission status: Runtime Error

Solution code:
N=int(input())
A=list(map(int, input().split()))
#1000

#1300
#35
L=[0]*N
if A[0]<A[1]:
    L[0]=1
    up=1
elif A[0]==A[1]:
    up==0
else:
    up=-1

for i in range(1,N):
    if i==N-1:
        L[i]=-1
        break
    if up==1:
        if A[i]>A[i+1]:
            up=-1
            L[i]=-1
    elif up==0:
        if A[i-1]<A[i]:
            L[i-1]=1
            up=1
        elif A[i-1]>A[i]:
            up=-1

    else:
        if A[i]<A[i+1]:
            up=1
            L[i]=1

#print(L)
now=1000
have=0
for i in range(len(L)):
    l=L[i]
    if l==1:
        have=now//A[i]
        now=now%A[i]
    elif l==-1:
        now+=A[i]*have
        have=0
print(now)

Submission status: Runtime Error

Solution code:
INF=float('inf')
N=int(input())
A=list(map(int,input().split()))
dp=[[-INF for i in range(20)] for i in range(N+1)]
dp[0][0]=1000#dp[i][j]=i日目に株をj個持っているときの最大所持金

for i in range(N):
    for j in range(20):
        if dp[i][j]==-INF:
            continue
        dp[i+1][j]=dp[i][j]
        for x in range(1,j+1):
            if j-x>=0:
                dp[i+1][j-x]=max(dp[i][j]+A[i]*x,dp[i+1][j-x])
            else:
                break
        for x in range(1,1000000):
            if dp[i][j]-A[i]*x>=0:
                dp[i+1][j+x]=max(dp[i][j]-A[i]*x,dp[i+1][j+x])
            else:
                break
print(max(dp[N]))

Submission status: Runtime Error

Solution code:
import sys
input = lambda: sys.stdin.readline().rstrip("\r\n")

n = int(input())
a = [int(x) for x in input().split()]

sold_day = set()
buy_day = set()

for i in range(1, n):
    if a[i] > a[i - 1]:
        sold_day.add(i)
        buy_day.discard(i - 1)

money = 1000
stock = 0

sold_day = list(sold_day)
sold_day.sort()

s = 0

for i in sold_day:
    temp = a[s:i]
    min_value = min(temp)
    x = money // min_value
    money -= min_value * x
    money += x * a[i]
    s = i + 1
print(money)

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python3
import sys


def solve(N: int, A: "List[int]"):
    def uniq(arr):
        ret = [arr[0]]
        for a in arr[1:]:
            if ret[-1] == a:
                continue
            ret.append(a)
        return ret

    def compress(arr):
        if len(arr) <= 2:
            return arr
        ret = [arr[0]]        
        for a0, a1, a2 in zip(arr, arr[1:], arr[2:]):
            if a0 < a1 < a2 or a0 > a1 > a2:
                continue
            ret.append(a1)
        ret.append(arr[-1])
        return ret

    B = uniq(A)
    C = compress(B)
    ans, m, s = 1000, 1000, 0
    for c0, c1 in zip(C, C[1:]):
        if c0 < c1:
            t = m // c0
            s += t
            m -= t * c0
        else:
            m += c0 * s
            s = 0
        ans = max(ans, m)
    else:
        m += c1 * s
        ans = max(ans, m)
    return ans

# Generated by 1.1.7.1 https://github.com/kyuridenamida/atcoder-tools
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    A = [int(next(tokens)) for _ in range(N)]  # type: "List[int]"
    print(solve(N, A))

def test():
    import doctest
    doctest.testmod()

if __name__ == '__main__':
    #test()
    main()

