Problem:


Score : 600 points

Problem Statement

The squirrel Chokudai has N acorns.
One day, he decides to do some trades in multiple precious metal exchanges to make more acorns.

His plan is as follows:

Get out of the nest with N acorns in his hands.

Go to Exchange A and do some trades.

Go to Exchange B and do some trades.

Go to Exchange A and do some trades.

Go back to the nest.

In Exchange X (X = A, B), he can perform the following operations any integer number of times (possibly zero) in any order:

Lose g_{X} acorns and gain 1 gram of gold.

Gain g_{X} acorns and lose 1 gram of gold.

Lose s_{X} acorns and gain 1 gram of silver.

Gain s_{X} acorns and lose 1 gram of silver.

Lose b_{X} acorns and gain 1 gram of bronze.

Gain b_{X} acorns and lose 1 gram of bronze.

Naturally, he cannot perform an operation that would leave him with a negative amount of acorns, gold, silver, or bronze.

What is the maximum number of acorns that he can bring to the nest?
Note that gold, silver, or bronze brought to the nest would be worthless because he is just a squirrel.

Constraints

1 \leq N \leq 5000

1 \leq g_{X} \leq 5000

1 \leq s_{X} \leq 5000

1 \leq b_{X} \leq 5000

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
g_A s_A b_A
g_B s_B b_B

Output

Print the maximum number of acorns that Chokudai can bring to the nest.

Sample Input 1

23
1 1 1
2 1 1

Sample Output 1

46

He can bring 46 acorns to the nest, as follows:

In Exchange A, trade 23 acorns for 23 grams of gold. {acorns, gold, silver, bronze}={ 0,23,0,0 }

In Exchange B, trade 23 grams of gold for 46 acorns. {acorns, gold, silver, bronze}={ 46,0,0,0 }

In Exchange A, trade nothing. {acorns, gold, silver, bronze}={ 46,0,0,0 }

He cannot have 47 or more acorns, so the answer is 46.



Sample input:
23
1 1 1
2 1 1


Sample output:
46

Submission status: Time Limit Exceeded

Solution code:
rr = raw_input
rrm = lambda: map(int, rr().split())

def solve(N, A, B):
    if cmp(A[0], B[0]) != cmp(A[1], B[1]):
        A[1],A[2] = A[2],A[1]
        B[1],B[2] = B[2],B[1]
    
    def exch1(N, A, B):
        # Have N, at A, going to B
        # what is most acorns can get at B?
        ans = N
        for g in xrange(N+1 if B[0]>=A[0] else 1):
            if g * A[0] > N: break
            for s in xrange(N+1 if B[1]>=A[1] else 1):
                cost = g*A[0] + s*A[1]
                if cost > N: break
                bns = N + g*(B[0] - A[0]) + s*(B[1] - A[1])
                if bns > ans: ans = bns
                b = (N-cost) / A[2]
                bns = N + g*(B[0] - A[0]) + s*(B[1] - A[1]) + b*(B[2] - A[2])
                if bns > ans: ans = bns
        return ans
    N2 = exch1(N, A, B)
    N3 = exch1(N2, B, A)
    return N3
                
N = int(rr())
A = rrm()
B = rrm()
print solve(N, A, B)

Submission status: Time Limit Exceeded

Solution code:
rr = raw_input
rrm = lambda: map(int, rr().split())

def solve(N, A, B):
    def exch1(N, A, B):
        # Have N, at A, going to B
        # what is most acorns can get at B?
        ans = N
        for g in xrange(N+1 if B[0]>A[0] else 1):
            if g * A[0] > N: break
            for s in xrange(N+1 if B[1]>A[1] else 1):
                cost = g*A[0] + s*A[1]
                if cost > N: break
                bns = N + g*(B[0] - A[0]) + s*(B[1] - A[1])
                if bns > ans: ans = bns
                b = (N-cost) / A[2]
                bns = N + g*(B[0] - A[0]) + s*(B[1] - A[1]) + b*(B[2] - A[2])
                if bns > ans: ans = bns
        return ans
    N2 = exch1(N, A, B)
    N3 = exch1(N2, B, A)
    return N3
                
N = int(rr())
A = rrm()
B = rrm()
print solve(N, A, B)

Submission status: Time Limit Exceeded

Solution code:
# 新ステージでは、一度全部どんぐりに直してから換金を始めるとしてよい

def F(N, A, B):
  # N個のどんぐりを、Aで換金してからBに持っていく
  # Bでどんぐりに直す
  dp = [0] * (N+1)
  for n in range(N+1):
    x = n
    for j in range(3):
      if n >= A[j]:
        y = dp[n-A[j]] + B[j]
        if x < y:
          x = y
    dp[n] = x
  return dp[N]

N = int(input())
A = [int(x) for x in input().split()]
B = [int(x) for x in input().split()]

answer = F(F(N,A,B),B,A)
print(answer)

