Question

I am wondering if there is a way to simplify the nested loop below. The difficulty is that the iterator for each loop depends on things from the previous loops. Here is the code:

# Find the number of combinations summing to 200 using the given list of coin

coin=[200,100,50,20,10,5,2,1]

total=[200,0,0,0,0,0,0,0]
# total[j] is the remaining sum after using the first (j-1) types of coin
# as specified by i below

count=0
# count the number of combinations

for i in range(int(total[0]/coin[0])+1):
    total[1]=total[0]-i*coin[0]
    for i in range(int(total[1]/coin[1])+1):
      total[2]=total[1]-i*coin[1]
      for i in range(int(total[2]/coin[2])+1):
          total[3]=total[2]-i*coin[2]
          for i in range(int(total[3]/coin[3])+1):
              total[4]=total[3]-i*coin[3]
              for i in range(int(total[4]/coin[4])+1):
                  total[5]=total[4]-i*coin[4]
                  for i in range(int(total[5]/coin[5])+1):
                      total[6]=total[5]-i*coin[5]
                      for i in range(int(total[6]/coin[6])+1):
                          total[7]=total[6]-i*coin[6]
                          count+=1

print count

Answer 1

1. You can get rid of all the int casting. An int/int is still an int in python ie integer division.

2. it looks like Recursion would clean this up nicly

   count  = 0
   coin=[200,100,50,20,10,5,2,1]
   total=[200,0,0,0,0,0,0,0]
   
   def func(i):
       global count,total,coin
       for x in range(total[i-1]/coin[i-1]+1):
           total[i]=total[i-1]-x*coin[i-1]
           if (i == 7):
               count += 1
           else:
               func(i+1)
   

   func(1)
   print count