Submission status: Runtime Error

Solution code:
n = int(input())
a = list(map(int, input().split()))
dp = [[[-1] * (5 * 10 ** 6) for _ in range(n)] for _ in range(2)]
dp[0][0][1000] = 0
dp[1][0][1000] = 0
for i in range(n):
    for j in range(5 * 10 ** 6):
        dp[0][i + 1][j], dp[1][i + 1][j] = dp[0][i][j], dp[1][i][j]
    for j in range(5 * 10 ** 6):
        u, v = dp[0][i][j], dp[1][i][j]
        if max(u, v) < 0:
            continue
        dp[0][i + 1][j] = u
        dp[1][i + 1][j] = v
        # print(i, j, u, v)
        dp[0][i + 1][j + max(u, v) * a[i]] = 0
        dp[1][i + 1][j % a[i]] = max(u, v) + j // a[i]
ans = 0
for j in range(10 ** 4):
    if dp[0][n][j] != -1 or dp[1][n][j] != -1:
        ans = max(ans, j)
print(ans)

Submission status: Runtime Error

Solution code:
def main():

    n = int(input())
    A = list(map(int, input().split()))

    dp = [[[0]*(10**2) for _ in range(10**4)] for _ in range(n+1)]
    dp[0][1000][0] = 1
    for i in range(n):
        for j in range(10**4):
            for k in range(10**2):
                if dp[i][j][k] != 0:
                    dp[i+1][j][k] = 1

        for j in range(10**4):
            for k in range(10**2):
                if dp[i][j][k] != 0:
                    dp[i+1][j+A[i]*k][0] = 1
        # buy
        for j in range(10**4):
            for k in range(10**2):
                if dp[i][j][k] != 0:
                    q, r = divmod(j, A[i])
                    dp[i+1][r][k+q] = 1

    for j in reversed(range(10**4)):
        for k in range(10**2):
            if dp[n][j][k] != 0:
                print(j)
                exit()

if __name__ == '__main__':
    main()

Submission status: Runtime Error

Solution code:
import sys
import heapq
import math
import fractions
import bisect
import itertools
from collections import Counter
from collections import deque
from operator import itemgetter
def input(): return sys.stdin.readline().strip()
def mp(): return map(int,input().split())
def lmp(): return list(map(int,input().split()))

n=int(input())
a=lmp()
a.insert(0,10000)
a.append(0)
l=[0]*(n+2)
for i in range(1,n+1):
    if a[i-1]<a[i]>=a[i+1]:
        l[i]=1
    elif a[i-1]>a[i]<=a[i+1]:
        l[i]=-1
sto=[0,1000]
for i in range(n+2):
    if l[i]==-1:
        sto[0],sto[1]=divmod(sto[1],a[i])
    if l[i]==1:
        sto[1]+=sto[0]*a[i]
        sto[0]=0
if sto[0]!=0:
    for i in range(n+2):
        if l[n+2-i]==-1:
            print(sto[1]+sto[0]*a[n+2-1])
            exit()
else:
    print(sto[1])

Submission status: Runtime Error

Solution code:
N = int(input())
a = list(map(int, input().split()))
slst = []
llst = []
stmp = 201
ltmp = 0
for i in a:
    if stmp >= i:
        stmp = i
    else:
        slst.append(stmp)
        stmp = i

for i in reversed(a):
    if ltmp <= i:
        ltmp = i
    else:
        llst.insert(0, ltmp)
        ltmp = i

total = 1000
for i in range(len(slst)):
    cnt = total // slst[i]
    total -= (slst[i] * cnt)
    total += (llst[i] * cnt)

print(total)N = int(input())
a = list(map(int, input().split()))
slst = []
llst = []
stmp = 201
ltmp = 0
for i in a:
    if stmp >= i:
        stmp = i
    else:
        slst.append(stmp)
        stmp = i

for i in reversed(a):
    if ltmp <= i:
        ltmp = i
    else:
        llst.insert(0, ltmp)
        ltmp = i

total = 1000
for i in range(len(slst)):
    cnt = total // slst[i]
    total -= (slst[i] * cnt)
    total += (llst[i] * cnt)

print(total)