Submission status: Time Limit Exceeded

Solution code:
rr = raw_input
rrm = lambda: map(int, rr().split())

def solve(N, A, B):
    def exch1(N, A, B):
        # Have N, at A, going to B
        # what is most acorns can get at B?
        ans = N
        for g in xrange(N+1):
            if g * A[0] > N: break
            for s in xrange(N+1):
                cost = g*A[0] + s*A[1]
                if cost > N: break
                bns = N + g*(B[0] - A[0]) + s*(B[1] - A[1])
                if bns > ans: ans = bns
                b = (N-cost) / A[2]
                bns = N + g*(B[0] - A[0]) + s*(B[1] - A[1]) + b*(B[2] - A[2])
                if bns > ans: ans = bns
        return ans
    N2 = exch1(N, A, B)
    N3 = exch1(N2, B, A)
    return N3
                
N = int(rr())
A = rrm()
B = rrm()
print solve(N, A, B)

Submission status: Accepted

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

cur = N
dp = list(range(cur + 1))
for i in range(cur + 1):
    if i >= As[0]:
        if dp[i] < dp[i - As[0]] + Bs[0]:
            dp[i] = dp[i - As[0]] + Bs[0]
    if i >= As[1]:
        if dp[i] < dp[i - As[1]] + Bs[1]:
            dp[i] = dp[i - As[1]] + Bs[1]
    if i >= As[2]:
        if dp[i] < dp[i - As[2]] + Bs[2]:
            dp[i] = dp[i - As[2]] + Bs[2]

cur = dp[cur]
dp = list(range(cur + 1))
As, Bs = Bs, As
for i in range(cur + 1):
    if i >= As[0]:
        if dp[i] < dp[i - As[0]] + Bs[0]:
            dp[i] = dp[i - As[0]] + Bs[0]
    if i >= As[1]:
        if dp[i] < dp[i - As[1]] + Bs[1]:
            dp[i] = dp[i - As[1]] + Bs[1]
    if i >= As[2]:
        if dp[i] < dp[i - As[2]] + Bs[2]:
            dp[i] = dp[i - As[2]] + Bs[2]


print(dp[cur])

Submission status: Accepted

Solution code:
def main(n,A,B):
  AB=[[a,b] for a,b in zip(A,B)]
  dp=[0]*(n+1)
  dp[0]=n
  # dp[i]:どんぐりをi個交換した時の最大獲得どんぐり
  for a,b in AB:
    #if a>b:continue
    ddp=[0]*(n+1)
    ddp[0]=n
    for i in range(n+1):
      ddp[i]=max(dp[i],ddp[i-a]+b-a if i-a>=0 else 0)
    dp=ddp
  n=max(dp)
  dp=[0]*(n+1)
  dp[0]=n
  for a,b in AB:
    if b>a:continue
    ddp=[0]*(n+1)
    ddp[0]=n
    for i in range(n+1):
      ddp[i]=max(dp[i],ddp[i-b]+a-b if i-b>=0 else 0)
    dp=ddp
  return max(dp)

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

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
N = int(input())
ga,sa,ba = map(int,input().split())
gb,sb,bb = map(int,input().split())

t1 = []
t2 = []
if ga < gb:
    t1.append((ga,gb))
else:
    t2.append((gb,ga))
if sa < sb:
    t1.append((sa,sb))
else:
    t2.append((sb,sa))
if ba < bb:
    t1.append((ba,bb))
else:
    t2.append((bb,ba))

dp = [0] * (N+1)
N1 = N
for i in range(1,N+1):
    for c,r in t1:
        if c <= i:
            dp[i] = max(dp[i], dp[i-c] + r)
    N1 = max(N1, N-i+dp[i])

ans = N1
dp = [0] * (N1+1)
for i in range(1,N1+1):
    for c,r in t2:
        if c <= i:
            dp[i] = max(dp[i], dp[i-c] + r)
    ans = max(ans, N1-i+dp[i])

print(ans)

