Problem:
 Score : 400 points    Problem Statement Dolphin is planning to generate a small amount of a certain chemical substance C. In order to generate the substance C, he must prepare a solution which is a mixture of two substances A and B in the ratio of M_a:M_b . He does not have any stock of chemicals, however, so he will purchase some chemicals at a local pharmacy. The pharmacy sells N kinds of chemicals. For each kind of chemical, there is exactly one package of that chemical in stock. The package of chemical i contains a_i grams of the substance A and b_i grams of the substance B, and is sold for c_i yen (the currency of Japan). Dolphin will purchase some of these packages. For some reason, he must use all contents of the purchased packages to generate the substance C. Find the minimum amount of money required to generate the substance C. If it is not possible to generate the substance C by purchasing any combination of packages at the pharmacy, report that fact.      Constraints  1≦N≦40   1≦a_i,b_i≦10   1≦c_i≦100   1≦M_a,M_b≦10   gcd(M_a,M_b)=1  a_i , b_i , c_i , M_a and M_b are integers.         Input The input is given from Standard Input in the following format:  N  M_a  M_b  a_1  b_1  c_1  a_2  b_2  c_2  :  a_N  b_N  c_N       Output Print the minimum amount of money required to generate the substance C. If it is not possible to generate the substance C, print -1 instead.        Sample Input 1 3 1 1
1 2 1
2 1 2
3 3 10      Sample Output 1 3  The amount of money spent will be minimized by purchasing the packages of chemicals 1 and 2 . In this case, the mixture of the purchased chemicals will contain 3 grams of the substance A and 3 grams of the substance B, which are in the desired ratio: 3:3=1:1 . The total price of these packages is 3 yen.       Sample Input 2 1 1 10
10 10 10      Sample Output 2 -1  The ratio 1:10 of the two substances A and B cannot be satisfied by purchasing any combination of the packages. Thus, the output should be -1 .

Solution (Python):
def push(k,v):
    if k in dic:
        dic[k] = min(dic[k],v)
    else:
        dic[k] = v
n,x,y = map(int,str(input()).split(' '))
dic = {}
for i in range(0,n):
    a = list(map(int,str(input()).split(' ')))
    k,v =a[0]*y-a[1]*x,a[2]
    l = []
    for j in dic:
        l.append([j,dic[j]])
    for jj in l:
        push(jj[0]+k,jj[1]+v)
    push(k,v)
if 0 in dic:
    print(dic[0])
else:
    print('-1')

Solution (Python):
from math import isinf

N, Ma, Mb = map(int, input().split())
a,b,c = [],[],[]
aappend = a.append
bappend = b.append
cappend = c.append
for i in range(N):
    ai,bi,ci = map(int, input().split())
    aappend(ai)
    bappend(bi)
    cappend(ci)

W_MAX = 40*10
dp = [[float('inf')]*(W_MAX+1) for _ in range(W_MAX+1)]
dp[0][0] = 0

for i in range(N):
    for wa in reversed(range(W_MAX+1)):
        for wb in reversed(range(W_MAX+1)):
            if isinf(dp[wa][wb]): continue
            if wa+a[i]<=W_MAX and wb+b[i]<=W_MAX:
                dp[wa+a[i]][wb+b[i]] = min(dp[wa+a[i]][wb+b[i]],
                                           dp[wa][wb]+c[i])

ans = float('inf')
for wa in range(1, W_MAX+1):
    for wb in range(1, W_MAX+1):
        if wa*Mb == wb*Ma:
            ans = min(ans, dp[wa][wb])

if isinf(ans): ans = -1
print(ans)

Solution (Python):
from math import isinf

N, Ma, Mb = map(int, input().split())
a,b,c = [],[],[]
for i in range(N):
    ai,bi,ci = map(int, input().split())
    a.append(ai)
    b.append(bi)
    c.append(ci)

W_MAX = 40*10
dp = [[float('inf')]*(W_MAX+1) for _ in range(W_MAX+1)]
dp[0][0] = 0

for i in range(N):
    for wa in reversed(range(W_MAX+1)):
        for wb in reversed(range(W_MAX+1)):
            if isinf(dp[wa][wb]): continue
            if wa+a[i]<=W_MAX and wb+b[i]<=W_MAX:
                dp[wa+a[i]][wb+b[i]] = min(dp[wa+a[i]][wb+b[i]],
                                           dp[wa][wb]+c[i])

ans = float('inf')
for wa in range(1, W_MAX+1):
    for wb in range(1, W_MAX+1):
        if wa*Mb == wb*Ma:
            ans = min(ans, dp[wa][wb])

if isinf(ans): ans = -1
print(ans)

Solution (Python):
from math import isinf

N, Ma, Mb = map(int, input().split())
a = [0]*N
b = [0]*N
c = [0]*N
for i in range(N):
    a[i],b[i],c[i] = map(int, input().split())

