Problem:


Problem A: The Balance

Ms. Iyo Kiffa-Australis has a balance and only two kinds of weights to measure a dose of medicine.

For example, to measure 200mg of aspirin using 300mg weights and 700mg weights, she can put
one 700mg weight on the side of the medicine and three 300mg weights on the opposite side
(Figure 1). Although she could put four 300mg weights on the medicine side and two 700mg
weights on the other (Figure 2), she would not choose this solution because it is less convenient
to use more weights.

You are asked to help her by calculating how many weights are required.

Figure 1: To measure 200mg of aspirin using three 300mg weights and one 700mg weight

Figure 2: To measure 200mg of aspirin using four 300mg weights and two 700mg weights

Input

The input is a sequence of datasets. A dataset is a line containing three positive integers a, b,
and d separated by a space. The following relations hold: a &ne; b, a ≤ 10000, b ≤ 10000, and
d ≤ 50000. You may assume that it is possible to measure d mg using a combination of a mg
and b mg weights. In other words, you need not consider “no solution” cases.

The end of the input is indicated by a line containing three zeros separated by a space. It is not
a dataset.

Output

The output should be composed of lines, each corresponding to an input dataset (a, b, d). An
output line should contain two nonnegative integers x and y separated by a space. They should
satisfy the following three conditions.

 You can measure d mg using x many a mg weights and y many b mg weights.

 The total number of weights (x + y) is the smallest among those pairs of nonnegative
  integers satisfying the previous condition.

 The total mass of weights (ax + by) is the smallest among those pairs of nonnegative
  integers satisfying the previous two conditions.

No extra characters (e.g. extra spaces) should appear in the output.

Sample Input

700 300 200
500 200 300
500 200 500
275 110 330
275 110 385
648 375 4002
3 1 10000
0 0 0

Output for the Sample Input

1 3
1 1
1 0
0 3
1 1
49 74
3333 1



Sample input:
700 300 200
500 200 300
500 200 500
275 110 330
275 110 385
648 375 4002
3 1 10000
0 0 0


Sample output:
1 3
1 1
1 0
0 3
1 1
49 74
3333 1

Submission status: Wrong Answer

Solution code:
def judge(x,y):
    global xx,yy,xy,axby
    if min(x,y) >= 0 and x+y <= xy:
        if x+y < xy or (x+y == xy and a*x+b*y < axby):
            xy = x+y
            axby = a*x+b*y
            xx,yy = x,y
    
while 1:
    a,b,d = map(int,raw_input().split())
    if a == 0: break
    xy = axby = 10**10
    for y in xrange(10001):
        if (d+b*y)%a == 0: judge((d+b*y)/a,y)
        if (b*y-d)%a == 0: judge((b*y-d)/a,y)
        if (d-b*y)%a == 0: judge((d-b*y)/a,y)
    print xx,yy

Submission status: Wrong Answer

Solution code:
def judge(x,y):
    global xx,yy,xy,axby
    if min(x,y) >= 0 and x+y <= xy:
        if x+y < xy or (x+y == xy and a*x+b*y < axby):
            xy = x+y
            axby = a*x+b*y
            xx,yy = x,y
    
while 1:
    a,b,d = map(int,raw_input().split())
    if a == 0: break
    xy = axby = 10**10
    for y in xrange(20001):
        if (d+b*y)%a == 0: judge((d+b*y)/a,y)
        if (b*y-d)%a == 0: judge((b*y-d)/a,y)
        if (d-b*y)%a == 0: judge((d-b*y)/a,y)
    print xx,yy

Submission status: Wrong Answer

Solution code:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(0,-1),(1,0),(0,1),(-1,0)]
ddn = [(0,-1),(1,-1),(1,0),(1,1),(0,1),(-1,-1),(-1,0),(-1,1)]

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)


def main():
    rr = []

    while True:
        a,b,c = LI()
        if a == 0:
            break
        r = inf
        x = inf
        y = inf
        for i in range(c+1):
            t = a * i
            if t < c and (c - t) % b == 0:
                tr = c
                tx = i
                ty = (c-t) // b
                if x+y > tx+ty or (x+y==tx+ty and r > tr):
                    r = tr
                    x = tx
                    y = ty

            if  t >= c and (t-c) % b == 0:
                tr = t - c + t
                tx = i
                ty = (t-c) // b
                if x+y > tx+ty or (x+y==tx+ty and r > tr):
                    r = tr
                    x = tx
                    y = ty

            if (t+c) % b == 0:
                tr = t + c + t
                tx = i
                ty = (t+c) // b
                if x+y > tx+ty or (x+y==tx+ty and r > tr):
                    r = tr
                    x = tx
                    y = ty

        rr.append('{} {}'.format(x,y))

    return '\n'.join(map(str,rr))


print(main())

