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.



Sample input:
3 1 1
1 2 1
2 1 2
3 3 10


Sample output:
3

Submission status: Accepted

Solution code:
N,Ma,Mb=[int(x) for x in input().split()]
A=[]
B=[]
C=[]
for i in range(N):
	a,b,c=[int(x) for x in input().split()]
	A.append(a)
	B.append(b)
	C.append(c)


ANS=[[[-1 for k in range(401)] for j in range(401)] for i in range(41)]

INF=1000000000000000000000

def f(ind,wa,wb):
	global Ma
	global Mb
	global N
	if ANS[ind][wa][wb]==-1:
		if ind==0:
			if (wa+A[0])*Mb==(wb+B[0])*Ma:
				ANS[ind][wa][wb] = C[0]
			elif wa*Mb==wb*Ma and (wa!=0 and wb!=0):
				ANS[ind][wa][wb] = 0
			else:
				ANS[ind][wa][wb] = INF
		else:
			ANS[ind][wa][wb] = min(f(ind-1,wa,wb),f(ind-1,wa+A[ind],wb+B[ind])+C[ind])
	return ANS[ind][wa][wb]

ans=f(N-1,0,0)

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

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline
n,ma,mb=map(int,input().split())
dp=[[[float("inf")]*500 for _ in range(500)] for i in range(n+1)]
dp[0][0][0]=0
for i in range(n):
    a,b,c=map(int,input().split())
    for j in range(450):
        for k in range(450):
            dp[i+1][j][k]=min(dp[i+1][j][k],dp[i][j][k])
            dp[i+1][j+a][k+b]=min(dp[i+1][j+a][k+b],dp[i][j][k]+c)
ans=float("inf")
i=1
#print(dp[-1])
while i*ma<450 and i*mb<450:
    ans=min(ans,dp[-1][ma*i][mb*i])
    i+=1
print(ans if ans!=float("inf") else -1)

Submission status: Accepted

Solution code:
n,ma,mb=map(int,input().split())
el=[list(map(int,input().split())) for i in range(n)]
sa=sum(i[0] for i in el)
sb=sum(i[1] for i in el)
sa1=sa+1
sb1=sb+1

inf=1000000
x=[[inf]*(sb1) for i in range(sa1)]
x[0][0]=0
for i in range(n):
    now=el[i]
    x_sub=[[0]*(sb1) for i in range(sa1)]
    for k in range(sa1):
        for l in range(sb1):
            if x[k][l]!=inf:
                if k+now[0]<sa1:
                    if l+now[1]<sb1:
                        x_sub[k+now[0]][l+now[1]]=x[k][l]+now[2]
    for k in range(sa1):
        for l in range(sb1):
                if x_sub[k][l]!=0:
                    x[k][l]=min(x[k][l],x_sub[k][l])
mi=min(sa//ma,sb//mb)
ans=inf
for i in range(1,mi+1):
    ans=min(ans,x[ma*i][mb*i])
if ans==inf:
    print(-1)
else:
    print(ans)

Submission status: Accepted

Solution code:
n,ma,mb=map(int,input().split())
el=[list(map(int,input().split())) for i in range(n)]
sa=sum(i[0] for i in el)
sb=sum(i[1] for i in el)
sa1=sa+1
sb1=sb+1

inf=10000000000
x=[[inf]*(sb1) for i in range(sa1)]
x[0][0]=0
for i in range(n):
    now=el[i]
    x_sub=[[0]*(sb1) for i in range(sa1)]
    for k in range(sa1):
        for l in range(sb1):
            if x[k][l]!=inf and k+now[0]<sa1 and l+now[1]<sb1:
                x_sub[k+now[0]][l+now[1]]=x[k][l]+now[2]
    for k in range(sa1):
        for l in range(sb1):
                if x_sub[k][l]!=0:
                    x[k][l]=min(x[k][l],x_sub[k][l])
mi=min(sa//ma,sb//mb)
ans=inf
for i in range(1,mi+1):
    ans=min(ans,x[ma*i][mb*i])
if ans==inf:
    print(-1)
else:
    print(ans)