W_MAX = 40*10
dp = [[float('inf')]*(W_MAX+1) for _ in range(W_MAX+1)]
dp[0][0] = 0

for i in range(N):
    for wa in reversed(range(W_MAX+1)):
        for wb in reversed(range(W_MAX+1)):
            if isinf(dp[wa][wb]): continue
            if wa+a[i]<=W_MAX and wb+b[i]<=W_MAX:
                dp[wa+a[i]][wb+b[i]] = min(dp[wa+a[i]][wb+b[i]],
                                           dp[wa][wb]+c[i])

ans = float('inf')
for wa in range(1, W_MAX+1):
    for wb in range(1, W_MAX+1):
        if wa*Mb == wb*Ma:
            ans = min(ans, dp[wa][wb])

if isinf(ans): ans = -1
print(ans)

Solution (Python):
G_MAX = 40*10
N_MAX = 40
INF = float('inf')

dp = [[[INF]*(G_MAX+1) for _ in range(G_MAX+1)] 
      for _ in range(N_MAX+1)]
N,Ma,Mb = map(int, input().split())
a,b,c = [],[],[]
for _ in range(N):
    ai,bi,ci = map(int, input().split())
    a.append(ai)
    b.append(bi)
    c.append(ci)

dp[0][0][0] = 0
from math import isinf
for i in range(N):
    for ca in range(G_MAX+1):
        for cb in range(G_MAX+1):
            if isinf(dp[i][ca][cb]): continue
            dp[i+1][ca][cb] = min(dp[i+1][ca][cb],
                                 dp[i][ca][cb])
            dp[i+1][ca+a[i]][cb+b[i]] = min(dp[i+1][ca+a[i]][cb+b[i]],
                                           dp[i][ca][cb]+c[i])
            
    
ans = INF
for ca in range(1,G_MAX+1):
    for cb in range(1,G_MAX+1):
        if ca*Mb==cb*Ma:
            ans = min(ans, dp[N][ca][cb])
            
if isinf(ans): ans = -1
print(ans)

Solution (Python):
G_MAX = 40*10
N_MAX = 40
INF = float('inf')

dp = [[[INF]*(G_MAX+1) for _ in range(G_MAX+1)] 
      for _ in range(N_MAX+1)]
N,Ma,Mb = map(int, input().split())
a,b,c = [],[],[]
for _ in range(N):
    ai,bi,ci = map(int, input().split())
    a.append(ai)
    b.append(bi)
    c.append(ci)

dp[0][0][0] = 0
from math import isinf
for i in range(N):
    for ca in range(G_MAX+1):
        for cb in range(G_MAX+1):
            if isinf(dp[i][ca][cb]): continue
            dp[i+1][ca][cb] = min(dp[i+1][ca][cb],
                                 dp[i][ca][cb])
            dp[i+1][ca+a[i]][cb+b[i]] = min(dp[i+1][ca+a[i]][cb+b[i]],
                                           dp[i][ca][cb]+c[i])
            
    
ans = INF
for ca in range(1,G_MAX+1):
    for cb in range(1,G_MAX+1):
        if ca*Mb==cb*Ma:
            ans = min(ans, dp[N][ca][cb])
            
if isinf(ans): ans = -1
print(ans)

Solution (Python):
N, Ma, Mb = map(int, input().split())
a = [0 for _ in range(N)]
b = [0 for _ in range(N)]
c = [0 for _ in range(N)]
for i in range(N):
    a[i], b[i], c[i] = map(int, input().split())
inf = 1000000
nmax = 40
abmax = 10
dp = [[[inf for _ in range(nmax * abmax + 1)] for _ in range(nmax * abmax + 1)] for _ in range(nmax + 1)]
dp[0][0][0] = 0
for i in range(N):
    for ca in range(nmax * abmax + 1):
        for cb in range(nmax * abmax + 1):
            if(dp[i][ca][cb] == inf):
                continue
            dp[i + 1][ca][cb] = min(dp[i + 1][ca][cb], dp[i][ca][cb])
            dp[i + 1][ca + a[i]][cb + b[i]] = min(dp[i + 1][ca + a[i]][cb + b[i]], dp[i][ca][cb] + c[i])
ans = inf
for ca in range(1, nmax * abmax + 1):
    for cb in range(1, nmax * abmax + 1):
        if ca * Mb == cb * Ma:
            ans = min(ans, dp[N][ca][cb])
print(-1 if ans == inf else ans)