Submission status: Accepted

Solution code:
N = int(input())
A = list(map(int,input().split()))
B = list(map(int,input().split()))
dp = [_ for _ in range(N+1)]
for i in range(N+1):
  donguri = dp[i]
  if i >= A[0]:
    gold = dp[i-A[0]]+B[0]
  else:
    gold = 0
  if i >= A[1]:
    silver = dp[i-A[1]]+B[1]
  else:
    silver = 0
  if i >= A[2]:
    bronze = dp[i-A[2]]+B[2]
  else:
    bronze = 0
  dp[i] = max(donguri,gold,silver,bronze)
M = dp[N]
#print(dp)
dp = [_ for _ in range(M+1)]
for i in range(M+1):
  donguri = dp[i]
  if i >= B[0]:
    gold = dp[i-B[0]]+A[0]
  else:
    gold = 0
  if i >= B[1]:
    silver = dp[i-B[1]]+A[1]
  else:
    silver = 0
  if i >= B[2]:
    bronze = dp[i-B[2]]+A[2]
  else:
    bronze = 0
  dp[i] = max(donguri,gold,silver,bronze)
ans = dp[M]
print(ans)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
N = int(input())
a = tuple(map(int, input().split()))
b = tuple(map(int, input().split()))
dp = [0] * (N + 1)
res = 0
for i in range(N, -1, -1):
  for j in range(3):
    if a[j] < b[j] and (i - a[j] >= 0): dp[i - a[j]] = max(dp[i - a[j]], dp[i] + b[j])
  res = max(res, i + dp[i])
#print(res)
d = []
for i in range(3):
  if a[i] > b[i]: d.append((b[i], a[i]))
if len(d) == 0: print(res)
elif len(d) == 1: print(res // d[0][0] * d[0][1] + res % d[0][0])
elif len(d) == 2:
  dp = [0] * (res + 1)
  rres = 0
  for i in range(res, -1, -1):
    for x, y in d:
      if i - x >= 0: dp[i - x] = max(dp[i - x], dp[i] + y)
    rres = max(rres, i + dp[i])
  print(rres)
else:
  dp = [0] * (res + 1)
  rres = 0
  for i in range(res, -1, -1):
    for j in range(3):
      if a[j] > b[j] and (i - b[j] >= 0): dp[i - b[j]] = max(dp[i - b[j]], dp[i] + a[j])
    rres = max(rres, i + dp[i])
  print(rres)

Submission status: Accepted

Solution code:
mod = 1000000007
eps = 10**-9
inf = 10**9


def main():
    import sys
    input = sys.stdin.readline

    N = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))

    dp = [[-inf] * (N+1) for _ in range(4)]
    dp[0][N] = N
    for i in range(3):
        for j in range(N, -1, -1):
            dp[i+1][j] = max(dp[i+1][j], dp[i][j])
            if j - A[i] >= 0:
                dp[i+1][j-A[i]] = max(dp[i+1][j-A[i]], dp[i+1][j] + B[i] - A[i])
    N = max(dp[-1])
    dp = [[-inf] * (N + 1) for _ in range(4)]
    dp[0][N] = N
    for i in range(3):
        for j in range(N, -1, -1):
            dp[i + 1][j] = max(dp[i + 1][j], dp[i][j])
            if j - B[i] >= 0:
                dp[i + 1][j - B[i]] = max(dp[i + 1][j - B[i]], dp[i+1][j] + A[i] - B[i])
    print(max(dp[-1]))


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline

n = int(input())
A = tuple(map(int, input().split()))
B = tuple(map(int, input().split()))
def f(n):
  dp = list(range(n+1))
  for a, b in zip(A, B):
    if b <= a:
      continue
    for i in range(n+1):
      if i-a >= 0:
        dp[i] = max(dp[i], dp[i-a]+b)
  return dp[n]
m = f(n)
A, B = B, A
ans = f(m)
print(ans)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline

n = int(input())
A = tuple(map(int, input().split()))
B = tuple(map(int, input().split()))
def f(n):
  dp = list(range(n+1))
  for a, b in zip(A, B):
    if b <= a:
      continue
    for i in range(n+1):
      if i-a >= 0:
        dp[i] = max(dp[i], dp[i-a]+b)
  return max(dp)
m = f(n)
A, B = B, A
ans = f(m)
print(ans)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline

n = int(input())
A = tuple(map(int, input().split()))
B = tuple(map(int, input().split()))
def f(n):
  dp = list(range(n+1))
  for a, b in zip(A, B):
    for i in range(n+1):
      if i-a >= 0:
        dp[i] = max(dp[i], dp[i-a]+b)
  return max(dp)
m = f(n)
A, B = B, A
ans = f(m)
print(ans)

Submission status: Accepted

Solution code:
N=int(input())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
DP=[[0]*(N+1) for i in range(4)]
for i in range(3):
  for j in range(N+1):
    DP[i+1][j]=max(DP[i][j],DP[i+1][j])
    if j+A[i]<=N:
      DP[i][j+A[i]]=max(DP[i][j+A[i]],DP[i][j]+B[i])
for i in range(N+1):
  N=max(N,i+DP[3][-i-1])
DP=[[0]*(N+1) for i in range(4)]
for i in range(3):
  for j in range(N+1):
    DP[i+1][j]=max(DP[i][j],DP[i+1][j])
    if j+B[i]<=N:
      DP[i][j+B[i]]=max(DP[i][j+B[i]],DP[i][j]+A[i])
for i in range(N+1):
  N=max(N,i+DP[3][-i-1])
print(N)