Submission status: Accepted

Solution code:
def judge(x,y):
    global xx,yy,xy,axby
    if min(x,y) >= 0 and x+y <= xy:
        if x+y < xy or (x+y == xy and a*x+b*y < axby):
            xy = x+y
            axby = a*x+b*y
            xx,yy = x,y
    
while 1:
    a,b,d = map(int,raw_input().split())
    if a == 0: break
    xy = axby = 10**10
    for y in xrange(50001):
        if (d+b*y)%a == 0: judge((d+b*y)/a,y)
        if (b*y-d)%a == 0: judge((b*y-d)/a,y)
        if (d-b*y)%a == 0: judge((d-b*y)/a,y)
    print xx,yy

Submission status: Accepted

Solution code:
def judge(x,y):
    global xx,yy,xy,axby
    if min(x,y) >= 0 and x+y <= xy:
        if x+y < xy or (x+y == xy and a*x+b*y < axby):
            xy = x+y
            axby = a*x+b*y
            xx,yy = x,y
    
while 1:
    a,b,d = map(int,raw_input().split())
    if a == 0: break
    xy = axby = 10**10
    for y in xrange(30001):
        if (d+b*y)%a == 0: judge((d+b*y)/a,y)
        if (b*y-d)%a == 0: judge((b*y-d)/a,y)
        if (d-b*y)%a == 0: judge((d-b*y)/a,y)
    print xx,yy

Submission status: Accepted

Solution code:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 10**9+7
dd = [(0,-1),(1,0),(0,1),(-1,0)]
ddn = [(0,-1),(1,-1),(1,0),(1,1),(0,1),(-1,-1),(-1,0),(-1,1)]

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)


def main():
    rr = []

    while True:
        a,b,c = LI()
        if a == 0:
            break
        r = inf
        x = inf
        y = inf
        for i in range(c*5):
            t = a * i
            if t < c and (c - t) % b == 0:
                tr = c
                tx = i
                ty = (c-t) // b
                if x+y > tx+ty or (x+y==tx+ty and r > tr):
                    r = tr
                    x = tx
                    y = ty

            if  t >= c and (t-c) % b == 0:
                tr = t - c + t
                tx = i
                ty = (t-c) // b
                if x+y > tx+ty or (x+y==tx+ty and r > tr):
                    r = tr
                    x = tx
                    y = ty

            if (t+c) % b == 0:
                tr = t + c + t
                tx = i
                ty = (t+c) // b
                if x+y > tx+ty or (x+y==tx+ty and r > tr):
                    r = tr
                    x = tx
                    y = ty

        rr.append('{} {}'.format(x,y))

    return '\n'.join(map(str,rr))


print(main())

Submission status: Accepted

Solution code:
#!/usr/bin/env python

from collections import deque
import itertools as it
import sys
import math

while True:
    A, B, C = map(int, raw_input().split())
    if A + B + C == 0:
        break
    lst = []
    for i in range(10001):
        if (C + A * i) % B == 0:
            num = (C + A * i) / B
            lst.append((i + num, A * i + B * num, i))
        if (C - A * i) % B == 0:
            num = (C - A * i) / B
            if num < 0:
                num *= -1
            lst.append((i + num, A * i + B * num, i))
    lst.sort()
    print str(lst[0][2]) + ' ' + str(lst[0][0] - lst[0][2])

Submission status: Accepted

Solution code:
#!usr/bin/env python3
from collections import defaultdict
from collections import deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return list(map(int, sys.stdin.readline().split()))
def I(): return int(sys.stdin.readline())
def LS():return list(map(list, sys.stdin.readline().split()))
def S(): return list(sys.stdin.readline())[:-1]
def IR(n):
    l = [None for i in range(n)]
    for i in range(n):l[i] = I()
    return l
def LIR(n):
    l = [None for i in range(n)]
    for i in range(n):l[i] = LI()
    return l
def SR(n):
    l = [None for i in range(n)]
    for i in range(n):l[i] = S()
    return l
def LSR(n):
    l = [None for i in range(n)]
    for i in range(n):l[i] = LS()
    return l
sys.setrecursionlimit(1000000)
mod = 1000000007

#A
def A():
    s = S()
    d = 0
    ans = 0
    k = 0
    for i in s:
        if i == "R":
            if d == 0:
                k = 1
            d += 1
            d %= 4
            if d == 0 and k:ans += 1
        else:
            if d == 0:
                k = 0
            d -= 1
            d %= 4
    print(ans)
    return

#B
def B():
    while 1:
        a,b,d = LI()
        if a == b == d == 0:
            quit()
        ans = []
        l = []
        m = float("inf")
        for x in range(-50000,50001):
            if (d-a*x)%b == 0:
                y = (d-a*x)//b
                k = abs(x)+abs(y)
                if k < m:
                    m = k
        for x in range(-50000,50001):
            if (d-a*x)%b == 0:
                y = (d-a*x)//b
                k = abs(x)+abs(y)
                if k == m:
                    ans.append((abs(x),abs(y)))
                    l.append(a*abs(x)+b*abs(y))
        print(*ans[l.index(min(l))])
    return

#C
def C():
    return

#D
def D():
    return

#E
def E():
    return

#F
def F():
    return

#G
def G():
    return

#H
def H():
    return

#I
def I_():
    return

#J
def J():
    return

#Solve
if __name__ == "__main__":
    B()