Solution (Python):


from copy import deepcopy

ABMAX = 400
HUGE = 10 ** 12

def main():
    n, ma, mb = map(int, input().split())
    sold = []
    for i in range(n):
        a, b, c = map(int, input().split())
        sold.append((a, b, c))
    mincost = dp(sold, n)
    print(find_mincost(mincost, ma, mb))

def find_mincost(mincost, ma, mb):
    res = HUGE
    for mult in range(1, ABMAX):
        if ma * mult > ABMAX:
            break
        if mb * mult > ABMAX:
            break
        res = min(res, mincost[ma * mult][mb * mult])
    return -1 if res == HUGE else res

def dp(sold, n):
    
    mincost = [[HUGE for b in range(ABMAX + 1)] for a in range(ABMAX + 1)]
    mincost[0][0] = 0
    for a, b, c in sold:
        update(mincost, a, b, c)
    return mincost

def update(mincost, a, b, c):
    for ia in reversed(range(ABMAX + 1)):  
        for ib in reversed(range(ABMAX + 1)):
            na = ia + a
            nb = ib + b
            if na <= ABMAX and nb <= ABMAX:
                mincost[na][nb] = min(mincost[na][nb], mincost[ia][ib] + c)

main()

Solution (Python):


from copy import deepcopy

ABMAX = 400
HUGE = 10 ** 12

def main():
    n, ma, mb = map(int, input().split())
    sold = []
    for i in range(n):
        a, b, c = map(int, input().split())
        sold.append((a, b, c))
    mincost = dp(sold, n)
    print(find_mincost(mincost, ma, mb))

def find_mincost(mincost, ma, mb):
    res = HUGE
    for mult in range(1, ABMAX):
        if ma * mult > ABMAX:
            break
        if mb * mult > ABMAX:
            break
        res = min(res, mincost[ma * mult][mb * mult])
    return -1 if res == HUGE else res

def dp(sold, n):
    
    mincost = [[HUGE for b in range(ABMAX + 1)] for a in range(ABMAX + 1)]
    mincost[0][0] = 0
    for a, b, c in sold:
        mincost = update(mincost, a, b, c)
    return mincost

def update(mincost, a, b, c):
    for ia in reversed(range(ABMAX + 1)):  
        for ib in reversed(range(ABMAX + 1)):
            na = ia + a
            nb = ib + b
            if na <= ABMAX and nb <= ABMAX:
                mincost[na][nb] = min(mincost[na][nb], mincost[ia][ib] + c)
    return mincost

main()

Solution (Python):


from copy import deepcopy

ABMAX = 400
HUGE = 10 ** 12

def main():
    n, ma, mb = map(int, input().split())
    sold = []
    for i in range(n):
        a, b, c = map(int, input().split())
        sold.append((a, b, c))
    mincost = dp(sold, n)
    print(find_mincost(mincost, ma, mb))

def find_mincost(mincost, ma, mb):
    res = HUGE
    for mult in range(1, ABMAX):
        if ma * mult > ABMAX:
            break
        if mb * mult > ABMAX:
            break
        res = min(res, mincost[ma * mult][mb * mult])
    return -1 if res == HUGE else res

def dp(sold, n):
    
    mincost = [[HUGE for b in range(ABMAX + 1)] for a in range(ABMAX + 1)]
    mincost[0][0] = 0
    for a, b, c in sold:
        mincost = update(mincost, a, b, c)
    return mincost

def update(prevcost, a, b, c):
    mincost = deepcopy(prevcost)
    for ia in range(ABMAX + 1):  
        for ib in range(ABMAX + 1):
            na = ia + a
            nb = ib + b
            if na <= ABMAX and nb <= ABMAX:
                mincost[na][nb] = min(mincost[na][nb], prevcost[ia][ib] + c)
    return mincost

main()

Solution (Python):
n,Ma,Mb=map(int,input().split())
inf=float("inf")
dp=[[[inf]*401 for _ in range(401)] for _ in range(n+1)]
dp[0][0][0]=0

l=[tuple(map(int,input().split())) for _ in range(n)]

for i in range(1,n+1):
    for j in range(401):
        for k in range(401):
            a,b,c=l[i-1]
            dp[i][j][k]=min(dp[i][j][k],dp[i-1][j][k])
            if j-a>=0 and k-b>=0:
                dp[i][j][k]=min(dp[i][j][k],dp[i-1][j-a][k-b]+c)

ans=inf
for i in range(1,1+400//max(Ma,Mb)):
    ans=min(ans,dp[n][Ma*i][Mb*i])

print(ans if ans!=inf else -1)

Solution (Python):
n,Ma,Mb=map(int,input().split())
inf=float("inf")
dp=[[[inf]*401 for _ in range(401)] for _ in range(n+1)]
dp[0][0][0]=0

l=[tuple(map(int,input().split())) for _ in range(n)]

for i in range(1,n+1):
    for j in range(401):
        for k in range(401):
            a,b,c=l[i-1]
            dp[i][j][k]=min(dp[i][j][k],dp[i-1][j][k])
            if j-a>=0 and k-b>=0:
                dp[i][j][k]=min(dp[i][j][k],dp[i-1][j-a][k-b]+c)

ans=inf
for i in range(1,1+min(400//Ma,400//Mb)):
    ans=min(ans,dp[n][Ma*i][Mb*i])

print(ans if ans!=inf else -1)