Submission status: Accepted

Solution code:
import math
#import numpy as np
import queue
from collections import deque,defaultdict
import heapq as hpq
from sys import stdin,setrecursionlimit
#from scipy.sparse.csgraph import dijkstra
#from scipy.sparse import csr_matrix
ipt = stdin.readline
setrecursionlimit(10**7)

def main():
    n = int(ipt())
    ga,sa,ba = map(int,ipt().split())
    gb,sb,bb = map(int,ipt().split())

    dp = [0]*(5005)
    for i in range(n+1):
        dp[i] = dp[i-1]
        if i >= ga and dp[i] < (gb-ga)+dp[i-ga]:
            dp[i] = gb-ga+dp[i-ga]
        if i >= sa and dp[i] < (sb-sa)+dp[i-sa]:
            dp[i] = sb-sa+dp[i-sa]
        if i >= ba and dp[i] < (bb-ba)+dp[i-ba]:
            dp[i] = bb-ba+dp[i-ba]
    ni = n+dp[n]

    dp = [0]*max(5005,ni+5)
    for i in range(ni+1):
        dp[i] = dp[i-1]
        if i >= gb and dp[i] < (ga-gb)+dp[i-gb]:
            dp[i] = ga-gb+dp[i-gb]
        if i >= sb and dp[i] < (sa-sb)+dp[i-sb]:
            dp[i] = sa-sb+dp[i-sb]
        if i >= bb and dp[i] < (ba-bb)+dp[i-bb]:
            dp[i] = ba-bb+dp[i-bb]
    print(ni+dp[ni])

    return None

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")


n = int(input())
ga,sa,ba = map(int, input().split())
gb,sb,bb = map(int, input().split())

def sub1(n, ga, gb):
    return n - (n//ga)*ga + (n//ga)*gb
def sub2(n, ga, gb, sa, sb):
    ans = -1
    for i in range((n//sa)+1):
        val = sub1(n - (i*sa), ga, gb) + (i*sb)
        ans = max(ans, val)
    return ans
def sub3(n, ga, gb, sa, sb, ba, bb):
    ans = -1
    for i in range((n//ba)+1):
        val = sub2(n - (i*ba), ga, gb, sa, sb) + (i*bb)
        ans = max(ans, val)
    return ans

arg1 = []
arg2 = []
for a,b in [(ga,gb), (sa,sb), (ba,bb)]:
    if a<b:
        arg1.extend([a,b])
    elif a>b:
        arg2.extend([b,a])
d = {
    0: lambda n: n,
    1: sub1,
    2: sub2,
    3: sub3
}
nn = d[len(arg1)//2](n, *arg1)
nnn = d[len(arg2)//2](nn, *arg2)
print(nnn)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline

def I(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(map(int, input().split()))

def main():
    mod=10**9+7
    N=I()
    A=LI()
    B=LI()
    
    dp=[0]*(N+1)
    #i番目まで見てj個使って何個増やせたか
    
    v=[]
    for i in range(3):
        vv=B[i]-A[i]#差分だけ増える
        v.append(vv)
        
    for i in range(3):
        for j in range(A[i],N+1,1):
            dp[j]=max(dp[j-A[i]]+v[i],dp[j])
            
    N2=N#A=>Bでどこまで増えたか
    for j in range(N+1):
        temp=N+dp[j]
        N2=max(N2,temp)

        
    #B=>A
    dp2=[0]*(N2+1)
    for i in range(3):
        for j in range(B[i],N2+1,1):
            dp2[j]=max(dp2[j-B[i]]-v[i],dp2[j])#価値が逆転
            
    ans=N2
    for j in range(N2+1):
        temp=N2+dp2[j]
        ans=max(ans,temp)
        
    print(ans)
            
  
            

main()

Submission status: Accepted

Solution code:
# coding: utf-8
import sys

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

"""
dp, 取引所Bで一度全てacornにする
取引所Aでの通貨の値段を重さとする
"""

N = ir()
A = lr()
B = lr()
dp = [x for x in range(N+1)]
for a, b in zip(A, B):
    for x in range(N):
        if x + a <= N:
            dp[x+a] = max(dp[x+a], dp[x] + b)

half_way = max(dp)
dp = [x for x in range(half_way+1)]
A, B = B, A
for a, b in zip(A, B):
    for x in range(half_way):
        if x + a <= half_way:
            dp[x+a] = max(dp[x+a], dp[x] + b)

answer = max(dp)
print(answer)

# 56

Submission status: Accepted

Solution code:
n = int(input())
ga, sa, ba = map(int, input().split())
gb, sb, bb = map(int, input().split())
dp = [0] * (n + 1)
for i in range(n):
    if i + ga <= n:
        dp[i + ga] = max(dp[i + ga], dp[i] + gb)
    if i + sa <= n:
        dp[i + sa] = max(dp[i + sa], dp[i] + sb)
    if i + ba <= n:
        dp[i + ba] = max(dp[i + ba], dp[i] + bb)
ans = 0
for i in range(n + 1):
    ans = max(ans, dp[i] + n - i)
p = min(25000024, ans)
dp = [0] * (p + 1)
for i in range(p):
    if i + gb <= p:
        dp[i + gb] = max(dp[i + gb], dp[i] + ga)
    if i + sb <= p:
        dp[i + sb] = max(dp[i + sb], dp[i] + sa)
    if i + bb <= p:
        dp[i + bb] = max(dp[i + bb], dp[i] + ba)
res = 0
for i in range(p + 1):
    res = max(res, dp[i] + ans - i)
print(res)

