# -*- coding: utf-8 -*- """ Created on Tue Sep 7 15:17:31 2021 @author: Marcus Galinski """ # 1 Stone which can be cut into 4 # Total weight is 40 kg # weight can go from 1 to 40 kg # To calculate the weight you have to sides which needs to be equal # i + j + k + l = 40 import time # Returns all Possible solutions how a 40kg rock can be split into 4 pieces and can # measure the weight of an object up to 40kg def getWeigths(): solution = [] combinations = [] # Assume 1 Piece is always 1kg -> reduce the code about 1 loop and increases # execution speed i = 1 # Since max weight of all Stones is 40 kg and we can have up to 4 Stones, # we have to consider this in the loops # 39kg - 1kg of first Piece, second Piece can be up to 37kg, since the loops # stop if the variable equals the comparation number, in this case 38 - 1 is the last # Number checked vor the second piece for j in range(1, 39 - i): # For the third piece its the same as for the second piece only that we # must consider the previous stone pieces for k in range(1, 39 - i - j): # fourth pieces is a subtraction of all previous pieces, with this calculation # we avoid an additional loop l = 40 - i - j - k # if somehow the combination of all 4 pieces is unequal 40 kg throw an error if(i + j + k + l != 40): print("error", i, j, k, l) exit(); else: # Assume the combination is a solution and begin the # iteration from 1kg to 40kg and check if one of the following # situations reach an equal if none is true set the solution to false and break possible_solution = True for weigth in range(1, 41): # Combinations which can be used to equal both sides of the scales # The number of combinations increases with the amount of possible pieces if(i + j + k + l == weigth): continue if(i + j + k == weigth): continue if(i + j == weigth): continue if(i + k == weigth): continue if(i == weigth): continue if(i + j + l == weigth): continue if(i + l == weigth): continue if(l == weigth): continue if(i + k + l == weigth): continue if(k + l == weigth): continue if(k == weigth): continue if(j + k + l == weigth): continue if(j + l == weigth): continue if(j + k == weigth): continue if(j == weigth): continue if(weigth + i == j): continue if(weigth + k == j): continue if(weigth + l == j): continue if(weigth + i + k == j): continue if(weigth + i + l == j): continue if(weigth + l + k == j): continue if(weigth + i + k + l == j): continue if(weigth + i == k): continue if(weigth + j == k): continue if(weigth + l == k): continue if(weigth + i + j == k): continue if(weigth + i + l == k): continue if(weigth + j + l == k): continue if(weigth + i + j + l == k): continue if(weigth + i == l): continue if(weigth + j == l): continue if(weigth + k == l): continue if(weigth + i + j == l): continue if(weigth + i + k == l): continue if(weigth + j + k == l): continue if(weigth + i + j + k == l): continue if(weigth + k == i + j): continue if(weigth + l == i + j): continue if(weigth + k + l == i + j): continue if(weigth + j == i + k): continue if(weigth + l == i + k): continue if(weigth + j + l == i + k): continue if(weigth + j == i + l): continue if(weigth + k == i + l): continue if(weigth + j + k == i + l): continue if(weigth + i == j + k): continue if(weigth + l == j + k): continue if(weigth + i + l == j + k): continue if(weigth + i == j + l): continue if(weigth + k == j + l): continue if(weigth + i + k == j + l): continue if(weigth + i == k + l): continue if(weigth + j == k + l): continue if(weigth + i + j == k + l): continue if(weigth + i == j + k + l): continue if(weigth + j == i + k + l): continue if(weigth + k == i + j + l): continue if(weigth + l == i + j + k): continue possible_solution = False break tmpSol = [i, j, k, l] tmpSol.sort() #print(tmpSol) if(possible_solution and tmpSol not in solution): solution.append(tmpSol) return solution startTime = time.time_ns() solution = getWeigths() stopTime = time.time_ns() print("finished") print("solution:", solution) print("duration:", str((stopTime - startTime) / 1000 / 1000)[0:6] + "ms")
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