Solution (Python):
n,Ma,Mb=map(int,input().split())
inf=float("inf")
dp=[[[inf]*401 for _ in range(401)] for _ in range(n+1)]
dp[0][0][0]=0

l=[tuple(map(int,input().split())) for _ in range(n)]

for i in range(1,n+1):
    for j in range(401):
        for k in range(401):
            a,b,c=l[i-1]
            dp[i][j][k]=min(dp[i][j][k],dp[i-1][j][k])
            if j-a>=0 and k-b>=0:
                dp[i][j][k]=min(dp[i][j][k],dp[i-1][j-a][k-b]+c)

ans=inf
for i in range(1,401):
    for j in range(1,401):
        if i*Mb==j*Ma:
            ans=min(ans,dp[n][i][j])

print(ans if ans!=inf else -1)

Solution (Python):
def main():
    INF = 10 ** 5
    n, ma, mb = map(int, input().split())
    dp = [[INF] * 401 for _ in range(401)]
    dp[0][0] = 0
    for _ in range(n):
        a, b, c = map(int, input().split())
        for i in range(400 - a, -1, -1):
            dpi = dp[i]
            dpia = dp[i + a]
            for j in range(400 - b, -1, -1):
                if dpia[j + b] > dpi[j] + c:
                    dpia[j + b] = dpi[j] + c
    
    ans = INF
    for i in range(1, 400):
        if ma * i > 400 or mb * i > 400:
            break
        ans = min(ans, dp[ma * i][mb * i])
    if ans >= INF:
        print(-1)
    else:
        print(ans)

main()

Solution (Python):
def main():
    INF = 10 ** 5
    n, ma, mb = map(int, input().split())
    dp = [[INF] * 401 for _ in range(401)]
    dp[0][0] = 0
    for _ in range(n):
        a, b, c = map(int, input().split())
        for i in range(400 - a, -1, -1):
            dpi = dp[i]
            dpia = dp[i + a]
            for j in range(400 - b, -1, -1):
                if dpia[j + b] > dpi[j] + c:
                    dpia[j + b] = dpi[j] + c
    
    ans = INF
    for i in range(1, 400):
        if ma * i > 400 or mb * i > 400:
            break
        ans = min(ans, dp[ma * i][mb * i])
    if ans >= INF:
        print(-1)
    else:
        print(ans)

main()

Solution (Python):


import sys

INF = float('inf')
MOD = 10 ** 9 + 7

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def II(): return int(sys.stdin.readline())
def SI(): return input()


n, ma, mb = LI()
src = []
a_max, b_max = 1, 1
for _ in range(n):
    a, b, c = LI()
    src.append((a, b, c))
    a_max += a
    b_max += b

dp = [[[INF] * b_max for _ in range(a_max)] for _ in range(n + 1)]
dp[0][0][0] = 0


for i in range(n):
    ai, bi, ci = src[i]
    for a in range(a_max - ai):
        for b in range(b_max - bi):
            if dp[i][a][b] == INF:
                continue
            dp[i + 1][a][b] = min(dp[i + 1][a][b], dp[i][a][b])
            dp[i + 1][a + ai][b + bi] = min(dp[i][a + ai][b + bi], dp[i][a][b] + ci)


ans = INF
c = 1
while True:
    a, b = c * ma, c * mb
    if a >= a_max or b >= b_max:
        break
    ans = min(ans, dp[n][a][b])
    c += 1

print(ans if ans != INF else -1)

Solution (Python):


import sys


INF = float('inf')
MOD = 10 ** 9 + 7

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def II(): return int(sys.stdin.readline())
def SI(): return input()


n, ma, mb = LI()
abc = [tuple(LI()) for _ in range(n)]
ab_max = n * 10 + 1

dp = [[[INF] * ab_max for _ in range(ab_max)] for _ in range(n + 1)]
dp[0][0][0] = 0


for i in range(n):
    ai, bi, ci = abc[i]
    for a in range(ab_max - ai):
        for b in range(ab_max - bi):
            if dp[i][a][b] == INF:
                continue
            dp[i + 1][a][b] = min(dp[i + 1][a][b], dp[i][a][b])
            dp[i + 1][a + ai][b + bi] = min(dp[i][a + ai][b + bi], dp[i][a][b] + ci)


ans = INF
c = 1
while True:
    a, b = c * ma, c * mb
    if a >= ab_max or b >= ab_max:
        break
    ans = min(ans, dp[n][a][b])
    c += 1

print(ans if ans != INF else -1)

Solution (Python):


"""
参考：https://img.atcoder.jp/abc054/editorial.pdf
・3次元DP
・送るDP
"""
 
import sys
def input(): return sys.stdin.readline().strip()
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
MOD = 10 ** 9 + 7
 