Submission status: Accepted

Solution code:
import sys

sys.setrecursionlimit(10 ** 8)
ni = lambda: int(sys.stdin.readline())
nm = lambda: map(int, sys.stdin.readline().split())

N = ni()
g1, s1, b1 = nm()
g2, s2, b2 = nm()

INF = 10 ** 15


def solve():
    x1 = [g1, s1, b1]
    x2 = [g2, s2, b2]

    # dp[i] := max future donguri when we use i donguri
    dp = [-INF] * (N + 1)
    dp[0] = N
    for i in range(3):
        t1 = x1[i]
        t2 = x2[i]
        if t1 >= t2:
            continue
        for j in range(t1, N + 1):
            r = dp[j - t1] - t1
            if r >= 0 and dp[j] < r + t2:
                dp[j] = r + t2

    don = max(dp)
    dp = [0] * (don + 1)
    dp[0] = don
    for i in range(3):
        t1 = x1[i]
        t2 = x2[i]
        if t1 <= t2:
            continue
        for j in range(t2, don + 1):
            r = dp[j - t2] - t2
            if r >= 0 and dp[j] < r + t1:
                dp[j] = r + t1
    return max(dp)


print(solve())

Submission status: Accepted

Solution code:
def solve(n, a, b):
  ab = [(ai, bi) for ai, bi in zip(a, b) if ai < bi]
  if len(ab) == 0:
    return n
  elif len(ab) == 1:
    a0, b0 = ab[0]
    return (n//a0)*b0 + n%a0
  elif len(ab) == 2:
    (a0, b0), (a1, b1) = ab
    if b0/a0 < b1/a1:
      a0, b0, a1, b1 = a1, b1, a0, b0
    return max(((n-a1*i)//a0)*b0 + (n-a1*i)%a0 + i*b1 for i in range(a0))
  else:
    dp = [j for j in range(n+1)]
    for ai, bi in ab:
      for j in range(ai, n+1):
        dp[j] = max(dp[j], dp[j-ai]+bi)
    return dp[-1]

N = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))

N = solve(N, A, B)
N = solve(N, B, A)
print(N)

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline

N = int(input())
ga, sa, ba = map(int, input().split())
gb, sb, bb = map(int, input().split())
INF = 10**18
A = [INF] * 3
B = [INF] * 3
values = [abs(ga - gb), abs(sa - sb), abs(ba - bb)]
if ga < gb:
    A[0] = ga
elif ga > gb:
    B[0] = gb
if sa < sb:
    A[1] = sa
elif sa > sb:
    B[1] = sb
if ba < bb:
    A[2] = ba
elif ba > bb:
    B[2] = bb

def calc(X):
    dp = [0] * (N+1)
    dp[0] = 0
    for x, v in zip(X, values):
        for i in range(N+1-x):
            dp[i+x] = max(dp[i+x], dp[i] + v)
    return dp[-1]

N += calc(A)
N += calc(B)
print(N)

Submission status: Accepted

Solution code:
import sys

sys.setrecursionlimit(10 ** 7)
rl = sys.stdin.readline


def solve():
    N = int(rl())
    ga, sa, ba = map(int, rl().split())
    gb, sb, bb = map(int, rl().split())
    
    dp1 = [0] * 30000000
    dp1[0] = N
    M = N
    for i in range(N + 1):
        dp1[i + ga] = max(dp1[i + ga], dp1[i] - ga + gb)
        dp1[i + sa] = max(dp1[i + sa], dp1[i] - sa + sb)
        dp1[i + ba] = max(dp1[i + ba], dp1[i] - ba + bb)
        M = max(M, dp1[i])
    
    dp2 = [0] * 30000000
    dp2[0] = M
    ans = M
    for i in range(M + 1):
        dp2[i + gb] = max(dp2[i + gb], dp2[i] - gb + ga)
        dp2[i + sb] = max(dp2[i + sb], dp2[i] - sb + sa)
        dp2[i + bb] = max(dp2[i + bb], dp2[i] - bb + ba)
        ans = max(ans, dp2[i])
    print(ans)


if __name__ == '__main__':
    solve()

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.buffer.readline

def main():
    N = int(input())

    a = list(map(int,input().split()))
    b = list(map(int,input().split()))

    dp = [0]*(N+1)
	
    for ua,ub in zip(a,b):
        for i in range(N):
            if i+ua > N:
                continue
            dp[i+ua] = max(dp[i+ua],dp[i]+(ub-ua))
    
    N += dp[-1]
    dp = [0]*(N+1)

    for ua,ub in zip(a,b):
        for i in range(N):
            if i+ub > N:
                continue
            dp[i+ub] = max(dp[i+ub],dp[i]+(ua-ub))
            
    print(N+dp[-1])
    
if __name__ == "__main__":
	main()