Submission status: Accepted

Solution code:
n,ma,mb=map(int,input().split())
el=[list(map(int,input().split())) for i in range(n)]
sa=sum(i[0] for i in el)
sb=sum(i[1] for i in el)
sa1=sa+1
sb1=sb+1

inf=10000000000
x=[[inf]*(sb1) for i in range(sa1)]
x[0][0]=0
for i in range(n):
    now=el[i]
    x_sub=[[0]*(sb1) for i in range(sa1)]
    for k in range(sa1):
        for l in range(sb1):
            if x[k][l]!=inf:
                if k+now[0]<sa1:
                    if l+now[1]<sb1:
                        x_sub[k+now[0]][l+now[1]]=x[k][l]+now[2]
    for k in range(sa1):
        for l in range(sb1):
                if x_sub[k][l]!=0:
                    x[k][l]=min(x[k][l],x_sub[k][l])
mi=min(sa//ma,sb//mb)
ans=inf
for i in range(1,mi+1):
    ans=min(ans,x[ma*i][mb*i])
if ans==inf:
    print(-1)
else:
    print(ans)

Submission status: Accepted

Solution code:
n,ma,mb=map(int,input().split())
el=[list(map(int,input().split())) for i in range(n)]
sa=sum(i[0] for i in el)
sb=sum(i[1] for i in el)
#mi=min(sa//ma,sb//mb)
inf=10000000000
x=[[inf for j in range(sb+1)] for i in range(sa+1)]
x[0][0]=0
for i in range(n):
    now=el[i]
    x_sub=[[0 for j in range(sb+1)] for i in range(sa+1)]
    for k in range(sa+1):
        for l in range(sb+1):
            if x[k][l]!=inf and k+now[0]<sa+1 and l+now[1]<sb+1:
                x_sub[k+now[0]][l+now[1]]=x[k][l]+now[2]
    for k in range(sa+1):
        for l in range(sb+1):
                if x_sub[k][l]!=0:
                    x[k][l]=min(x[k][l],x_sub[k][l])
mi=min(sa//ma,sb//mb)
ans=inf
for i in range(1,mi+1):
    ans=min(ans,x[ma*i][mb*i])
if ans==inf:
    print(-1)
else:
    print(ans)

Submission status: Accepted

Solution code:
def main():
	n, ma, mb, *L = map(int, open(0).read().split())
	M = 1 << 30
	dp = [[M] * 420 for _ in range(420)]
	dp[0][0] = 0
	ua = ub = 15
	for a, b, c in zip(*[iter(L)] * 3):
		for i in range(ua, -1, -1):
			for j in range(ub, -1, -1):
				t = dp[i][j] + c
				if dp[i + a][j + b] > t:
					dp[i + a][j + b] = t
					if ua < i + a:
						ua = i + a
					if ub < j + b:
						ub = j + b
	ans = M
	_ma, _mb = ma, mb
	while _ma < 410 > _mb:
		ans = min(ans, dp[_ma][_mb])
		_ma += ma
		_mb += mb
	print(ans if ans < M else -1)


if __name__ == "__main__":
	main()

Submission status: Accepted

Solution code:
def main():
	n, ma, mb, *L = map(int, open(0).read().split())
	M = 1<<30
	dp = [[M] * 420 for _ in range(420)]
	dp[0][0] = 0
	for a, b, c in zip(*[iter(L)] * 3):
		for i in range(400, -1, -1):
			for j in range(400, -1, -1):
				t = dp[i][j] + c
				if dp[i + a][j + b] > t:
					dp[i + a][j + b] = t
	ans = M
	_ma, _mb = ma, mb
	while _ma < 410 > _mb:
		ans = min(ans, dp[_ma][_mb])
		_ma += ma
		_mb += mb
	print(ans if ans < M else -1)

if __name__=="__main__":
	main()

Submission status: Accepted

Solution code:
N, Ma, Mb = map(int, input().split())
items = [[int(x) for x in input().split()] for _ in range(N)]

A, B = 0, 0
for a, b, _ in items:
    A += a
    B += b

dp = [[[float("inf")] * (B + 1) for _ in range(A + 1)] for _ in range(N + 1)]
for i in range(N + 1):
    dp[i][0][0] = 0

for i in range(N):
    a, b, c = items[i]
    for j in range(A + 1):
        for k in range(B + 1):
            if j - a >= 0 and k - b >= 0:
                dp[i + 1][j][k] = min(dp[i][j - a][k - b] + c, dp[i][j][k])
            else:
                dp[i + 1][j][k] = dp[i][j][k]


ans = float("inf")
for x in range(1, min(A // Ma, B // Mb) + 1):
    a = Ma * x
    b = Mb * x
    ans = min(dp[N][a][b], ans)