N, Ma, Mb = map(int, input().split())
l = [[0] * 3 for i in range(N)]
for i in range(N):
    l[i][0], l[i][1], l[i][2] = map(int, input().split())


dp = [[[INF] * 401  for i in range(401)] for i in range(N+1)]
dp[0][0][0] = 0
for i in range(N):
    for j in range(401):
        for k in range(401):
            
            if dp[i][j][k] == INF: continue
            dp[i+1][j][k] = min(dp[i][j][k], dp[i+1][j][k])
            dp[i+1][j+l[i][0]][k+l[i][1]] = min(dp[i][j][k] + l[i][2], dp[i+1][j+l[i][0]][k+l[i][1]])

ans = INF
for j in range(1, 401):
    for k in range(1, 401):
        
        if j * Mb == k * Ma:
            ans = min(dp[N][j][k], ans)

if ans == INF:
    print(-1)
else:
    print(ans)

Solution (Python):


"""
参考：https://img.atcoder.jp/abc054/editorial.pdf
・3次元DP
・送るDP
"""
 
import sys
def input(): return sys.stdin.readline().strip()
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
MOD = 10 ** 9 + 7
 
N, Ma, Mb = map(int, input().split())
l = [[0] * 3 for i in range(N)]
for i in range(N):
    l[i][0], l[i][1], l[i][2] = map(int, input().split())


dp = [[[INF] * 401  for i in range(401)] for i in range(N+1)]
dp[0][0][0] = 0
for i in range(N):
    for j in range(401):
        for k in range(401):
            
            if dp[i][j][k] == INF: continue
            dp[i+1][j][k] = min(dp[i][j][k], dp[i+1][j][k])
            dp[i+1][j+l[i][0]][k+l[i][1]] = min(dp[i][j][k] + l[i][2], dp[i+1][j+l[i][0]][k+l[i][1]])

ans = INF
for j in range(1, 401):
    for k in range(1, 401):
        
        if j * Mb == k * Ma:
            ans = min(dp[N][j][k], ans)

if ans == INF:
    print(-1)
else:
    print(ans)

Solution (Python):
N, Ma, Mb = (list)(map(int, input().split()))
l = []
inf = 10**6
dp = [[[inf]*401 for _ in range(401)] for _ in range(41)]


for _ in range(N):
    l.append((list)(map(int, input().split())))

dp[0][0][0] = 0

for i in range(N):
    for ca in range(401):
        for cb in range(401):
            if dp[i][ca][cb] != inf:
                dp[i+1][ca][cb] = min(dp[i+1][ca][cb], dp[i][ca][cb])
                t_a = l[i][0]
                t_b = l[i][1]
                dp[i+1][ca+t_a][cb+t_b] =\
                    min(dp[i+1][ca+t_a][cb+t_b], dp[i][ca][cb]+l[i][2])

ans = inf
for i in range(1, 401):
    for j in range(1, 401):
        if i*Mb == j*Ma:
            ans = min(ans, dp[N][i][j])

if ans == inf:
    ans = -1
print(ans)

Solution (Python):
N, Ma, Mb = map(int, input().split())
items = []
ap = items.append
a_sum =0
b_sum = 0
for i in range(N):
    a, b, c = map(int, input().split())
    ap((a, b, c))
    a_sum += a
    b_sum += b

inf = float("inf")
dp = [[[inf for _ in range(b_sum + 10)] for _ in range(a_sum + 10)] for i in range(N + 1)]
dp[0][0][0] = 0
for i in range(N):
    for a in range(a_sum):
        for b in range(b_sum):
            if dp[i + 1][a][b] > dp[i][a][b]:
                dp[i + 1][a][b] = dp[i][a][b]
            if dp[i + 1][a + items[i][0]][b + items[i][1]] > dp[i][a][b] + items[i][2]:
                dp[i + 1][a + items[i][0]][b + items[i][1]] = dp[i][a][b] + items[i][2]

ans = inf
for a in range(1, a_sum + 1):
    for b in range(1, b_sum + 1):
        if a * Mb == b * Ma:
            ans = min(ans, dp[N][a][b])
if ans != inf:
    print(ans)
else:
    print(-1)

Solution (Python):
N, Ma, Mb = map(int, input().split())
items = []
for i in range(N):
    a, b, c = map(int, input().split())
    items.append((a, b, c))

a_sum = sum([item[0] for item in items])
b_sum = sum([item[1] for item in items])
inf = float("inf")
dp = [[[inf for _ in range(b_sum + 11)] for _ in range(a_sum + 11)] for i in range(N + 1)]
dp[0][0][0] = 0
for i in range(N):
    for a in range(a_sum):
        for b in range(b_sum):
            if dp[i + 1][a][b] > dp[i][a][b]:
                dp[i + 1][a][b] = dp[i][a][b]
            if dp[i + 1][a + items[i][0]][b + items[i][1]] > dp[i][a][b] + items[i][2]:
                dp[i + 1][a + items[i][0]][b + items[i][1]] = dp[i][a][b] + items[i][2]

ans = inf
for a in range(1, a_sum + 1):
    for b in range(1, b_sum + 1):
        if a * Mb == b * Ma:
            ans = min(ans, dp[N][a][b])
if ans != inf:
    print(ans)
else:
    print(-1)

