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
100111=>2
101000=>4
101001=>4
101010=>6
101011=>5
101100=>3
101101=>3
101110=>3
101111=>3
110000=>2
110001=>2
110010=>3
110011=>2
110100=>4
110101=>5
110110=>3
110111=>3
111000=>2
111001=>2
111010=>4
111011=>3
111100=>2
111101=>3
111110=>2
111111=>1
0000000=>1
0000001=>2
0000010=>3
0000011=>2
0000100=>3
0000101=>4
0000110=>2
0000111=>2
0001000=>3
0001001=>3
0001010=>5
0001011=>4
0001100=>2
0001101=>3
0001110=>2
0001111=>2
0010000=>3
0010001=>3
0010010=>3
0010011=>3
0010100=>5
0010101=>6
0010110=>4
0010111=>4
0011000=>2
0011001=>2
0011010=>4
0011011=>3
0011100=>2
0011101=>3
0011110=>2
0011111=>2
0100000=>3
0100001=>3
0100010=>3
0100011=>3
0100100=>3
0100101=>4
0100110=>3
0100111=>3
0101000=>5
0101001=>5
0101010=>7
0101011=>6
0101100=>4
0101101=>4
0101110=>4
0101111=>4
0110000=>2
0110001=>2
0110010=>3
0110011=>2
0110100=>4
0110101=>5
0110110=>3
0110111=>3
0111000=>2
0111001=>2
0111010=>4
0111011=>3
0111100=>2
0111101=>3
0111110=>2
0111111=>2
1000000=>2
1000001=>2
1000010=>3
1000011=>2
1000100=>3
1000101=>4
1000110=>2
1000111=>2
1001000=>3
1001001=>3
1001010=>5
1001011=>4
1001100=>2
1001101=>3
1001110=>2
1001111=>2
1010000=>4
1010001=>4
1010010=>4
1010011=>4
1010100=>6
1010101=>7
1010110=>5
1010111=>5
1011000=>3
1011001=>3
1011010=>4
1011011=>3
1011100=>3
1011101=>3
1011110=>3
1011111=>3
1100000=>2
1100001=>2
1100010=>3
1100011=>2
1100100=>3
1100101=>4
1100110=>2
1100111=>2
1101000=>4
1101001=>4
1101010=>6
1101011=>5
1101100=>3
1101101=>3
1101110=>3
1101111=>3
1110000=>2
1110001=>2
1110010=>3
1110011=>2
1110100=>4
1110101=>5
1110110=>3
1110111=>3
1111000=>2
1111001=>2
1111010=>4
1111011=>3
1111100=>2
1111101=>3
1111110=>2
1111111=>1
00000000=>1
00000001=>2
00000010=>3
00000011=>2
00000100=>3
00000101=>4
00000110=>2
00000111=>2
00001000=>3
00001001=>3
00001010=>5
00001011=>4
00001100=>2
00001101=>3
00001110=>2
00001111=>2
00010000=>3
00010001=>3
00010010=>3
00010011=>3
00010100=>5
00010101=>6
00010110=>4
00010111=>4
00011000=>2
00011001=>2
00011010=>4
00011011=>3
00011100=>2
00011101=>3
00011110=>2
00011111=>2
00100000=>3
00100001=>3
00100010=>3
00100011=>3
00100100=>3
00100101=>4
00100110=>3
00100111=>3
00101000=>5
00101001=>5
00101010=>7
00101011=>6
00101100=>4
00101101=>4
00101110=>4
00101111=>4
00110000=>2
00110001=>2
00110010=>3
00110011=>2
00110100=>4
00110101=>5
00110110=>3
00110111=>3
00111000=>2
00111001=>2
00111010=>4
00111011=>3
00111100=>2
00111101=>3
00111110=>2
00111111=>2
01000000=>3
01000001=>3
01000010=>3
01000011=>3
01000100=>3
01000101=>4
01000110=>3
01000111=>3
01001000=>3
01001001=>3
01001010=>5
01001011=>4
01001100=>3
01001101=>3
01001110=>3
01001111=>3
01010000=>5
01010001=>5
01010010=>5
01010011=>5
01010100=>7
01010101=>8
01010110=>6
01010111=>6
01011000=>4
01011001=>4
01011010=>4
01011011=>4
01011100=>4