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

Submission status: Accepted

Solution code:
import sys



n, ma, mb = map(int, input().split())
abc = []

for _ in range(n):
    a, b, cost = map(int, input().split())
    abc.append((a, b, cost))

def main():
    sa = 0
    sb = 0
    for i in range(n):
        sa += abc[i][0]
        sb += abc[i][1]

    res = [[float('infinity')] * (sb + 1) for _ in range(sa + 1)]
    res[0][0] = 0

    for a, b, c in abc:

        for j in range(sa, -1, -1):
            for k in range(sb, -1, -1):
                if j >= a and k >= b:
                    res[j][k] = min(res[j][k], res[j-a][k-b] + c)

    ans = float('infinity')
    for i in range(1, min(sa//ma, sb//mb) + 1):
        ans = min(ans, res[ma*i][mb*i])

    if ans == float('infinity'):
        return -1
    else:
        return ans

if __name__ == '__main__':
    ans = main()
    print(ans)

Submission status: Accepted

Solution code:
n, ma, mb = [int(i) for i in input().split()]

# a,b,cを入力
lst = [[int(i) for i in input().split()] for _ in range(n)]

# コストの小さい順に並び替える
lst.sort(key=lambda x: x[2])
#print(lst)

dic = {}
#####
# 動的計画法

# 値の更新
def push(k,v):
    if k in dic:
        dic[k] = min(dic[k],v)
    else:
        dic[k] = v

for i in lst:
    # v = i[2]: コスト
    k, v = i[0] * mb - i[1] * ma, i[2]
    l = [[j, dic[j]] for j in dic]
    #print(l)
    for item in l:
        push(item[0] + k, item[1] + v)
    push(k, v)

#####
print(dic[0] if 0 in dic else '-1')

Submission status: Accepted

Solution code:
import sys

read = sys.stdin.readline
N, Ma, Mb = map(int, read().split())
abc = [tuple(map(int, read().split())) for _ in range(N)]
d = [(Mb * a - Ma * b, c) for a, b, c in abc]
dic = dict()
for i, j in d:
    for key, value in tuple(dic.items()):
        n = key + i
        if dic.get(n):
            dic[n] = min(value + j, dic[n])
        else:
            dic[n] = value + j
    if dic.get(i):
        dic[i] = min(j, dic[i])
    else:
        dic[i] = j

if dic.get(0):
    print(dic[0])
else:
    print(-1)

Submission status: Accepted

Solution code:
def main():
    N, Ma, Mb = map(int, input().split())
    A = []
    B = []
    C = []
    for _ in range(N):
        a, b, c = map( int, input().split())
        A.append(a)
        B.append(b)
        C.append(c)
    dp = [[10**5]*401 for _ in range(401)]
    dp[0][0] = 0
    for t in range(N):
        a, b, c = A[t], B[t], C[t]
        for i in range(400,-1,-1):
            for j in range(400,-1,-1):
                if i-a >= 0 and j-b >= 0:
                    if dp[i-a][j-b] + c < dp[i][j]:
                        dp[i][j] = dp[i-a][j-b] + c
    ans = 10**5
    for i in range(1, 401):
        if i*Ma > 400 or i*Mb > 400:
            break
        if dp[i*Ma][i*Mb] < ans:
            ans = dp[i*Ma][i*Mb]
    if ans == 10**5:
        print(-1)
    else:
        print(ans)
    
if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
N, Ma, Mb = list(map(int, input().split()))
D = [tuple(map(int, input().split())) for _ in range(N)]

def listup(L, D):
    for a, b, c in D:
        for (ka, kb), kc in L.copy().items():
            key = (ka+a, kb+b)
            L[key] = min(L[key], kc+c) if key in L else kc+c
        

L1 = {(0,0):0}
L2 = {(0,0):0}
listup(L1, D[:N//2])
listup(L2, D[N//2:])

ans = 10**9
for m in range(1,401):
    ma = Ma * m
    mb = Mb * m
    if ma>400 or mb>400: break
    for key1 in L1:
        ta1, tb1 = key1
        ta2 = ma - ta1
        tb2 = mb - tb1
        key2 = (ta2, tb2)
        if key2 in L2: ans = min(ans, L1[key1]+L2[key2])

print(ans if ans!=10**9 else -1)

Submission status: Accepted

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, MA, MB = R()
    ABC = [R() for _ in range(N)]
    dp = [[INF]*(420) for _ in range(420)]
    dp[0][0] = 0

    for a, b, c in ABC:
        # 400 * 400 * 40 = 64 * 10**5
        for i in range(400, -1, -1):
            for j in range(400, -1, -1):
                dp[i+a][j+b] = min(dp[i][j]+c, dp[i+a][j+b])
    ans = INF
    for i in range(1, 401):
        for j in range(1, 401):
            if MA*j == MB*i:
                ans = min(ans, dp[i][j])
    else:
        if ans == INF:
            ans = -1
    print(ans)
    # 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()

