Answer by juanpa.arrivillaga for Flip bits in array using python

Cleaned up and made Pythonic

arr1 = [1, 0, 0, 1, 0, 0, 1, 0]arr2 = [1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1]arr3 = [0,0,0,1,1,0,1,0,1,1,0,0,1,1,1]def maximum_ones(arr):"""    Returns max possible number of ones after flipping a span of bit array"""    total_one = 0    net = 0    maximum = 0    for bit in arr:        if bit:            total_one += 1            net -= 1        else:            net += 1        maximum = max(maximum, net)        if net < 0:            net = 0    return total_one + maximumprint(maximum_ones(arr1))print(maximum_ones(arr2))print(maximum_ones(arr3))

Output:

61411

If we want the L and R indices

Not so sure about this one. It can probably be made cleaner.

arr1 = [1, 0, 0, 1, 0, 0, 1, 0]arr2_0 = [1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1]arr2_1 = [1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1]arr2_2 = [1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1]arr3 = [0,0,0,1,1,0,1,0,1,1,0,0,1,1,1]def maximum_ones(arr):"""    Returns max possible number of ones after flipping a span of bit array    and the (L,R) indices (inclusive) of such a flip"""    total_one = 0    net = 0    maximum = 0    L = R = 0    started_flipping = False    for i, bit in enumerate(arr):        if bit:            total_one += 1            net -= 1        else:            net += 1            if not started_flipping:                started_flipping = True                L = i        if net > maximum:            maximum = net            R = i        if net < 0:            net = 0            if i < R:                L = i    return (total_one + maximum, (L,R))print(maximum_ones(arr1))print(maximum_ones(arr2_0))print(maximum_ones(arr2_1))print(maximum_ones(arr2_2))print(maximum_ones(arr3))

Output:

(6, (1, 5))(14, (1, 16))(14, (2, 16))(14, (3, 16))(11, (0, 2))

First Iteration

Here is what I had originally, if you want to see the evolution of the thought processes. Here, I was essentially transliterating what I came up with on paper.

Essentially, we traverse the array and start flipping bits (ok, not really), keeping track of cumulative flipped zeros and cumulative flipped ones in two separate arrays along with the total flipped ones in an integer counter. If the difference between flipped ones and zeroes at a given index - the "net" - drops below zero, we 'reset' the cumulative counts back at zero at that index (but nothing else). Along the way, we also keep track of the maximum net we've achieved and the index at which that occurs. Thus, the total is simply the total 1's we've seen, plus the net at the maximum index.

arr = [1, 0, 0, 1, 0, 0, 1, 0]total_one = 0one_flip =  [0 for _ in range(len(arr))]zero_flip = [0 for _ in range(len(arr))]# deal with first element of arrayif arr[0]:    total_one += 1else:    zero_flip[0] = 1maximum = dict(index=0,value=0) #index, valuei = 1# now deal with the restwhile i < len(arr):    # if element is 1 we definitely increment total_one, else, we definitely flip    if arr[i]:        total_one += 1        one_flip[i] = one_flip[i-1] + 1        zero_flip[i] = zero_flip[i-1]    else:        zero_flip[i] = zero_flip[i-1] + 1        one_flip[i] = one_flip[i-1]    net = zero_flip[i] - one_flip[i]    if net > 0:        if maximum['value'] < net:            maximum['value'] = net            maximum['index'] = i    else: # net == 0, we restart counting our "net"        one_flip[i] = 0        zero_flip[i] = 0    i += 1maximum_flipped = total_one - one_flip[maximum['index']] + zero_flip[maximum['index']]

Results:

print(total_one, -one_flip[maximum['index']], zero_flip[maximum['index']] )print(maximum_flipped)print('________________________________________________')print(zero_flip, arr, one_flip, sep='\n')print('maximum index', maximum['index'])

Output:

3 -1 46________________________________________________[0, 1, 2, 2, 3, 4, 4, 5][1, 0, 0, 1, 0, 0, 1, 0][0, 0, 0, 1, 1, 1, 2, 2]maximum index 5

if

arr = [1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1]

6 -4 1214________________________________________________[0, 1, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 9, 10, 10, 11, 12, 12][1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1][0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5]maximum index 16

Finally, if

arr = [0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1]

8 0 311________________________________________________[1, 2, 3, 3, 3, 4, 4, 5, 5, 0, 1, 2, 2, 0, 0][0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1][0, 0, 0, 1, 2, 2, 3, 3, 4, 0, 0, 0, 1, 0, 0]maximum index 2

Great, now tear it apart, people!