01011101=>4
01011110=>4
01011111=>4
01100000=>2
01100001=>2
01100010=>3
01100011=>2
01100100=>3
01100101=>4
01100110=>2
01100111=>2
01101000=>4
01101001=>4
01101010=>6
01101011=>5
01101100=>3
01101101=>3
01101110=>3
01101111=>3
01110000=>2
01110001=>2
01110010=>3
01110011=>2
01110100=>4
01110101=>5
01110110=>3
01110111=>3
01111000=>2
01111001=>2
01111010=>4
01111011=>3
01111100=>2
01111101=>3
01111110=>2
01111111=>2
10000000=>2
10000001=>2
10000010=>3
10000011=>2
10000100=>3
10000101=>4
10000110=>2
10000111=>2
10001000=>3
10001001=>3
10001010=>5
10001011=>4
10001100=>2
10001101=>3
10001110=>2
10001111=>2
10010000=>3
10010001=>3
10010010=>3
10010011=>3
10010100=>5
10010101=>6
10010110=>4
10010111=>4
10011000=>2
10011001=>2
10011010=>4
10011011=>3
10011100=>2
10011101=>3
10011110=>2
10011111=>2
10100000=>4
10100001=>4
10100010=>4
10100011=>4
10100100=>4
10100101=>4
10100110=>4
10100111=>4
10101000=>6
10101001=>6
10101010=>8
10101011=>7
10101100=>5
10101101=>5
10101110=>5
10101111=>5
10110000=>3
10110001=>3
10110010=>3
10110011=>3
10110100=>4
10110101=>5
10110110=>3
10110111=>3
10111000=>3
10111001=>3
10111010=>4
10111011=>3
10111100=>3
10111101=>3
10111110=>3
10111111=>3
11000000=>2
11000001=>2
11000010=>3
11000011=>2
11000100=>3
11000101=>4
11000110=>2
11000111=>2
11001000=>3
11001001=>3
11001010=>5
11001011=>4
11001100=>2
11001101=>3
11001110=>2
11001111=>2
11010000=>4
11010001=>4
11010010=>4
11010011=>4
11010100=>6
11010101=>7
11010110=>5
11010111=>5
11011000=>3
11011001=>3
11011010=>4
11011011=>3
11011100=>3
11011101=>3
11011110=>3
11011111=>3
11100000=>2
11100001=>2
11100010=>3
11100011=>2
11100100=>3
11100101=>4
11100110=>2
11100111=>2
11101000=>4
11101001=>4
11101010=>6
11101011=>5
11101100=>3
11101101=>3
11101110=>3
11101111=>3
11110000=>2
11110001=>2
11110010=>3
11110011=>2
11110100=>4
11110101=>5
11110110=>3
11110111=>3
11111000=>2
11111001=>2
11111010=>4
11111011=>3
11111100=>2
11111101=>3
11111110=>2
11111111=>1
000000000=>1
000000001=>2
000000010=>3
000000011=>2
000000100=>3
000000101=>4
000000110=>2
000000111=>2
000001000=>3
000001001=>3
000001010=>5
000001011=>4
000001100=>2
000001101=>3
000001110=>2
000001111=>2
000010000=>3
000010001=>3
000010010=>3
000010011=>3
000010100=>5
000010101=>6
000010110=>4
000010111=>4
000011000=>2
000011001=>2
000011010=>4
000011011=>3
000011100=>2
000011101=>3
000011110=>2
000011111=>2
000100000=>3
000100001=>3
000100010=>3
000100011=>3
000100100=>3
000100101=>4
000100110=>3
000100111=>3
000101000=>5
000101001=>5
000101010=>7
000101011=>6
000101100=>4
000101101=>4
000101110=>4
000101111=>4
000110000=>2
000110001=>2
000110010=>3
000110011=>2
000110100=>4
000110101=>5
000110110=>3
000110111=>3
000111000=>2
000111001=>2
000111010=>4
000111011=>3
000111100=>2
000111101=>3
000111110=>2
000111111=>2
001000000=>3
001000001=>3
001000010=>3
001000011=>3