Submission status: Accepted

Solution code:
inf = 10 ** 18

a = []
b = []
c = []
n, ma, mb = map(int, input().split())

for _ in range(n):
    a_, b_, c_ = map(int, input().split())
    a.append(a_)
    b.append(b_)
    c.append(c_)

abmax = 10
p = n * abmax
dp = [[[inf for _ in range(p + 1)] for _ in range(p + 1)]
      for _ in range(n + 1)]
dp[0][0][0] = 0

for i in range(n):
    for j in range(p + 1):
        for k in range(p + 1):
            if dp[i][j][k] == inf:
                continue
            dp[i + 1][j][k] = min(dp[i+1][j][k], dp[i][j][k])
            dp[i + 1][j + a[i]][k + b[i]
                                ] = min(dp[i + 1][j + a[i]][k + b[i]], dp[i][j][k] + c[i])

ans = inf
for j in range(p)[1::]:
    for k in range(p)[1::]:
        if j * mb == k * ma:
            ans = min(ans, dp[n][j][k])

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

Submission status: Accepted

Solution code:
from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
import math
import bisect
import random
from itertools import permutations, accumulate, combinations, product
import sys
from pprint import pprint
from copy import deepcopy
import string
from bisect import bisect_left, bisect_right
from math import factorial, ceil, floor
from operator import mul
from functools import reduce
from pprint import pprint


sys.setrecursionlimit(2147483647)
INF = 10 ** 20
def LI(): return list(map(int, sys.stdin.buffer.readline().split()))
def I(): return int(sys.stdin.buffer.readline())
def LS(): return sys.stdin.buffer.readline().rstrip().decode('utf-8').split()
def S(): return sys.stdin.buffer.readline().rstrip().decode('utf-8')
def IR(n): return [I() for i in range(n)]
def LIR(n): return [LI() for i in range(n)]
def SR(n): return [S() for i in range(n)]
def LSR(n): return [LS() for i in range(n)]
def SRL(n): return [list(S()) for i in range(n)]
def MSRL(n): return [[int(j) for j in list(S())] for i in range(n)]
mod = 1000000007


def gcd(i, j):
    while j:
        i, j = j, i % j
    return i


n, a_ratio, b_ratio = LI()
solution = LIR(n)
dp = {(0, 0): 0}
for a, b, c in solution:
    for (ai, bi), ci in list(dp.items()):
        # listにしないとduring iteration dictionary changeみたいなerrorでる。
        # メモ：defaultdictはもともと存在しないkeyを参照するだけでkey:valueが追加される。
        # これによって、key: INFが追加されるのはまずい。だからgetで
        dp[(ai + a, bi + b)] = min(dp.get((ai + a, bi + b), INF), ci + c)


ans = INF
for i in range(1, max(400 // a_ratio, 400 // b_ratio)):
    ans = min(ans, dp.get((a_ratio * i, b_ratio * i), INF))

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

Submission status: Accepted

Solution code:
N,Ma,Mb = map(int,input().split())
Data = []
for _ in range(N):
    a,b,c = map(int,input().split())
    Data.append([a,b,c])

DP = []
for _ in range(N+1):
    temp = [[-1]*(N*10+1) for _ in range(N*10+1)]
    DP.append(temp)
DP[0][0][0] = 0

for i in range(1,N+1):
    A,B,C = Data[i-1]
    for a in range(0,N*10+1):
        for b in range(0,N*10+1):
            if DP[i-1][a][b] != -1:
                # 使わない
                if DP[i][a][b] == -1:
                    DP[i][a][b] = DP[i-1][a][b]
                else:
                    DP[i][a][b] = min(DP[i][a][b],DP[i-1][a][b])

                #使う
                if DP[i][a+A][b+B] == -1:
                    DP[i][a+A][b+B] = DP[i-1][a][b]+C
                else:
                    DP[i][a+A][b+B] = min(DP[i][a+A][b+B],DP[i-1][a][b]+C)
ans = -1
for a in range(1,N*10+1):
    for b in range(1,N*10+1):
        if DP[N][a][b] != -1 and a * Mb == b * Ma:
            if ans == -1:
                ans = DP[N][a][b]
            else:
                ans = min(ans,DP[N][a][b])
print(ans)