5 Best Ways to Find the Longest Consecutive Run of 1s in Binary Representation of an Integer in Python

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💡 Problem Formulation: The task at hand requires determining the length of the longest sequence of consecutive 1s in the binary representation of a given non-negative integer. For instance, if the input is 13, which in binary form is 1101, the desired output would be 2 as the longest consecutive run of 1s is ’11’.

Method 1: Using Built-in Functions

This method involves converting the integer to its binary representation using the bin() function, stripping the leading ‘0b’ from the binary string, and then using the split() and max() functions to find the longest run of ‘1’s.

Here’s an example:

def longest_run_of_ones(n):
    binary_n = bin(n)[2:]
    return max(map(len, binary_n.split('0')))

print(longest_run_of_ones(13))

Output: 2

The function longest_run_of_ones() converts the input number to a binary string, splits it into a list divided by ‘0’s, maps the len() function to find the length of each run of ‘1’s, and then uses max() to determine the longest run.

Method 2: Iterative Approach

An iterative approach can be used to examine each bit of the binary representation of the number, to keep a running count of consecutive 1s, updating the maximum length found as necessary.

Here’s an example:

def longest_run_of_ones_iterative(n):
    binary_n = bin(n)[2:]
    max_count = count = 0
    for bit in binary_n:
        if bit == '1':
            count += 1
            max_count = max(max_count, count)
        else:
            count = 0
    return max_count

print(longest_run_of_ones_iterative(13))

Output: 2

The function longest_run_of_ones_iterative() iterates over the binary representation of the given number, counting consecutive 1s and resetting the count when a ‘0’ is found. The maximum run length is updated accordingly during iteration.

Method 3: Regular Expressions

Using Python’s re module, one can find the longest consecutive run of 1s in the binary representation of a number by matching the longest sequence of ‘1’s using regular expressions.

Here’s an example:

import re

def longest_run_of_ones_regex(n):
    binary_n = bin(n)[2:]
    ones_sequences = re.findall('1+', binary_n)
    return max(map(len, ones_sequences))

print(longest_run_of_ones_regex(13))

Output: 2

The function longest_run_of_ones_regex() finds all sequences of ‘1’s in the binary string of the input number using regular expression matching, then determines the length of the longest sequence from these matches.

Method 4: Bit Manipulation

This method directly manipulates the bits of the integer. Sequentially shifting and checking bits, it efficiently counts the length of the longest run of 1s without converting to a binary string.

Here’s an example:

def longest_run_of_ones_bit_manipulation(n):
    max_count = count = 0
    while n:
        if n & 1:
            count += 1
            max_count = max(max_count, count)
        else:
            count = 0
        n >>= 1
    return max_count

print(longest_run_of_ones_bit_manipulation(13))

Output: 2

Function longest_run_of_ones_bit_manipulation() checks each bit by using the bitwise AND and right shift operations. If the rightmost bit is 1, it increments the counter, otherwise resets the counter. This is a memory-efficient method since binary string conversion isn’t needed.

Bonus One-Liner Method 5: Using the bin function and list comprehension

This one-liner approach utilizes Python’s powerful list comprehension feature in combination with bin() to quickly calculate the longest run.

Here’s an example:

print(max(map(len, bin(13)[2:].split('0'))))

Output: 2

This concise one-liner converts the number to binary, strips the ‘0b‘ prefix, splits by ‘0’, and uses a combination of map() and len() wrapped in max() to directly print the length of the longest sequence of 1s.

Summary/Discussion

  • Method 1: Built-in Functions. Simple and Pythonic. Not the fastest due to string manipulation. Good for readability and conciseness.
  • Method 2: Iterative Approach. More control over the process. Slightly faster than Method 1, but more verbose.
  • Method 3: Regular Expressions. Very concise and excellent for complex patterns. Not as fast as bit manipulation, and might be less clear for those not familiar with regex.
  • Method 4: Bit Manipulation. Highly efficient and fast. Most optimal for performance-critical applications. May be harder to read for some because it uses low-level operations.
  • Bonus Method 5: One-Liner. Quick and concise. Real “Pythonic” feel, but not suitable for all situations, especially if clarity is prioritized over brevity.