001000100=>3
001000101=>4
001000110=>3
001000111=>3
001001000=>3
001001001=>3
001001010=>5
001001011=>4
001001100=>3
001001101=>3
001001110=>3
001001111=>3
001010000=>5
001010001=>5
001010010=>5
001010011=>5
001010100=>7
001010101=>8
001010110=>6
001010111=>6
001011000=>4
001011001=>4
001011010=>4
001011011=>4
001011100=>4
001011101=>4
001011110=>4
001011111=>4
001100000=>2
001100001=>2
001100010=>3
001100011=>2
001100100=>3
001100101=>4
001100110=>2
001100111=>2
001101000=>4
001101001=>4
001101010=>6
001101011=>5
001101100=>3
001101101=>3
001101110=>3
001101111=>3
001110000=>2
001110001=>2
001110010=>3
001110011=>2
001110100=>4
001110101=>5
001110110=>3
001110111=>3
001111000=>2
001111001=>2
001111010=>4
001111011=>3
001111100=>2
001111101=>3
001111110=>2
001111111=>2
010000000=>3
010000001=>3
010000010=>3
010000011=>3
010000100=>3
010000101=>4
010000110=>3
010000111=>3
010001000=>3
010001001=>3
010001010=>5
010001011=>4
010001100=>3
010001101=>3
010001110=>3
010001111=>3
010010000=>3
010010001=>3
010010010=>3
010010011=>3
010010100=>5
010010101=>6
010010110=>4
010010111=>4
010011000=>3
010011001=>3
010011010=>4
010011011=>3
010011100=>3
010011101=>3
010011110=>3
010011111=>3
010100000=>5
010100001=>5
010100010=>5
010100011=>5
010100100=>5
010100101=>5
010100110=>5
010100111=>5
010101000=>7
010101001=>7
010101010=>9
010101011=>8
010101100=>6
010101101=>6
010101110=>6
010101111=>6
010110000=>4
010110001=>4
010110010=>4
010110011=>4
010110100=>4
010110101=>5
010110110=>4
010110111=>4
010111000=>4
010111001=>4
010111010=>4
010111011=>4
010111100=>4
010111101=>4
010111110=>4
010111111=>4
011000000=>2
011000001=>2
011000010=>3
011000011=>2
011000100=>3
011000101=>4
011000110=>2
011000111=>2
011001000=>3
011001001=>3
011001010=>5
011001011=>4
011001100=>2
011001101=>3
011001110=>2
011001111=>2
011010000=>4
011010001=>4
011010010=>4
011010011=>4
011010100=>6
011010101=>7
011010110=>5
011010111=>5
011011000=>3
011011001=>3
011011010=>4
011011011=>3
011011100=>3
011011101=>3
011011110=>3
011011111=>3
011100000=>2
011100001=>2
011100010=>3
011100011=>2
011100100=>3
011100101=>4
011100110=>2
011100111=>2
011101000=>4
011101001=>4
011101010=>6
011101011=>5
011101100=>3
011101101=>3
011101110=>3
011101111=>3
011110000=>2
011110001=>2
011110010=>3
011110011=>2
011110100=>4
011110101=>5
011110110=>3
011110111=>3
011111000=>2
011111001=>2
011111010=>4
011111011=>3
011111100=>2
011111101=>3
011111110=>2
011111111=>2
100000000=>2
100000001=>2
100000010=>3
100000011=>2
100000100=>3
100000101=>4
100000110=>2
100000111=>2
100001000=>3
100001001=>3
100001010=>5
100001011=>4
100001100=>2
100001101=>3
100001110=>2
100001111=>2
100010000=>3
100010001=>3
100010010=>3
100010011=>3
100010100=>5
100010101=>6
100010110=>4
100010111=>4
100011000=>2
100011001=>2
100011010=>4
100011011=>3
100011100=>2
