mirror of
https://github.com/jlengrand/project_euler.git
synced 2026-03-10 08:41:20 +00:00
51 lines
1.8 KiB
Python
51 lines
1.8 KiB
Python
#!/usr/bin/env python
|
|
'''
|
|
Created on 10 feb. 2012
|
|
|
|
@author: Julien Lengrand-Lambert
|
|
|
|
DESCRIPTION: Solves problem 31 of Project Euler
|
|
In England the currency is made up of pound and pence, p, and there are eight coins in general circulation:
|
|
1p, 2p, 5p, 10p, 20p, 50p, L1 (100p) and L2 (200p).
|
|
It is possible to make L2 in the following way:
|
|
|
|
1 * L1 + 1 * 50p + 2 * 20p + 1 * 5p + 1 * 2p + 3 * 1p
|
|
How many different ways can L2 be made using any number of coins?
|
|
'''
|
|
|
|
def listmul(list1, list2):
|
|
"""Multiplies each elements of list1 and list 2 with each other"""
|
|
if len(list1) != len(list2):
|
|
raise ValueError("Lists are supposed to have the same length!")
|
|
|
|
else:
|
|
out = []
|
|
for ii in range(len(list1)):
|
|
out.append(list1[ii] * list2[ii])
|
|
|
|
return out
|
|
|
|
if __name__ == '__main__':
|
|
|
|
values = [1, 2, 5, 10, 20, 50, 100, 200]
|
|
goal = 200
|
|
|
|
max_vals = [goal / val for val in values]
|
|
# we have to solve the equation a * 1 + b * 2 + c * 5 + d * 10 + e * 20 + f * 50 + g *100 + h * 200 = goal
|
|
cur_vals = [0] * len(values)
|
|
|
|
sols = 0
|
|
for cur_vals[0] in range(max_vals[0] + 1):
|
|
print cur_vals[0]
|
|
for cur_vals[1] in range(max_vals[1] + 1):
|
|
print cur_vals[1]
|
|
for cur_vals[2] in range(max_vals[2] + 1):
|
|
for cur_vals[3] in range(max_vals[3] + 1):
|
|
for cur_vals[4] in range(max_vals[4] + 1):
|
|
for cur_vals[5] in range(max_vals[5] + 1):
|
|
for cur_vals[6] in range(max_vals[6] + 1):
|
|
for cur_vals[7] in range(max_vals[7] + 1):
|
|
if sum(listmul(cur_vals, values)) == goal:
|
|
sols += 1
|
|
print sols
|
|
|