- FindStat

Identifier

St000983: Binary words ⟶ ℤ

Values

0 => 1

1 => 1

00 => 1

01 => 2

10 => 2

11 => 1

000 => 1

001 => 2

010 => 3

011 => 2

100 => 2

101 => 3

110 => 2

111 => 1

0000 => 1

0001 => 2

0010 => 3

0011 => 2

0100 => 3

0101 => 4

0110 => 2

0111 => 2

1000 => 2

1001 => 2

1010 => 4

1011 => 3

1100 => 2

1101 => 3

1110 => 2

1111 => 1

00000 => 1

00001 => 2

00010 => 3

00011 => 2

00100 => 3

00101 => 4

00110 => 2

00111 => 2

01000 => 3

01001 => 3

01010 => 5

01011 => 4

01100 => 2

01101 => 3

01110 => 2

01111 => 2

10000 => 2

10001 => 2

10010 => 3

10011 => 2

10100 => 4

10101 => 5

10110 => 3

10111 => 3

11000 => 2

11001 => 2

11010 => 4

11011 => 3

11100 => 2

11101 => 3

11110 => 2

11111 => 1

000000 => 1

000001 => 2

000010 => 3

000011 => 2

000100 => 3

000101 => 4

000110 => 2

000111 => 2

001000 => 3

001001 => 3

001010 => 5

001011 => 4

001100 => 2

001101 => 3

001110 => 2

001111 => 2

010000 => 3

010001 => 3

010010 => 3

010011 => 3

010100 => 5

010101 => 6

010110 => 4

010111 => 4

011000 => 2

011001 => 2

011010 => 4

011011 => 3

011100 => 2

011101 => 3

011110 => 2

011111 => 2

100000 => 2

100001 => 2

100010 => 3

100011 => 2

100100 => 3

100101 => 4

100110 => 2

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Description

The length of the longest alternating subword.
This is the length of the longest consecutive subword of the form $010...$ or of the form $101...$.

Code

# code from https://codereview.stackexchange.com/questions/164326

def zigzags(input):
    input = iter(input)
    stack = None
    try:
        stack = [next(input)]
        while True:
            if len(stack) < 2:
                stack.append(next(input))
            else:
                stack = stack[-2:]
            a, b = stack
            if a == b:
                yield (a,)
                stack = [b]
                continue
            zig = a > b
            while True:
                prev = stack[-1]
                this = next(input)
                if prev == this or zig == (prev > this):
                    break
                stack.append(this)
                zig = not zig
            yield tuple(stack)
            stack.append(this)
    except StopIteration:
        pass
    if stack:
        yield tuple(stack)

def statistic(input):
    return max(len(z) for z in zigzags(input))

Created

Sep 12, 2017 at 16:26 by Christian Stump

Updated

Jan 14, 2021 at 22:36 by Martin Rubey