100011101=>3
100011110=>2
100011111=>2
100100000=>3
100100001=>3
100100010=>3
100100011=>3
100100100=>3
100100101=>4
100100110=>3
100100111=>3
100101000=>5
100101001=>5
100101010=>7
100101011=>6
100101100=>4
100101101=>4
100101110=>4
100101111=>4
100110000=>2
100110001=>2
100110010=>3
100110011=>2
100110100=>4
100110101=>5
100110110=>3
100110111=>3
100111000=>2
100111001=>2
100111010=>4
100111011=>3
100111100=>2
100111101=>3
100111110=>2
100111111=>2
101000000=>4
101000001=>4
101000010=>4
101000011=>4
101000100=>4
101000101=>4
101000110=>4
101000111=>4
101001000=>4
101001001=>4
101001010=>5
101001011=>4
101001100=>4
101001101=>4
101001110=>4
101001111=>4
101010000=>6
101010001=>6
101010010=>6
101010011=>6
101010100=>8
101010101=>9
101010110=>7
101010111=>7
101011000=>5
101011001=>5
101011010=>5
101011011=>5
101011100=>5
101011101=>5
101011110=>5
101011111=>5
101100000=>3
101100001=>3
101100010=>3
101100011=>3
101100100=>3
101100101=>4
101100110=>3
101100111=>3
101101000=>4
101101001=>4
101101010=>6
101101011=>5
101101100=>3
101101101=>3
101101110=>3
101101111=>3
101110000=>3
101110001=>3
101110010=>3
101110011=>3
101110100=>4
101110101=>5
101110110=>3
101110111=>3
101111000=>3
101111001=>3
101111010=>4
101111011=>3
101111100=>3
101111101=>3
101111110=>3
101111111=>3
110000000=>2
110000001=>2
110000010=>3
110000011=>2
110000100=>3
110000101=>4
110000110=>2
110000111=>2
110001000=>3
110001001=>3
110001010=>5
110001011=>4
110001100=>2
110001101=>3
110001110=>2
110001111=>2
110010000=>3
110010001=>3
110010010=>3
110010011=>3
110010100=>5
110010101=>6
110010110=>4
110010111=>4
110011000=>2
110011001=>2
110011010=>4
110011011=>3
110011100=>2
110011101=>3
110011110=>2
110011111=>2
110100000=>4
110100001=>4
110100010=>4
110100011=>4
110100100=>4
110100101=>4
110100110=>4
110100111=>4
110101000=>6
110101001=>6
110101010=>8
110101011=>7
110101100=>5
110101101=>5
110101110=>5
110101111=>5
110110000=>3
110110001=>3
110110010=>3
110110011=>3
110110100=>4
110110101=>5
110110110=>3
110110111=>3
110111000=>3
110111001=>3
110111010=>4
110111011=>3
110111100=>3
110111101=>3
110111110=>3
110111111=>3
111000000=>2
111000001=>2
111000010=>3
111000011=>2
111000100=>3
111000101=>4
111000110=>2
111000111=>2
111001000=>3
111001001=>3
111001010=>5
111001011=>4
111001100=>2
111001101=>3
111001110=>2
111001111=>2
111010000=>4
111010001=>4
111010010=>4
111010011=>4
111010100=>6
111010101=>7
111010110=>5
111010111=>5
111011000=>3
111011001=>3
111011010=>4
111011011=>3
111011100=>3
111011101=>3
111011110=>3
111011111=>3
111100000=>2
111100001=>2
111100010=>3
111100011=>2
111100100=>3
111100101=>4
111100110=>2
111100111=>2
111101000=>4
111101001=>4
111101010=>6
111101011=>5
111101100=>3
111101101=>3
111101110=>3
111101111=>3
111110000=>2
111110001=>2
111110010=>3
111110011=>2
111110100=>4
111110101=>5
111110110=>3