Submission status: Runtime Error

Solution code:
n = int(input())
a = list(map(int, input().split()))
dp = [[[-1] * (10 ** 4) for _ in range(n)] for _ in range(2)]
dp[0][0][1000] = 0
dp[1][0][1000] = 0
for i in range(n):
    for j in range(10 ** 4):
        dp[0][i + 1][j], dp[1][i + 1][j] = dp[0][i][j], dp[1][i][j]
    for j in range(10 ** 4):
        u, v = dp[0][i][j], dp[1][i][j]
        if max(u, v) < 0:
            continue
        dp[0][i + 1][j] = u
        dp[1][i + 1][j] = v
        # print(i, j, u, v)
        dp[0][i + 1][j + max(u, v) * a[i]] = 0
        dp[1][i + 1][j % a[i]] = max(u, v) + j // a[i]
ans = 0
for j in range(10 ** 4):
    if dp[0][n][j] != -1 or dp[1][n][j] != -1:
        ans = max(ans, j)
print(ans)

Submission status: Runtime Error

Solution code:
n = int(input())
a = list(map(int, input().split()))
dp = [[[-1] * (10 ** 4) for _ in range(80)] for _ in range(2)]
dp[0][0][1000] = 0
dp[1][0][1000] = 0
for i in range(n):
    for j in range(10 ** 4):
        dp[0][i + 1][j], dp[1][i + 1][j] = dp[0][i][j], dp[1][i][j]
    for j in range(10 ** 4):
        u, v = dp[0][i][j], dp[1][i][j]
        if max(u, v) < 0:
            continue
        dp[0][i + 1][j] = u
        dp[1][i + 1][j] = v
        # print(i, j, u, v)
        dp[0][i + 1][j + max(u, v) * a[i]] = 0
        dp[1][i + 1][j % a[i]] = max(u, v) + j // a[i]
ans = 0
for j in range(10 ** 4):
    if dp[0][n][j] != -1 or dp[1][n][j] != -1:
        ans = max(ans, j)
print(ans)

Submission status: Runtime Error

Solution code:
N = int(input())
A = list(map(int,input().split()))

A = [A[0]] + [b for a,b in zip(A,A[1:]) if a != b]

diff = [a-b for a,b in zip(A[1:],A)]
B = [A[0]] if diff[0] > 0 else []

for i,(d1,d2) in enumerate(zip(diff, diff[1:]),start=1):
    if d1*d2 < 0:
        B.append(A[i])
B.append(A[-1])
t = iter(B)
c = 1000
for a,b in zip(t,t):
    c = c//a*b + c%a

print(c)

Submission status: Runtime Error

Solution code:
n = int(input())
given_a = list(map(int, input().split()))

money = 1000
kabu = 0

a = []

for kabuka in given_a:
    if len(a) > 0 and a[-1] == kabuka:
        continue
    else:
        a.append(kabuka)

n = len(a)
for i in range(n):
   if i == 0:
       if a[i+1] < a[i]:
           continue
       else:
           kabu += money // a[i]
           money %= a[i]
   elif i == n-1:
       money += kabu * a[i]
       kabu = 0
   else:
       if a[i-1] < a[i] and a[i] > a[i+1]:
           money += kabu * a[i]
           kabu = 0
       if a[i-1] > a[i] and a[i] < a[i+1]:
           kabu += money // a[i]
           money %= a[i]

print(money)

Submission status: Runtime Error

Solution code:
INF = 10 ** 10
n = int(input())
a = [INF] + list(map(int, input().split())) + [-INF]
l = []
for i in range(n):
    if len(l) % 2 == 0:
        if a[i] > a[i + 1] <= a[i + 2]:
            l.append(a[i + 1])
    else:
        if a[i] < a[i + 1] >= a[i + 2]:
            l.append(a[i + 1])
t = 1000
for i in range(0, len(l), 2):
    t = t // l[i] * l[i + 1] + t % l[i]
print(t)