Solution (Python):
N, Ma, Mb = map(int, input().split())
items = []
for i in range(N):
    a, b, c = map(int, input().split())
    items.append((a, b, c))

a_sum = sum([item[0] for item in items])
b_sum = sum([item[1] for item in items])
inf = float("inf")
dp = [[[inf for _ in range(a_sum + 50)] for _ in range(b_sum + 50)] for i in range(N + 1)]
dp[0][0][0] = 0

for i in range(N):
    for a in range(a_sum):
        for b in range(b_sum):
            if dp[i + 1][a][b] > dp[i][a][b]:
                dp[i + 1][a][b] = dp[i][a][b]
            if dp[i + 1][a + items[i][0]][b + items[i][1]] > dp[i][a][b] + items[i][2]:
                dp[i + 1][a + items[i][0]][b + items[i][1]] = dp[i][a][b] + items[i][2]

ans = inf
for a in range(1, a_sum + 1):
    for b in range(1, b_sum + 1):
        if a * Mb == b * Ma:
            ans = min(ans, dp[N][a][b])
if ans != inf:
    print(ans)
else:
    print(-1)

Solution (Python):
N, Ma, Mb = map(int, input().split())
items = []
for i in range(N):
    a, b, c = map(int, input().split())
    items.append((a, b, c))

a_sum = sum([item[0] for item in items])
b_sum = sum([item[1] for item in items])
inf = float("inf")
dp = [[[inf for _ in range(a_sum + 60)] for _ in range(b_sum + 60)] for i in range(N + 1)]
dp[0][0][0] = 0

for i in range(N):
    for a in range(a_sum):
        for b in range(b_sum):
            if dp[i + 1][a][b] > dp[i][a][b]:
                dp[i + 1][a][b] = dp[i][a][b]
            if dp[i + 1][a + items[i][0]][b + items[i][1]] > dp[i][a][b] + items[i][2]:
                dp[i + 1][a + items[i][0]][b + items[i][1]] = dp[i][a][b] + items[i][2]

ans = inf
for a in range(1, a_sum + 1):
    for b in range(1, b_sum + 1):
        if a * Mb == b * Ma:
            ans = min(ans, dp[N][a][b])
if ans != inf:
    print(ans)
else:
    print(-1)

Solution (Python):
N, Ma, Mb = map(int, input().split())
items = []
for i in range(N):
    a, b, c = map(int, input().split())
    items.append((a, b, c))

a_sum = sum([item[0] for item in items])
b_sum = sum([item[1] for item in items])
inf = float("inf")
dp = [[[inf for _ in range(a_sum + 100)] for _ in range(b_sum + 100)] for i in range(N + 1)]
dp[0][0][0] = 0

for i in range(N):
    for a in range(a_sum + 1):
        for b in range(b_sum + 1):
            if dp[i + 1][a][b] > dp[i][a][b]:
                dp[i + 1][a][b] = dp[i][a][b]
            if dp[i + 1][a + items[i][0]][b + items[i][1]] > dp[i][a][b] + items[i][2]:
                dp[i + 1][a + items[i][0]][b + items[i][1]] = dp[i][a][b] + items[i][2]

ans = inf
for a in range(1, a_sum + 1):
    for b in range(1, b_sum + 1):
        if a * Mb == b * Ma:
            ans = min(ans, dp[N][a][b])
if ans != inf:
    print(ans)
else:
    print(-1)

Solution (Python):
N, Ma, Mb = map(int, input().split())
items = []
for i in range(N):
    a, b, c = map(int, input().split())
    items.append((a, b, c))

a_sum = sum([item[0] for item in items])
b_sum = sum([item[1] for item in items])
inf = float("inf")
dp = [[[inf for _ in range(401)] for _ in range(401)] for i in range(N+1)]
dp[0][0][0] = 0

for i in range(N):
    for a in range(a_sum + 1):
        for b in range(b_sum + 1):
            dp[i + 1][a][b] = min(dp[i + 1][a][b], dp[i][a][b])
            dp[i + 1][a + items[i][0]][b + items[i][1]] = min(dp[i + 1][a + items[i][0]][b + items[i][1]],
                                                              dp[i][a][b] + items[i][2])
ans = inf
for a in range(1, a_sum + 1):
    for b in range(1, b_sum + 1):
        if a * Mb == b * Ma:
            ans = min(ans, dp[N][a][b])
if ans != inf:
    print(ans)
else:
    print(-1)