Submission status: Accepted

Solution code:
N=int(input())
ga,sa,ba=map(int,input().split())
gb,sb,bb=map(int,input().split())

check=(gb>ga)+(sb>sa)+(bb>ba)
if check==3:
    donguri=N

    inc=0
    for i in range(0,donguri//ga+1):
        x=(ga<gb)*i
        for j in range(0,donguri//sa+1):
            y=(sa<sb)*j
            if donguri>=x*ga+y*sa:
                z=((donguri-x*ga-y*sa)//ba)*(bb>ba)
                inc=max(inc,x*(gb-ga)+y*(sb-sa)+z*(bb-ba))

    donguri+=inc
    print(donguri)
elif check==0:
    donguri=N
    inc=0
    for i in range(0,donguri//gb+1):
        x=(ga>gb)*i
        for j in range(0,donguri//sb+1):
            y=(sa>sb)*j
            if donguri>=x*gb+y*sb:
                z=((donguri-x*gb-y*sb)//bb)*(ba>bb)
                inc=max(inc,-x*(gb-ga)-y*(sb-sa)-z*(bb-ba))

    donguri+=inc
    print(donguri)

elif check==2:
    donguri=N
    inc=0
    for i in range(0,donguri//ga+1):
        x=(ga<gb)*i
        for j in range(0,donguri//sa+1):
            y=(sa<sb)*j
            if donguri>=x*ga+y*sa:
                z=((donguri-x*ga-y*sa)//ba)*(bb>ba)
                inc=max(inc,x*(gb-ga)+y*(sb-sa)+z*(bb-ba))

    donguri+=inc
    if ga>gb:
        plus=(donguri//gb)*(ga-gb)
        print(donguri+plus)
    elif sa>sb:
        plus=(donguri//sb)*(sa-sb)
        print(donguri+plus)
    elif ba>bb:
        plus=(donguri//bb)*(ba-bb)
        print(donguri+plus)
    else:
        print(donguri)

else:
    donguri=N
    inc=0
    if ga<gb:
        plus=(donguri//ga)*(gb-ga)
        donguri+=plus
        if sa>sb:
            for i in range(0,donguri//sb+1):
                j=(donguri-i*sb)//bb
                inc=max(inc,i*(sa-sb)+j*(ba-bb))
            print(donguri+inc)
        else:
            inc=(donguri//bb)*(ba-bb)
            print(donguri+inc)

    elif sa<sb:
        plus=(donguri//sa)*(sb-sa)
        donguri+=plus
        if ga>gb:
            for i in range(0,donguri//gb+1):
                j=(donguri-i*gb)//bb
                inc=max(inc,i*(ga-gb)+j*(ba-bb))
            print(donguri+inc)
        else:
            inc=(donguri//bb)*(ba-bb)
            print(donguri+inc)
    else:
        plus=(donguri//ba)*(bb-ba)
        donguri+=plus
        if ga>gb:
            for i in range(0,donguri//gb+1):
                j=(donguri-i*gb)//sb
                inc=max(inc,i*(ga-gb)+j*(sa-sb))
            print(donguri+inc)
        else:
            inc=(donguri//sb)*(sa-sb)
            print(donguri+inc)

Submission status: Accepted

Solution code:
n = int(input())
a = list(map(int,input().split()))
b = list(map(int,input().split()))
change_a = [i for i in range(3) if a[i] < b[i]]
change_b = [i for i in range(3) if a[i] > b[i]]
if len(change_a) == 0:
  if len(change_b) == 0:
    print(n)
  elif len(change_b) == 1:
    i = n // b[change_b[0]]
    n = n % b[change_b[0]]
    n += i * a[change_b[0]]
    print(n)
  elif len(change_b) == 2:
    tmp = n
    for i in range(5001):
      m = n
      m -= i * b[change_b[0]]
      if m < 0:
        break
      j = m // b[change_b[1]]
      m = m % b[change_b[1]]
      m += i * a[change_b[0]] + j * a[change_b[1]]
      tmp = max(tmp, m)
    print(tmp)
  else:      
    tmp = n
    for i in range(5001):
      for j in range(5001):
        m = n
        m -= i * b[change_b[0]]
        if m < 0:
          break
        m -= j * b[change_b[1]]
        if m < 0:
          break
        k = m // b[change_b[2]]
        m = m % b[change_b[2]]
        m += i * a[change_b[0]] + j * a[change_b[1]] + k * a[change_b[2]]
        tmp = max(tmp, m)
    print(tmp)
elif len(change_a) == 1:
  i = n // a[change_a[0]]
  n = n % a[change_a[0]]
  n += i * b[change_a[0]]
  if len(change_b) == 0:
    print(n)
  elif len(change_b) == 1:
    i = n // b[change_b[0]]
    n = n % b[change_b[0]]
    n += i * a[change_b[0]]
    print(n)
  elif len(change_b) == 2:
    tmp = n
    for i in range(n // b[change_b[0]] + 1):
      m = n
      m -= i * b[change_b[0]]
      if m < 0:
        break
      j = m // b[change_b[1]]
      m = m % b[change_b[1]]
      m += i * a[change_b[0]] + j * a[change_b[1]]
      tmp = max(tmp, m)
    print(tmp)
elif len(change_a) == 2:
  tmp = n
  for i in range(5001):
    m = n
    m -= i * a[change_a[0]]
    if m < 0:
      break
    j = m // a[change_a[1]]
    m = m % a[change_a[1]]
    m += i * b[change_a[0]] + j * b[change_a[1]]
    tmp = max(tmp, m)
  n = tmp
  if len(change_b) == 0:
    print(n)
  elif len(change_b) == 1:
    i = n // b[change_b[0]]
    n = n % b[change_b[0]]
    n += i * a[change_b[0]]
    print(n)
else:    
  tmp = n
  for i in range(5001):
    for j in range(5001):
      m = n
      m -= i * a[change_a[0]]
      if m < 0:
        break
      m -= j * a[change_a[1]]
      if m < 0:
        break
      k = m // a[change_a[2]]
      m = m % a[change_a[2]]
      m += i * b[change_a[0]] + j * b[change_a[1]] + k * b[change_a[2]]
      tmp = max(tmp, m)
  print(tmp)

