基于Python的回溯算法

Question

我试图实现一个算法，它包含两个整数n和k，其中n是一排的座位数，k是试图坐在那一排的学生数。问题是每一个学生必须在两边至少有两个座位。我所拥有的是一个生成所有子集的函数（一个0或1s的数组，1表示有人坐在那里），我把它发送给一个函数来检查它是否是一个有效的子集。这是这个函数的代码

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

这段代码适用于k和n的小输入，但是如果我得到更高的值，我会得到一个列表外的索引错误，因为某些原因，我无法理解。
任何帮助都很好谢谢。

O输入a是如下所示的列表

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

编辑：

调用进程的代码：

'''
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()

如果我使用这些数字，我得到的错误是

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