111110111=>3
111111000=>2
111111001=>2
111111010=>4
111111011=>3
111111100=>2
111111101=>3
111111110=>2
111111111=>1
0000000001=>2
0010000001=>3
0010101101=>6
0010101011=>8
0010100111=>5
0010011101=>3
0010011011=>3
0010010111=>4
0010001111=>3
0001110101=>5
0001110011=>2
0001101101=>3
0001101011=>5
0001100111=>2
0001011101=>4
0001011011=>4
0001010111=>6
0001001111=>3
0000111101=>3
0000111011=>3
0000110111=>3
0000101111=>4
0000011111=>2
0000000000=>1
0000000110=>2
0000011000=>2
0000011110=>2
0000010010=>3
0001100000=>2
0001100110=>2
0001111000=>2
0001111110=>2
0001110010=>3
0001001000=>3
0001001110=>3
0001000010=>3
0001011010=>4
0010101010=>9
0010101000=>7
0010101100=>6
0010100100=>5
0010010100=>5
0001010100=>7
0010101110=>6
0010100000=>5
0010000100=>3
0000010100=>5
0000000010=>3
0000001110=>2
0000111110=>2
0000000100=>3
0000001010=>5
0000010110=>4
0000101110=>4
0001011110=>4
0001101110=>3
0001110110=>3
0001111010=>4
0001111100=>2
0000000101=>4
0000001101=>3
0000011101=>3
0001111101=>3
0000001001=>3
0000010101=>6
0000101101=>4
0010110001=>4
0001100001=>2
0001000001=>3
0000111111=>2
0001110100=>4
0001101100=>3
0010011100=>3
0001011100=>4
0000111100=>2
0001101010=>6
0010011010=>4
0000111010=>4
0010100110=>5
0010010110=>4
0001010110=>6
0000110110=>3
0010001110=>3
0001101001=>4
0000110001=>2
0000010001=>3
0000001100=>2
0000011001=>2
0000110011=>2
0000110100=>4
0000000011=>2
0000011011=>3
0001101111=>3
0000110101=>5
0010000010=>3
0001000011=>3
0010011110=>3
0001010000=>5
0001000100=>3
0001010101=>8
0001001011=>4
0001100011=>2
0001110111=>3
0010000000=>3
0000000111=>2
0000001111=>2
0001111111=>2
0000001011=>4
0000010111=>4
0001011111=>4
0001111001=>2
0000011010=>4
0000101010=>7
0000100101=>4
0010010001=>3
0010000101=>4
0010010101=>6
0010010011=>3
0000101011=>6
0001000111=>3
0000100111=>3
0010010010=>3
0001001010=>5
0001001001=>3
0001000101=>4
0000100011=>3
0000100100=>3
0000100010=>3
0010110000=>4
0000011100=>2
0000001000=>3
0000101100=>4
0010101111=>6
0000101000=>5
0010001000=>3
0001001100=>3
0001000110=>3
0001100100=>3
0001100010=>3
0000100110=>3
0000110010=>3
0010010000=>3
0001010010=>5
0001000000=>3
0001011001=>4
0001100101=>4
0001110001=>2
0010011001=>3
0010100101=>5
0010101001=>7
0010011111=>3
0000111001=>2
0010001101=>3
0001001101=>3
0001010001=>5
0001010011=>5
0001111011=>3
0010011000=>3
0001011000=>4
0000100000=>3
0010001011=>4
0010000111=>3
0000010011=>3
0010001100=>3
0010000110=>3
0000110000=>2
0000100001=>3
0010100011=>5
0010100001=>5
0000111000=>2
0001101000=>4
0000010000=>3
0000101001=>5
0010100010=>5
0010001001=>3
0010000011=>3
0010001010=>5
0001110000=>2
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
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 $101...$.
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
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