Submission status: Accepted

Solution code:
def examA():
    N = I()
    X = [LI()for _ in range(N)]
    l = 0; r = inf
    for _ in range(100):
        now = (l+r)/2
        x_l = -inf; x_r = inf
        y_l = -inf; y_r = inf
        for x,y,c in X:
            move = now / c
            x_l = max(x_l,x-move)
            x_r = min(x_r,x+move)
            y_l = max(y_l,y-move)
            y_r = min(y_r,y+move)
        if x_l<x_r and y_l<y_r:
            r = now
        else:
            l = now
    ans = r
    print(ans)
    return

def examB():
    N = I()
    C = LI()
    C.sort()
    base = pow(2,2*N-1,mod)
    inv = pow(2,mod-2,mod)
    ans = 0
    for i in range(N):
        cur = C[i]*base*(1+(N-1-i)*inv)
        ans += cur
        ans %= mod
    print(ans)
    return

def examC():
    N = I()
    Ag,As,Ab = LI()
    Bg,Bs,Bb = LI()
    dp = [i for i in range(N+1)]
    for i in range(N):
        if dp[i+1]<dp[i]:
            dp[i+1] = dp[i]
        if i+Ag<=N and dp[i+Ag]<dp[i]+Bg:
            dp[i+Ag] = dp[i]+Bg
        if i+As<=N and dp[i+As]<dp[i]+Bs:
            dp[i+As] = dp[i]+Bs
        if i+Ab<=N and dp[i+Ab]<dp[i]+Bb:
            dp[i+Ab] = dp[i]+Bb
    ne_N = dp[-1]
    #print(dp)
    dp2 = [i for i in range(ne_N+1)]
    for i in range(ne_N):
        if dp2[i+1]<dp2[i]:
            dp2[i+1] = dp2[i]
        if i+Bg<=ne_N and dp2[i+Bg]<dp2[i]+Ag:
            dp2[i+Bg] = dp2[i]+Ag
        if i+Bs<=ne_N and dp2[i+Bs]<dp2[i]+As:
            dp2[i+Bs] = dp2[i]+As
        if i+Bb<=ne_N and dp2[i+Bb]<dp2[i]+Ab:
            dp2[i+Bb] = dp2[i]+Ab
    ans = dp2[-1]
    print(ans)
    return


import sys,bisect,itertools,heapq,math,random
from copy import deepcopy
from heapq import heappop,heappush,heapify
from collections import Counter,defaultdict,deque
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
def I(): return int(readline())
def LI(): return list(map(int,readline().split()))
def LSI(): return list(map(str,sys.stdin.readline().split()))
def LS(): return sys.stdin.readline().split()
def SI(): return sys.stdin.readline().strip()
global mod,mod2,inf,alphabet,_ep
mod = 10**9 + 7
mod2 = 998244353
inf = 10**18
_ep = 10**(-7)
alphabet = [chr(ord('a') + i) for i in range(26)]

sys.setrecursionlimit(10**7)

if __name__ == '__main__':
    examC()

"""
142
12 9 1445 0 1
asd dfg hj o o
aidn
"""

