Backtracking algorithm with Python

Question

I am trying to implement an algorithm that takes in two ints n and k where n is the number of seats in a row, and k is the number of students trying to sit in that row. The thing is that each student must be at least two seats from each other on both side. What I have is a function that generates all subsets (an array of either 0 or 1 s, 1 meaning someone is sitting there) and I send this to a function to check to see if it is a valid subset. This is the code I have for that function

def process(a,num,n):
    c = a.count('1')
    #If the number of students sitting down (1s) is equal to the number k, check the subset
    if(c == num):
        printa = True
        for i in range(0,n):
            if(a[i] == '1'):
                if(i == 0):
                    if( (a[i+1] == '0') and (a[i+2] == '0') ):
                        break
                    else:
                        printa = False
                elif(i == 1):
                    if( (a[i-1] == '0') and (a[i+1] == '0') and (a[i+2] == '0') ):
                        break
                    else:
                        printa = False
                elif(i == (n-1)):
                    if( (a[i-2] == '0') and (a[i-1] == '0') and (a[i+1] == '0') ):
                        break
                    else:
                        printa = False
                elif(i == n):
                    if( (a[i-2] == '0') and (a[i-1] == '0') ):
                        break
                else:
                    printa = False                    
            else:
                if( (a[i-2] == '0') and (a[i-1] == '0') and (a[i+1] == '0') and (a[i+2] == '0') ):
                    break
                else:
                    printa = False
        if(printa):
            print a
    else:
        return

The code works for small inputs of k and n but if I get higher values I get an index out of list error for some reason I can't figure out.
Any help out be great thanks.

O the input a is the list that looks something like this

['1','0','0','1','0'] # a valid subset for n=5 and k=2
['0','0','0','1','1'] # an invalid subset

EDIT:

Code that calls process:

'''
This function will recursivly call itself until it gets down to the leaves then sends that
subset to process function.  It appends
either a 0 or 1 then calls itself
'''
def seatrec(arr,i,n,k):
    if(i==n):
        process(arr,k,n)
        return
    else:
        arr.append("0")
        seatrec(arr,i+1,n,k)
        arr.pop()
        arr.append("1")
        seatrec(arr,i+1,n,k)
        arr.pop()
    return
'''
This is the starter function that sets up the recursive calls
'''
def seat(n,k):
    q=[]
    seat(q,0,n,k)

def main():
    n=7
    k=3
    seat(n,k)

if __name__ == "__main__":
    main()

The error I get if I use these numbers are

if( (a[i-2] == '0') and (a[i-1] == '0') and (a[i+1] == '0') ):
IndexError: list index out of range

Answer 1

It is sufficient to exclude invalid seating arrangements, namely, when the students seat next to each other ['1', '1'] or when there is only one seat between them ['1', '0', '1'] all other arrangements that have correct numbers of '1', and '0' are valid, example:

def isvalid(a, n, k):
    if not isinstance(a, basestring):
       a = ''.join(a) # `a` is a list of '1', '0'
    return (len(a) == n and a.count('1') == k and a.count('0') == (n-k) and
            all(p not in a for p in ['11', '101']))

There are more efficient algorithms to generate valid subsets without checking all subsets e.g.,

def subsets(n, k):
    assert k >= 0 and n >= 0
    if k == 0: # no students, all seats are empty
        yield '0'*n
    elif k == 1 and (n == 1 or n == 2): # the last student at the end of the row
        yield '1' + '0'*(n-1) # either '1' or '10'
        if n == 2: yield '01'
    elif n > 3*(k-1): # there are enough empty seats left for k students
        for s in subsets(n-3, k-1):
            yield '100' + s # place a student
        for s in subsets(n-1, k):
            yield '0' + s   # add empty seat

Example

n, k = 5, 2
for s in subsets(n, k):
    assert isvalid(s, n, k)
    print(s)

Output

10010
10001
01001

Answer 2

The indexes for an array of length n is from 0 to n-1. Thus accessing n is out of list.

The code that generates the lists must have a bug if you haven't noticed this on smaller values.