Solution (Python):
N, Ma, Mb = map(int, input().split())
items = []
for i in range(N):
    a, b, c = map(int, input().split())
    items.append((a, b, c))

a_sum = sum([item[0] for item in items])
b_sum = sum([item[1] for item in items])
inf = float("inf")
dp = [[[inf for _ in range(a_sum + 100)] for _ in range(b_sum + 100)] for i in range(N+1)]
dp[0][0][0] = 0

for i in range(N):
    for a in range(a_sum + 1):
        for b in range(b_sum + 1):
            dp[i + 1][a][b] = min(dp[i + 1][a][b], dp[i][a][b])
            dp[i + 1][a + items[i][0]][b + items[i][1]] = min(dp[i + 1][a + items[i][0]][b + items[i][1]],
                                                              dp[i][a][b] + items[i][2])
ans = inf
for a in range(1, a_sum + 1):
    for b in range(1, b_sum + 1):
        if a * Mb == b * Ma:
            ans = min(ans, dp[N][a][b])
if ans != inf:
    print(ans)
else:
    print(-1)

Solution (Python):
I=lambda:list(map(int,input().split()))
n,Ma,Mb=I()
m=[[0,0,0]]+[I()for _ in range(n)]
dp=[[[10**18]*(10*n+1)for _ in range(10*n+1)]for _ in range(n+1)]
dp[0][0][0]=0
for i in range(1,n+1):
    for j in range(10*n+1):
        if j-m[i][0]<0:
            dp[i][j]=dp[i-1][j]
            continue
        for k in range(10*n+1):
            if k-m[i][1]<0:
                dp[i][j][k]=dp[i-1][j][k]
            else:
                dp[i][j][k]=min(dp[i-1][j-m[i][0]][k-m[i][1]]+m[i][2],dp[i-1][j][k])
ans=10**18
for i in range(1,10*n+1):
    j=Mb*i/Ma
    if j==int(j) and j<10*n+2:
        ans=min(ans,dp[-1][i][int(j)])
print(-(ans==10**18)or ans)

Solution (Python):
N, Ma, Mb = map(int, input().split())
A, B, C = [], [], []
for i in range(N):
    ai, bi, ci = map(int, input().split())
    A.append(ai)
    B.append(bi)
    C.append(ci)

INF = float('inf')
dp = [[[INF] * 401 for i in range(401)] for j in range(N + 1)]
dp[0][0][0] = 0

for i in range(1, N + 1):
    for a in range(401):
        for b in range(401):
            if a - A[i - 1] >= 0 and b - B[i - 1] >= 0:
                dp[i][a][b] = min(dp[i][a][b], dp[i - 1][a][b], dp[i - 1][a - A[i - 1]][b - B[i - 1]] + C[i - 1])
            else:
                dp[i][a][b] = min(dp[i][a][b], dp[i - 1][a][b])
ans = INF
for i in range(1, 401):
    target_a = Ma * i
    target_b = Mb * i
    if target_a > 400 or target_b > 400:
        break
    ans = min(ans, dp[N][target_a][target_b])

print(ans if ans != INF else -1)

Solution (Python):
N, Ma, Mb = map(int, input().split())
Items = [list(map(int, input().split())) for i in range(N)]


dp = [[[float('inf')] * 401 for j in range(401)] for i in range(N + 1)]
dp[0][0][0] = 0

for i in range(1, N + 1):
    ai, bi, ci = Items[i - 1]
    for a in range(401):
        for b in range(401):
            if a - ai >= 0 and b - bi >= 0:
                dp[i][a][b] = min(dp[i][a][b], dp[i - 1][a][b], dp[i - 1][a - ai][b - bi] + ci)
            else:
                dp[i][a][b] = min(dp[i][a][b], dp[i - 1][a][b])

ans = float('inf')
i = 1
while Ma * i <= 400 and Mb * i <= 400:
    ans = min(ans, dp[N][Ma * i][Mb * i])
    i += 1

print(ans if ans != float('inf') else -1)

Solution (Python):
N, Ma, Mb = map(int, input().split())
Items = [list(map(int, input().split())) for i in range(N)]


dp = [[[float('inf')] * 401 for j in range(401)] for i in range(N + 1)]
dp[0][0][0] = 0

for i in range(N):
    ai, bi, ci = Items[i]
    for a in range(401):
        for b in range(401):
            if a + ai <= 400 and b + bi <= 400:
                dp[i + 1][a + ai][b + bi] = min(dp[i][a][b] + ci, dp[i + 1][a + ai][b + bi])
            dp[i + 1][a][b] = min(dp[i][a][b], dp[i + 1][a][b])

ans = float('inf')
i = 1
while Ma * i <= 400 and Mb * i <= 400:
    ans = min(ans, dp[N][Ma * i][Mb * i])
    i += 1

print(ans if ans != float('inf') else -1)