Submission status: Accepted

Solution code:
def examA():
    N = I()
    X = [LI()for _ in range(N)]
    l = 0; r = inf
    while(r-l>_ep):
        now = (l+r)/2
        x_l = -inf; x_r = inf
        y_l = -inf; y_r = inf
        for x,y,c in X:
            move = now / c
            x_l = max(x_l,x-move)
            x_r = min(x_r,x+move)
            y_l = max(y_l,y-move)
            y_r = min(y_r,y+move)
        if x_l+_ep<x_r and y_l+_ep<y_r:
            r = now
        else:
            l = now
    ans = r
    print(ans)
    return

def examB():
    N = I()
    C = LI()
    C.sort()
    base = pow(2,2*N-1,mod)
    inv = pow(2,mod-2,mod)
    ans = 0
    for i in range(N):
        cur = C[i]*base*(1+(N-1-i)*inv)
        ans += cur
        ans %= mod
    print(ans)
    return

def examC():
    N = I()
    Ag,As,Ab = LI()
    Bg,Bs,Bb = LI()
    dp = [i for i in range(N+1)]
    for i in range(N):
        dp[i+1] = max(dp[i],dp[i+1])
        if i+Ag<=N:
            dp[i+Ag] = max(dp[i+Ag],dp[i]+Bg)
        if i+As<=N:
            dp[i+As] = max(dp[i+As],dp[i]+Bs)
        if i+Ab<=N:
            dp[i+Ab] = max(dp[i+Ab],dp[i]+Bb)
    ne_N = dp[-1]
    #print(dp)
    dp2 = [i for i in range(ne_N+1)]
    for i in range(ne_N):
        dp2[i+1] = max(dp2[i],dp2[i+1])
        if i+Bg<=ne_N:
            dp2[i+Bg] = max(dp2[i+Bg],dp2[i]+Ag)
        if i+Bs<=ne_N:
            dp2[i+Bs] = max(dp2[i+Bs],dp2[i]+As)
        if i+Bb<=ne_N:
            dp2[i+Bb] = max(dp2[i+Bb],dp2[i]+Ab)
    ans = dp2[-1]
    print(ans)
    return


import sys,bisect,itertools,heapq,math,random
from copy import deepcopy
from heapq import heappop,heappush,heapify
from collections import Counter,defaultdict,deque
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
def I(): return int(readline())
def LI(): return list(map(int,readline().split()))
def LSI(): return list(map(str,sys.stdin.readline().split()))
def LS(): return sys.stdin.readline().split()
def SI(): return sys.stdin.readline().strip()
global mod,mod2,inf,alphabet,_ep
mod = 10**9 + 7
mod2 = 998244353
inf = 10**18
_ep = 10**(-4)
alphabet = [chr(ord('a') + i) for i in range(26)]

sys.setrecursionlimit(10**7)

if __name__ == '__main__':
    examC()

"""
142
12 9 1445 0 1
asd dfg hj o o
aidn
"""

Submission status: Accepted

Solution code:
N=int(input())
A=list(map(int,input().split()))
B=list(map(int,input().split()))
l1=[i for i in range(3) if B[i]>A[i]]
l2=[i for i in range(3) if B[i]<A[i]]
r=[B[i]-A[i] for i in range(3)]
def b(l):
    global N
    if len(l)==3:
        M=0
        for i in range(N//A[0]+1):
            for j in range((N-i*A[0])//A[1]+1):
                k=(N-i*A[0]-j*A[1])//A[2]
                M=max(M,i*B[0]+j*B[1]+k*B[2]+(N-i*A[0]-j*A[1]-k*A[2]))
        N=M
    elif len(l)==2:
        M=0
        for i in range(N//A[l[0]]+1):
            j=(N-i*A[l[0]])//A[l[1]]
            M=max(M,i*B[l[0]]+j*B[l[1]]+(N-i*A[l[0]]-j*A[l[1]]))
        N=M
    elif len(l)==1:
        i=N//A[l[0]]
        N=i*B[l[0]]+N-i*A[l[0]]
def b2(l):
    global N
    if len(l)==3:
        M=0
        for i in range(N//B[0]+1):
            for j in range((N-i*B[0])//B[1]+1):
                k=(N-i*B[0]-j*B[1])//B[2]
                M=max(M,i*A[0]+j*A[1]+k*A[2]+(N-i*B[0]-j*B[1]-k*B[2]))
        N=M
    elif len(l)==2:
        M=0
        for i in range(N//B[l[0]]+1):
            j=(N-i*B[l[0]])//B[l[1]]
            M=max(M,i*A[l[0]]+j*A[l[1]]+(N-i*B[l[0]]-j*B[l[1]]))
        N=M
    elif len(l)==1:
        i=N//B[l[0]]
        N=i*A[l[0]]+N-i*B[l[0]]
b(l1)
r=list(map(lambda x: -x,r))
b2(l2)
print(N)

Submission status: Accepted

Solution code:
n= int(input())
gsb = [tuple(map(int,input().split())) for _ in range(2)]

def increase(num, gsb0, gsb1):
    dp = [ [num] * (num+1) for _ in range(3+1)]
    for i in range(1,4):
        w = gsb0[i-1]
        v = gsb1[i-1]
        for j in range(num+1):
            if(j < w):
                dp[i][j] = dp[i-1][j]
            else:
                dp[i][j] = max(dp[i-1][j], dp[i][j-w] + v-w)

    return(dp[-1][-1])

num = increase(n,gsb[0],gsb[1])
num = increase(num,gsb[1],gsb[0])

print(num)