Euler program (python) problem 31

Coin Sumsproblem 31

In England the currency was made up of Pound,￡, and Pence, p, and there were eight coins in general circulation:

1p, 2p, 5p, 10p, 20p, 50p,￡1 (100p) and￡2 (200p).

It's possible to make￡2 in the following-to-be:

1x￡1 + 1x50p + 2x20p + 1x5p + 1x2p + 3x1p

How many different ways can￡2 is made using any number of coins?

Go to the "thread for Problem" in the forum.

Download Overview for Problem 31.

The first thing I feel when I see this topic is to use my first post on an introduction to integer partitioning: address as follows

http://blog.csdn.net/zhangzhengyi03539/article/details/40298397 The idea of solving problems

Attach the MATLAB code and Python code:

MATLAB consists of three functions

Main function:

CLEAR;CLC;
Global T; % need to divide the number of
Global p; % records match the number of criteria divided
P=0;
t=200;
A=[];
Func (a);
Disp (' final division of Species P= ')
P

Func function

function F=func (a)
Global T; % need to divide the number of
Global p; % records match the number of criteria divided
COUNT=[1,2,5,10,20,50,100,200];
Temp=mysum (a);
K=length (a);
If k>0% enters the recursive function for the first time into the else
Result=min ([T-temp Count (A (k))]); % determines the number of assignments to be assigned this step
Else
Result=t-temp;
End
Result=find (count<=result,1, ' last ');
For I=result:-1:1
B=[a i];
If MySum (b) ==t% meets output condition of B output
p=p+1;
Else% B recursion that does not meet the output condition
If MySum (b) <t
Func (b);
End
End
End

MySum function:

function Sum=mysum (a)
COUNT=[1,2,5,10,20,50,100,200];
sum=0;
K=length (a);
For I=1:k
Sum=sum+count (A (i));
End

Then the Python code:

From Functools import reduce


def getvalue (key):
return {1:1,2:2,3:5,4:10,5:20,6:50,7:100,8:200}[key]


def func (a):
Global P
If Len (a) <2:
If Len (a) ==0:
Result=8
Else
RESULT=A[0]
Else
Print (str (p) + ' +str (a[0]))
Minb=reduce (Min,map (getvalue,a))
Result=min (T-sum (Map (getvalue,a)), MINB)
For I in Range (1,9):
If GetValue (i) >result:
Result=i-1
Break
For I in Range (result,0,-1):
B=a.copy ()
B.append (i)
Temp=sum (Map (getvalue,b))
If temp==t:
P+=1
Else
If temp<t:
Func (b)


P=0
t=200
A=[]
Func (a)
Print (P)

Euler program (python) problem 31