Solution (Python):
import sys
stdin = sys.stdin
 
sys.setrecursionlimit(10**5) 
 
def li(): return map(int, stdin.readline().split())
def li_(): return map(lambda x: int(x)-1, stdin.readline().split())
def lf(): return map(float, stdin.readline().split())
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(stdin.readline())
def nf(): return float(stdin.readline())

n,ma,mb = li()
drugs = []
for _ in range(n):
    drugs.append(tuple(li()))
    
dp = [[[10**10]*(401) for _ in range(401)] for _ in range(n+1)]
dp[0][0][0] = 0

for i in range(n):
    ca, cb, cc = drugs[i]
    for aa in range(401):
        for bb in range(401):
            if 0 <= aa - ca <= 400 and 0 <= bb - cb <= 400:
                dp[i+1][aa][bb] = min(dp[i][aa-ca][bb-cb] + cc,
                                      dp[i][aa][bb])
                
            else:
                dp[i+1][aa][bb] = dp[i][aa][bb]

ans = 10**10     
for aa in range(1,401):
    for bb in range(1,401):
        if (aa/bb) == (ma/mb):
            ans = min(ans, dp[n][aa][bb])
            
if ans == 10**10:
    print(-1)
else:
    print(ans)

Solution (Python):
N, Ma, Mb = [int(_) for _ in input().split()]
ABC = [[int(_) for _ in input().split()] for _ in range(N)]
dp = {}
dp[0] = 0
dp[ABC[0][0] + 1000 * ABC[0][1]] = ABC[0][2]
ans = 5000
for i in range(N - 1):
    dp_old = dp.copy()
    for ab in dp_old.keys():
        a = ab % 1000
        b = ab // 1000
        if a * Mb == b * Ma > 0:
            ans = min(ans, dp_old[ab])
        dp[a + ABC[i + 1][0] + 1000 * (b + ABC[i + 1][1])] = min(
            dp_old[ab] + ABC[i + 1][2],
            dp_old.get(a + ABC[i + 1][0] + 1000 * (b + ABC[i + 1][1]), 5000))
for ab in dp.keys():
    a = ab % 1000
    b = ab // 1000
    if a * Mb == b * Ma > 0:
        ans = min(ans, dp[ab])
if ans == 5000:
    print(-1)
else:
    print(ans)

Solution (Python):
from collections import defaultdict
n, ma, mb = map(int, input().split())
d = []
for i in range(n):
    d.append([int(m) for m in input().split()])

def gcd(a,b):
    if b == 0:
        return a
    return gcd(b, a % b)


"""dp = []
for i in range(401):
    for j in range(401):
        dp.append([i,j])"""

cost = []
for i in range(401):
    cost.append([])
for i in range(401):
    for j in range(401):
        cost[i].append([])
for i in range(401):
    for j in range(401):
        cost[i][j] = float("INF")
cost[0][0] = 0
pos = []
pos.append([0,0])
pos2 = set()
pos2.add((0,0))


cppos2 = set()
cppos2.add((0,0))

cpcost = {}
cpcost = defaultdict(lambda: float("INF"))
for i in range(n):
    for v in range(2):
        for w in range(len(pos)):
            p = pos[w][0] + v * d[i][0]
            q = pos[w][1] + v * d[i][1]
            if (p, q) not in pos2:
                
                cppos2.add((p, q))
            if cost[p][q] > cost[pos[w][0]][pos[w][1]] + d[i][2]:
                if cpcost[p, q] > cost[pos[w][0]][pos[w][1]] + d[i][2]:
                    cpcost[p, q] = cost[pos[w][0]][pos[w][1]] + d[i][2]
    
    for u in cppos2:
        pos2.add(u)
        pos.append(list(u))
    for u in cpcost:
        cost[u[0]][u[1]] = cpcost[u]
    cppos = []
    cppos2 = set()
    cpcost = {}
    cpcost = defaultdict(lambda: float("INF"))

realcost = []
for i in range(401):
    for j in range(401):
        if gcd(i, j) != 0:
            if i // gcd(i, j) == ma and j // gcd(i, j) == mb and cost[i][j] != float("INF"):
                realcost.append(cost[i][j])

if len(realcost) > 0:
    print(min(realcost))
else:
    print(-1)

Solution (Python):
n, ma, mb = list(map(int, input().split()))

a, b, c = [], [], []

for i in range(n):
    aa,bb,cc = list(map(int,input().split()))
    a.append(aa)
    b.append(bb)
    c.append(cc)

dp = [[float("inf")]*(sum(b)+1) for i in range(sum(a)+1)]
dp[0][0] = 0
max_a = 0
max_b = 0
for i in range(n):
    max_a += a[i]
    max_b += b[i]
    for ai in range(a[i], max_a+1)[::-1]:
        for bi in range(b[i], max_b+1)[::-1]:
            dp[ai][bi] = min(dp[ai][bi], dp[ai-a[i]][bi-b[i]] + c[i])

ans = float("inf")
for i in range(1, min(max_a//ma, max_b//mb)):
    ans = min(ans, dp[i*ma][i*mb])
if ans == float("inf"):
    print(-1)
else:
    print(ans)